zotero-db/storage/UJTB5A4M/.zotero-ft-cache

The Ionocraft: Flying Microrobots With No Moving Parts
Daniel Drew
Electrical Engineering and Computer Sciences University of California at Berkeley
Technical Report No. UCB/EECS-2018-164 http://www2.eecs.berkeley.edu/Pubs/TechRpts/2018/EECS-2018-164.html
December 10, 2018

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The Ionocraft: Flying Microrobots With No Moving Parts
by Daniel S. Drew
A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in
Engineering - Electrical Engineering and Computer Sciences in the
Graduate Division of the
University of California, Berkeley
Committee in charge: Professor Kristofer S. J. Pister, Chair
Professor Michel Maharbiz Professor Liwei Lin
Fall 2018

The Ionocraft: Flying Microrobots With No Moving Parts
Copyright 2018 by
Daniel S. Drew

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Abstract
The Ionocraft: Flying Microrobots With No Moving Parts
by
Daniel S. Drew
Doctor of Philosophy in Engineering - Electrical Engineering and Computer Sciences
University of California, Berkeley
Professor Kristofer S. J. Pister, Chair
Enabling a future full of insect-scale robots will require progress on a huge number of fronts, one of which is the development of mobility platforms designed to operate beyond the scaling frontier of commercially available solutions. The vast majority of researchers seeking to create functional centimeter-scale ﬂying robots have turned towards biomimetic propulsion mechanisms, speciﬁcally ﬂapping wings. In this work I take a very diﬀerent tack, investigating a propulsion mechanism with no natural analogue — electrohydrodynamic thrust.
Electrohydrodynamics (EHD), speciﬁcally in the context of corona discharge based systems, has been a long studied and, until relatively recently, often poorly understood phenomenon. The beginning of this dissertation focuses on the theoretical underpinnings of the thrust mechanism. The bulk of my work has focused on developing proof of concept demonstrators for EHD at the meso-scale. Starting with rapidly prototyped materials and quickly moving to microfabricated electrodes, a series of prototypes elucidate the potential for EHD to yield high thrust-to-weight ratio ﬂiers. Initial demonstrations have been backed up by more rigorous investigations of electrode geometric and density eﬀects.
Quadrotor systems begin to suﬀer from decreased performance at and below the centimeter scale, especially with regards to increasing demands on durability of rotory components (which may not exist at scale), eﬃciency of available DC motors, and propeller ﬁgures of merit [64]. Simply replacing the rotors with EHD thrusters, however, allows us to sidestep some of the unfavorable scaling laws of propeller-based propulsion while maintaining the ability to transfer domain knowledge from the rich world of quadcopter design and control. Demonstrating repeatable takeoﬀ and rudimentary (open-loop) attitude control is trivial with external power supplied to the simple quad-thruster design. Through a combination of design and methodology (e.g., with regards to assembly) improvements, functional EHDbased “ionocraft” can now be built in about half an hour, with near 100% success rate. Controlled ﬂight is now within reach.
Merely hovering with tethered power and an oﬀ-board controller is only the beginning. The ﬁnal sections of this work outline a variety of paths forward, towards better performance

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of a meso-scale ionocraft, autonomous operation, and further miniaturization. Ultimately, I believe the future is bright for ionocraft. While electrohydrodynamics may not be the most power eﬃcient mechanism, nor the easiest to grasp conceptually, it is certainly the simplest to design; put two asymmetric electrodes close to eachother, apply a high voltage, and away it goes! In the words of a respected professor, how hard could it be?

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To all the amazing people who have entered my life these past six years, and those from before who have supported me from afar

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Contents

Contents

ii

List of Figures

iv

List of Tables

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1 Introduction

1

1.1 A Future Full of Microrobots . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Electrohydrodynamic Force for Propulsion, In Brief . . . . . . . . . . . . . . 7

1.3 A Brief History and Modern Applications of Corona Discharge and EHD . . 8

2 Theoretical Framework and Numerical Modeling

11

2.1 Corona Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Electrohydrodynamic Force . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3 FEA for Corona-discharge Based Electrohydrodynamics . . . . . . . . . . . . 20

3 Experimental Scaling Validation and Proof of Concepts

28

3.1 A Rapidly Prototyped Meso-scale EHD Flier . . . . . . . . . . . . . . . . . . 28

3.2 An EHD Thruster Using Microfabricated Silicon Electrodes . . . . . . . . . . 34

3.3 Pushing the Limits of Corona Scaling for Microfabricated Silicon Electrodes 41

4 Design and Realization of a Flying Microrobot

50

4.1 First Takeoﬀ of a Centimeter-scale EHD Quadthruster . . . . . . . . . . . . 51

4.2 Improved Assembly, Lifetime, and Payload Capacity . . . . . . . . . . . . . . 55

4.3 Towards Controlled Flight of the Ionocraft . . . . . . . . . . . . . . . . . . . 65

5 A Path to Power Autonomy and Other Future Directions

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5.1 A Preface on Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.2 Future Power System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5.3 Multi-stage Thrusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.4 Designs With Airfoils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.5 Field Emission for EHD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

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6 Conclusion

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Bibliography

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A Appendix A: The Meso-ionocraft Mask Collection

107

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List of Figures
1.1 Schematic depiction of the cross-sectional view of an emitter wire and collector grid electrode pair. Thrust is produced when ions, drifting in the applied electric ﬁeld, collide with neutral air molecules and impart momentum. Bipolar ions are generated in the corona plasma region localized at the sharp tips of the emitter electrode, but only positive ions (mainly N2+) will drift towards the collector grid. 8
2.1 Schematic depiction of positive and negative polarity corona discharges in a point to plane conﬁguration. Relative species concentrations and device geometries have been exaggerated for clarity. . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Schematic depiction of the wire to plane versus wire to wire geometries, and how the image charge method can be used to derive the former from a solution to the latter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Schematic depiction of the wire to plane two dimensional geometry, with parameters relevant to calculating the electric ﬁeld labeled. . . . . . . . . . . . . . . . 16
2.4 Screen captures of the exact COMSOL ﬁelds in which coupling between the physics modules is achieved. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.5 Meshing strategy for COMSOL multiphysics coupled FEA. Reﬁnement around the emitters and around ﬂow barriers such as the collector grid is critical for convergence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.6 Plots of the space charge distribution given a static applied voltage, assumed to be above the corona ignition voltage. The spacing between both emitter wires and collector grid lines are varied, although only the former is assumed to be signiﬁcant electrostatically. It is clear that emitter wire neighbor spacing aﬀects space charge distributions of both the interior and exterior wires; although closer spacing may impinge interior ﬂow and create a more uniform vertical “jet”, it also creates an elongated horizontal distribution at the exterior (clearly visible in the plotted white ﬁeld lines). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.7 Plots of the resultant ﬂuid velocity at a given applied voltage, assumed to be above the corona ignition voltage. The spacing between both emitter wires and collector grid lines are varied. For the closer wire pitch, impinged ﬂow case, recirculation patterns are evident at the collector electrode. . . . . . . . . . . . . 25

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2.8 Plots of the resultant ﬂuid velocity at a given applied voltage, assumed to be above the corona ignition voltage. In this case, the alignment between the emitter wires (i.e., whether emitters fall directly over grid crosspoints or over open spaces) is varied. The assumption would be that the former is “better” electrostatically, while the latter is better for aerodynamic drag. The latter result seems supported by the simulation results (i.e., the wires present less of a ﬂow boundary and there is less of a drag “bubble” underneath them), but would require experimental validation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.9 Plots of the resultant ﬂuid velocity through a three-dimensional microgrid given an inlet at the top of the model. Although the ﬂow would be ducted by the boundary conditions of the model sides, they are placed far enough to not affect the grid ﬂow. Not shown is the associated pressure plot from which drag coeﬃcient can be extracted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1 A fully assembled testing aparatus used to determine ionocraft output force. It is comprised of two 3D printed components: a serpentine spring frame and a square base. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Fabricated meso-scale ionocraft. Components: Tungsten wire (50µm diameter), aluminum mesh, balsa wood frame. . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 Full system block diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.4 Plot showing measured force and current versus supply voltage for ionocraft with
a 4mm gap between electrodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.5 Simulated and actual system responses with PD controller implemented. The
presence of ringing and a signiﬁcant settling time in the experimental data indicate the system is underdamped. Kd = 0.183, Kp = 0.43. . . . . . . . . . . . . 33 3.6 Electrical testing was performed at a probe station. Glass cover slips were used to vary the inter-electrode distance and contact was made via tungsten probe tips. The collector grids were elevated from the probe station chuck by glass slips. . . 35 3.7 Current versus voltage for varying inter-electrode gaps: 50µm wide wire, 6mm × 6mm grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.8 Current versus voltage for varying emitter wire widths: 2mm inter-electrode gap, 6mm × 6mm grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.9 Air velocity versus voltage for varying inter-electrode gaps: 50µm wide wire, 6mm × 6mm grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.10 Direct thrust measurements by deﬂection of a physical pendulum. Current and voltage information was collected alongside video and then still frames were extracted to take individual data points. . . . . . . . . . . . . . . . . . . . . . . . 38 3.11 Plotting theoretical electrostatic force versus experimentally measured force for extraction of the geometric loss factor. . . . . . . . . . . . . . . . . . . . . . . . 39 3.12 The microfabricated silicon components and silicon capillary tubes were assembled by hand. This roughly 100 cubic millimeter device has a mass of about 2.5mg. Inset: Attachment mechanism with guiding slot and locking cantilevers. 40

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3.13 (a) The emitter wires have triangular protrusions (“spines”). The distance between spines, height, and tip angle are all varied. Some wires are created with spines only along one half of the wire, while others are fully populated. In all cases the cross section of the rectangular portion of the wire is 40 µm by 40 µm; (b) Silicon collector grids have varied separation and wire width. The grids are designed to keep the total interior area constant at 25 mm2. Because the wire width is also controlled, the separation is scaled around the set point to accomplish this. In all cases the thickness of the grid is 40 µm. . . . . . . . . . . . . . . . . . . . 42
3.14 (a) A pair of fabricated electrodes next to a U.S. one cent coin for scale; (b) A schematic view of the characterization setup. The entire setup is contained within a probe station. Distance between the electrodes is set by glass cover slips. The electrode set is elevated oﬀ the probe station chuck by glass spacers so that the conductive chuck does not interfere with measurements and so that the hot wire anemometer can be placed underneath the outlet. Not shown is the second tungsten probe tip which makes electrical contact with the collector grid and the third tungsten probe tip which makes mechanical contact with the other side of the wire to keep it stable during testing. . . . . . . . . . . . . . . . . . . 43
3.15 Response models generated by least squares regression analysis of the 21 run dataset. A p value below 0.05 generally represents a statistically signiﬁcant factor (rejection of the null hypothesis). (a) The regression model for corona inception voltage; (b) The regression model for C coeﬃcient. . . . . . . . . . . . . . . . . 44
3.16 Response prediction proﬁles for the four factors varied in this experiment based on regression analysis for corona inception voltage (top) and for C (bottom). These plots in conjunction with the signiﬁcance proﬁles from Figure 3.15 can be used to select an optimized geometry. . . . . . . . . . . . . . . . . . . . . . . . . 45
3.17 All tests performed with a gap distance of 500 µm and a collector grid separation of 500 µm. (a) The current-voltage characteristics of the lowest inception voltage conﬁguration, highest C conﬁguration, and a bare wire; (b) The current-voltage characteristics of the “optimized” wire, with separation of 750 µm, tip angle of 15◦, height of 250 µm, and full ﬁll. This electrode had an inception voltage of 1542 V and a C of 5.63 ×10−11 A/V2. . . . . . . . . . . . . . . . . . . . . . . . 45
3.18 (a) Changing the grid wire separation from 500 µm to 250 µm had an insigniﬁcant eﬀect on discharge characteristics with a bare wire at a 1 mm gap distance; (b) Decreasing the wire separation changed the loss factor by over 30%. Because there is no change in IV characteristics the increased losses can presumably be attributed to increased drag. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.19 Both of these ﬁgures are for 500 µm grid wire separations with a bare wire as the emitter electrode. (a) Changing the grid wire width from 25 µm to 50 µm at a 1 mm electrode gap increased loss factor by about 20% without a signiﬁcant eﬀect on discharge current; (b) Changing the grid wire width from 25 µm to 50 µm at a 0.5 mm electrode gap increased loss factor by about 19% without a signiﬁcant eﬀect on discharge current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

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3.20 (a) Changing the electrode gap distance from 1 mm to 500 µm with all else held constant increased loss factor by over 30%. Test performed with a bare wire, a 500 µm grid wire separation, and a 25 µm wire width; (b) Measured outlet air velocity versus applied voltage for the two electrode gap distances. As expected by combining Equations (2.13) and (2.15) with the mass ﬂow equation, the voltage-velocity relationship is linear above the corona onset voltage. . . . . 47
3.21 A typical failure mode of an electrode set. Permanent damage is sometimes observed following sparkover from a wire tip to the collector grid. This may be due to the relatively high current density following dielectric breakdown causing rapid Joule heating in the grid wires, or due to physical ablation during the high current breakdown. After a destructive event such as this, both electrodes were replaced despite there being no visible damage to the emitter wire. . . . . . . . 48
3.22 The corona discharge is characterized by a purple/violet glow visible in low light conditions. With the probe station door shut during electrical testing it was possible to take still images capturing the corona plasma. The ﬁrst pane is the device with the light turned on, before testing. In the middle pane the device is at about 2500 V applied potential, where the plasma is clearly localized to the spine tips. The third pane is a still frame taken during a sustained breakdown event after the device had failed around 3000 V. . . . . . . . . . . . . . . . . . . 48
4.1 The simple two mask silicon-on-insulator (SOI) process to fabricate the silicon electrodes. First the 40µm device silicon is patterned. The wafer is ﬂipped and loosely bonded to a handle wafer using a thermally conductive grease. The 500 µm handle silicon is aligned, patterned, and then etched to plasma dice the individual devices. Finally, tweezers are used to physically remove the electrodes, breaking the buried oxide in the process. The electrodes are placed into a vapor HF etcher to clear the remaining oxide. . . . . . . . . . . . . . . . . . . . . . . . 52
4.2 Fused silica capillary tubes are inserted vertically through slots in the microfabricated silicon electrodes and secured with UV-curable epoxy applied via probe tip. A machined aluminum ﬁxture (far right) provides help with alignment and stability. Tabs on the emitter wire and collector grid (latter not shown) provide a place to attach the power connections using silver epoxy applied via probe tip. 52
4.3 These “quad-thrusters” are made of microfabricated silicon electrodes and fused silica capillary tubes and assembled by hand. They are 1.8cm x 1.8cm, 10mg, with four individually addressable electrode sets, and a 1mm electrode gap. They should be capable of producing around 1mN of force for a thrust to weight ratio of about 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.4 Electrical characterization of a quad-thruster with number of actuated wires varied. Calculated corona onset voltage is 2309V with a standard deviation of 50V. Measured currents agreed with geometric prediction (e.g. one wire produces one fourth the current of four wires at a given voltage) to within about 5% on average. Tests concluded when an arc occurred, destroying the wire. . . . . . . . . . . . . 54

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4.5 Takeoﬀ of a microfabricated ionocraft captured at 1000fps. At about 2400V it took ﬂight silently. The ﬂight ended in around a second when the power connection became tangled with the collector grid, leading to an arc. . . . . . . 54
4.6 By applying voltage to only two of the four grids we can control roll/pitch of the robot. In this video, captured at 1000fps, the ionocraft ﬂips over its center axis when the two rear thrusters are actuated at about 2400V. . . . . . . . . . . . . 55
4.7 Photograph of the assembled ionocraft. With four individual addressable thrusters, it is about 1.8cm by 1.8cm and masses 13.6mg. It is comprised of 13 individual components connected by a combination of mechanical slots and UV-curable epoxy. The design includes various tabs for handling and connection to power tethers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.8 3D model renders of the assembly process. Pre-cut silica tubes are inserted into slots in a CNC-milled aluminum jig. The ionocraft frame is slid down the guiding posts. The emitter wires are rotated out of plane and tapered guides are inserted into the silica tubes. The inter-electrode distance is now determined by a combination of lithography, slot depth, and tube length. . . . . . . . . . . . . 57
4.9 Left: The rotary blade capillary tube cutter allows for more uniform, repeatable cuts. Center: A new tube is shown on the left while a typical edge on one of the old is shown on the right. This was key in the transition towards enabling perpendicular (i.e., emitters pointed towards the collector grids) electrode design. Right: The standard ceramic cutting tool used for capillary tubes. . . . . . . . 58
4.10 Flex PCB IMU board on a U.S. penny. The board is about 5mm by 5.5mm and masses 40mg including all components. It contains an InvenSense MPU-9250 9-axis IMU and three associated passives. . . . . . . . . . . . . . . . . . . . . . 59
4.11 Current and force versus voltage curves for thrusters with diﬀerent electrode gaps or diﬀerent drawn emitter tip angles. The current-voltage data from MARSS2017 [2] is a 20µm by 40µm cross section silicon “wire” with no lithographically deﬁned asperities at an electrode gap of 1mm. The 250µm electrode gap device uses a collector grid with 250µm spacing. The plotted lines in the force-voltage plot are 2-degree polynomial ﬁt lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.12 An ionocraft with assembled 40mg Flex PCB IMU board attached to the airframe center pad. At about 2100V, the ionocraft is able to take oﬀ from the table; the power and ground wires prevent the ionocraft from going any higher. There is only one high voltage line attached here, with connections between the emitter wires done on the ionocraft itself. The IMU board is not wired or active during takeoﬀ in this particular work (see Section 4.3). . . . . . . . . . . . . . . . . . . 62
4.13 Current-voltage and force-voltage curves produced by varying the number of emitter wires in a thruster. Tests are for 5-degree emitter tips, an electrode gap of 500µm, and a collector grid spacing of 500µm. The plotted lines in the forcevoltage plot are 2-degree polynomial ﬁt lines. . . . . . . . . . . . . . . . . . . . 63

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4.14 Device lifetime quantiﬁed by measured ion current versus time at a constant operating voltage. Bare silicon emitter wires saw immediate performance degradation during testing, while wires coated by about 100nm of sputtered TiN had stable performance up to the measured 1000s of operation. Devices are 10-degree tips at a 500µm gap with 1800V applied. . . . . . . . . . . . . . . . . . . . . . . . . 64
4.15 An assembled ionocraft next to a United States quarter. The ionocraft itself is approximately 2cm by 2cm and masses 30mg. Also shown is the 37mg FlexPCB board with 9-axis IMU and associated passives attached to the center of the airframe. The ionocraft is built from 41 discrete components, each connected by a combination of mechanical slots and UV-curable epoxy. Inset: A single emitter electrode. The 500µm long, 5deg tip angle lithographically deﬁned asperities are aligned with the grid and used to reduce operating voltage. . . . . . . . . . . . . 66
4.16 3D model renders of the assembly process. (1) Pre-cut silica tubes are inserted into slots in a CNC-milled aluminum jig. (2) The ionocraft airframe is slid down the guiding posts. (3) The emitter wires are rotated out of plane and tapered guides are inserted into the silica tubes. The distance between the emitter wires and collector grid is now determined by a combination of lithography, the length of the silica tubes, and the depth of the guide slots milled into the jig. (4) Silicon “jumpers” are lowered onto guide posts on the emitter wires. These both help with alignment between adjacent emitter wires and serve as electrical connection points after application of silver epoxy. . . . . . . . . . . . . . . . . . . . . . . . 67
4.17 Plots showing measured current (left) and measured output force (right) of the ionocraft as a function of its input voltage. The upper horizontal line shows the current (left) and force (right) required for hovering with the IMU onboard. The lower line shows the current and force needed for takeoﬀ without the IMU. While collecting this data, all four of the thrusters were electrically connected. Tip angle refers to the nominal apex angle of the lithographic asperities on the emitter wires. 69
4.18 Circuit schematic of the actuator dynamic response test setup. A high voltage op-amp is used to modulate the control inputs around a DC bias point by raising and lowering the voltage of the collector grid. . . . . . . . . . . . . . . . . . . . 70
4.19 The output force from an ionocraft with a 1800V DC bias applied to the emitter wires and a 200V peak-to-peak, 10Hz sine wave applied to the collector grids. The data is collected with a sampling period of 16 ms. Top: Measured output force with DC bias force (approximately 0.22mN) and weight of the ionocraft subtracted, then ﬁltered by a digital 20Hz cutoﬀ low pass ﬁlter. Bottom: A Fourier transform of the zero centered, unﬁltered strain data shows the distinct 10Hz peak. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

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4.20 Open-loop, uncontrolled takeoﬀ of the ionocraft while carrying an InvenSense MPU-9250, a state of the art 9-axis IMU. The IMU is reporting accelerations and Euler angles at roughly 100Hz, the latter of which is calculated using InvenSense’s proprietary MotionFusion algorithm on-board the IMU. Each image of the ionocraft was taken at the time corresponding to the black line below it. Erratic transient response from the IMU at the time of high voltage application indicates that further electromagnetic shielding may be necessary. . . . . . . . . 72
4.21 Plot of the wind tunnel drag data shown with a ﬁtted hyperplane using (4.3). The upper left diagram shows the deﬁnition of angle of incidence. . . . . . . . . 73
4.22 Left: A simulated ﬂight of the ionocraft over a 4 second ﬂight about a square. The square is navigated by supplying sinusoidal proﬁles as desired states to pitch and roll controllers independently, and the trajectory of its center of mass is shown in the dotted black line. Right: Control inputs and state variables for the simulated ﬂight. Note that global Z position is only for evaulating simulation performance, and is not a variable being controlled. The pitch and roll measurements have noise, but the magnitudes are substantially lower than the controlled movement. 73
4.23 Overall structure of the control scheme. The errors between the estimates of vertical acceleration, pitch, and roll (zˆ¨, θˆ, and φˆ, respectively) and the desired states z¨d, θd, and φd are fed through three PID controllers. The outputs of the controllers are then converted into a vector input as shown in (4.5). Not shown is a saturation block that prevents the thrusters from trying to apply more force than the maximum value before breakdown (approximately 0.25 mN per thruster). 75
5.1 Silicon wires remaining post-DRIE, with aspect ratios on the order of 800. It is possible these wires are a result of etching and subsequent redeposition of the oxide hard mask in this process; they demonstrate the possibility of producing structures with high enough aspect ratio and low enough tip radius for potential increase in d/r ratio of an EHD thruster. . . . . . . . . . . . . . . . . . . . . . . 79
5.2 Surface plot of Equation 5.4 in the region satisfying Equation 5.8. . . . . . . . . 83 5.3 Rendered depictions of the proposed pico air vehicle platforms in [16]. On the
left is an atmospheric ion thruster powered ﬁxed wing vehicle. . . . . . . . . . . 86 5.4 A multi-stage EHD thruster based on ﬁeld emitted electrons. . . . . . . . . . . . 89 5.5 Hemisphere on a post geometry for ﬁeld emission modeling. Adapted from [27]. 89 5.6 Unattached electron fraction as a function of distance at 1Td and STP. . . . . . 91 5.7 Field emission turn-on voltage simulation as a function of tip sharpness and tip
depth model parameters. Assumed parameters: 1µm cathode-anode distance, 240nm tip depth (left), 20nm tip sharpness (right). . . . . . . . . . . . . . . . . 92

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5.8 Silicon ﬁeld emitter array process ﬂow. 1. A thermal oxide layer is grown and selectively etched. 2. A timed RIE etch undercuts the oxide discs, leaving silicon pyramids. 3. A buﬀered HP dip leaves blunted tips; subsequent thermal oxide sharpening sharpens them. 4. High-temperature oxide is deposited to set the cathode-anode distance. 5. A layer of doped polysilicon (i.e., the gate material), is deposited. 6. CMP ﬂattens the resulting polysilicon “bump” and reveals the previously deposted oxide. 7. A timed BHF dip reveals the gated silicon ﬁeld emitter tips. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.9 Silicon ﬁeld emitter arrays fabricated in the Marvell Nanolab. It would be expected that ﬁeld emission devices with these geometries would be unstable when used in air unless hermetically sealed under vacuum prior to operation. . . . . . 93
A.1 Since a fateful meeting in Kris’s oﬃce, where I decided to refocus from ﬁeld emission devices and move back to meso-scale corona discharge based thrusters, I made fairly rapid progress. Here is the menagerie of photolithography masks (device-side only) that made it happen. Is it art? . . . . . . . . . . . . . . . . . 108

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List of Tables
1.1 Qualitative comparison between actuation candidates for centimeter-scale ﬂight based on theory. X = Worst, XXX = Best . . . . . . . . . . . . . . . . . . . . . 4
1.2 Quantiative comparison between actuation candidates for centimeter-scale ﬂight. It should be noted that in some cases, data for the comparison chart on the right has been estimated or derived with some assumptions from published work. . . . 5
2.1 How varying environmental factors aﬀect ion mobility. . . . . . . . . . . . . . . 19 2.2 Overview of Multiphysics FEA Setup: Modules . . . . . . . . . . . . . . . . . . 22 3.1 Corona inception voltage (in kV) calculated by three diﬀerent methods for varying
electrode geometries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2 The electrode geometric factors and their values that were investigated in this
work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 5.1 Energy storage requirements as a function of various performance parameters for
a 5 minute mission assuming battery mass can only account for half of the total robot mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

xiii
Acknowledgments
I chose to attend Berkeley for graduate school largely because, even during visit day, there was a palpable air of enthusiasm, camaraderie, and excitement during the various events. It didn’t let me down.
Since the ﬁrst day walking up the ﬁre trails talking about Sandkings, Kris Pister has been an inspiration. You have taught me how to chase dreams while playing the game just right. Maybe you didn’t realize it, but your evident conﬁdence in me as I became a more senior researcher was very important to me. This is not the end; let’s write some science ﬁction (“grants”) together.
Bjoern Hartmann, my unoﬃcial co-advisor, was instrumental to my success. Thanks for giving me a diﬀerent perspective and pushing me towards excellence in my writing and editing process. Your class, and our subsequent research together, have changed my career and my life.
Emily Marron, you have been the greatest force of good in my life I ever could have imagined. Your empathy, patience, and humor are incredible. I could not imagine these past years without you and could not imagine taking the next steps with anyone else; I love you.
My parents, Terry and Scott Drew. Thank you for being my constant champions. I couldn’t ask for more supportive sources of unconditional love. Thank you to my sisters, Lauren and Samantha, for being such sources of joy for our parents and for keeping me on my toes.
Joey Greenspun, you’re the brother I never had; we are alike enough to have fun and work well together, diﬀerent enough to push each other (and get on each others nerves) in just the right way. Thank you for being there for me through this whole thing, from visit day hosting to graduation, and almost every big adventure in between.
Thanks to all the members of the Pister lab. I feel honored to have been among you these years; there aren’t many places you can be surrounded by such intelligent, pleasant coworkers. To the older students - thank you for charting a course through, at times, uncertain waters. To the younger ones - thank you for keeping things fresh and forcing me to be a better, more patient, mentor.
Friends and loved ones like Riley, Yukiko, Dan Crankshaw, Michelle, Galen, Kathleen and Mike Marron, Corin, Alicia, thank you for making me feel loved and supported through these years. Thanks for all the good times we have had together.
To the stalwart adventurers of Varisia; thank you for your companionship through the years of struggle to prevent the return of Karzoug. We had lots of laughs, beer, and pizza together. I am so grateful to have friends who could have fun ﬂexing their imaginations with me.
To the members, old and new, of Playa Circuit Boogie; thank you for keeping that part of my life a source of excitement and wonder. Let’s keep getting dusty.
I can’t name everyone who has made an impact on my life through these years. Honestly, I have never before been surrounded by so many people I truly respect, appreciate, and like. Thanks to all of you.

1
Chapter 1
Introduction
1.1 A Future Full of Microrobots
Motivation
With the inception of the internet, inter-personal communication was changed forever. Now, both information and social engagement can be shared and explored at will, subject only to the ever-spreading availability of network connections. The incredible advances of the semiconductor and electronics industries brought the size of an equivalent computer from a building, to a room, to a desk, to a box of tissues, to a deck of cards, in a remarkably short amount of time. But the smartphone did more than just increase internet usage; it put incredible computing power, and versatile integrated sensors, in every pocket, opening a huge new space of applications just by virtue of it being with us. Now, spreading connectivity to the things that surround us— objects, rooms, clothing — is the dream of the Internet of Things, which has taken almost every market sector by storm.
All of these advancements have come short of fulﬁlling the true dream of the Internet; a whole world, indelibly and eﬀortlessly connected. Despite it being increasingly diﬃcult to imagine a world without connected objects and environs, the digital world and our access to it remains almost entirely mediated by the glass windows in our pockets. Since Kris Pister’s “Smart Dust,” the tantalizing image of ubiquitous, distributed sensing and actuation has ﬂoated just out of reach despite major academic and commercial interest, largely supplanted in recent years by a (in my opinion, regressive) march towards embedding computers into consumer products. By shoving the internet into a wine bottle we tie ourselves to it and other locii, increasing speciﬁcity of our connections while relying more and more on obtuse statistical methods to extract generality from whatever meager trickles of data we can (or are allowed to) siphon; we instead can dream of a future where the user possesses the power to extract information from the world around them at will.
I believe that one of the greatest barriers to realization of “Smart Dust” was over-reliance on static nodes. Paradoxically, it seems that some major industrial sectors (e.g. oil and gas) have actually been at the vanguard of implementing the systems that may move us closer

CHAPTER 1. INTRODUCTION

2

to the greater dream of wireless sensor networks. Research has been focused on increasing “autonomy” through eﬃciency, either delaying the inevitable replacement of batteries or compromising functionality until they can function with fully harvested energy. A human is typically still required for installation, maintenance, and even data retrieval. Eﬃciency of this cycle is largely tied to the application environment; a mote deployed indoors may not harvest energy the same as one outside. Being forced to train and employ human operators for these networks (as well as the relatively high unit cost) has led to relatively few implementations — and those that do exist are relatively sparse. A technology that could deploy itself, maintain and reconﬁgure itself, and add a physical traﬃc layer to its data transmission would make a huge change in the current economic calculus.
Mobile sensing and actuation platforms already exist; they’re called robots. Development of both fully autonomous and semi-autonomous robots is an active research topic being explored for a huge variety of applications. The majority of robotics research, however, has a vision somewhat orthogonal to that of “Smart Dust.” In a quest to make ever more functional robots capable of performing all the myriad of tasks currently performed by humans, researchers have packed more and more system components into platforms expanding in size, complexity, and cost. A ubiquitous platform, however, will need to be small enough to be placed unobtrusively, inexpensive enough to be purchased in enormous quantities, and both simple and versatile enough to be easily deployed across a large swath of potential scenarios. Luckily, nature has provided a blueprint for such a system.
Besides micro-organisms, the most successful story of life on Earth may be from the insects. The estimated 17 quintillion insects alive at any time is a number that boggles the mind. Although an individual ant may only have around 250,000 neurons, supercolonies of over 300 million individuals are not uncommon; this collective intelligence would contain over 75 trillion total neurons, compared to the around 100 billion in a human brain. Insects have a variety of amazing sensing capabilities, including reliably detecting speciﬁc chemicals and visual cues at astounding distances, decoding visual and sonic messages from their neighbors, and reading ambient airﬂow to feel a predator coming before they can see them [75, 88, 60]. Insects can work together to build structures tens of thousands of times larger than themselves, form bridges and rafts out of their own bodies, and work together to collectively transport objects hundreds of times their own weight [35]. Clearly, there is the possibility for incredible functionality at the centimeter scale; what challenges do we face in getting there?
Sensor miniaturization has been progressing for decades, with signiﬁcant gains made largely through the success of MEMS and continued progress in CMOS. Chip-scale inertial measurement units, microphones, and cameras can all be found with impressive functionality for their size and cost. Modern system-on-chip (SoC) integrated circuits combine digital logic with wireless transceivers in small, aﬀordable packages. Low-power embedded networking architectures now exist to make the most of the limited battery life of autonomous motes. Despite all this, developing centimeter- and millimeter- scale actuation capabilities remains a signiﬁcant challenge. Resource scarcity at the centimeter scale complicates things further; many robotic control algorithms are prohibitively expensive in terms of both computation and power for a centimeter scale SoC and battery, and there is no budget for either dedicated

CHAPTER 1. INTRODUCTION

3

navigational sensors or ineﬃcient actuation schemes. Ultimately, the core challenge of developing an insect-scale robot is one of systems engineering; every piece must be streamlined and multifunctional, with minimal overhead. This makes every prospective implementation walk a ﬁne line between functionality and versatility. Even optimistic views on what is achievable with current technology put a centimeter-scale autonomous robot just at the bleeding edge of what is possible — and that’s part of what makes it such an interesting problem.
Arguments for Scale
The most common question raised when discussing microrobots is – “why bother making them so small?” While few question the massive impact robotics stands to make across every aspect of our lives, it seems to be moving along just ﬁne without devoting such a signiﬁcant amount of eﬀort to miniaturization. I think that answering this question well (and succinctly) is both extremely important to the future of the ﬁeld of microrobotics as well as extremely diﬃcult.
I believe that there are at least three diﬀerent directions to formulate an answer from — the following are Properties of Microbots:
Well-suited for applications where wide area dispersion and/or data granularity are key. While modern drones can ﬂy autonomously and can carry a sizable suite of sensors, they can still only be in one place at a time, and commercial work has largely focused on single-drone deployments. For example, state of the art precision agriculture practice typically involves ﬂying a single drone through the farm over the course of a day, then stitching together and analyzing the data oﬄine; this will be repeated only a handful (e.g. three) times a year. A swarm of artiﬁcial insects dispersed throughout the farm, persistently monitoring conditions in real-time at the individual row or even individual plant level, could aﬀord unique opportunities for pest and disease control as well as extremely precise nutrient delivery.
A small form factor confers speciﬁc advantages for certain applications. Consider the use of microrobots for search and rescue operations. Besides the advantage of wide area dispersion from large numbers of agents, there is the additional beneﬁt of being able to more easily maneuver in tight or crowded environments due to scale; a robotic cockroach would be much better suited for exploring a collapsed building than a humanoid biped.
Low unit cost through batch fabrication techniques leads to both disposability and democratization. The ability to fabricate an entire swarm for a fraction of the cost of a single large robot opens up some interesting use cases. Instead of closely guarded, carefully maintained institutional or industrial investments, microrobots may serve as practically single-use (“on a whim”) tools. For the cost of a cordless drill you could put a pack of microrobots in your toolbox, using them as needed without a signiﬁcant care for whether they get damaged or lost.

CHAPTER 1. INTRODUCTION

4

Candidate Propulsion Mechanisms for Flight
Focusing more narrowly on ﬂying microrobots, the next question to answer is – “why use atmospheric ion thrusters?” Conventional wisdom would be to draw on either well-understood mechanisms or inspiration from nature when designing systems with as many (ﬁgurative) moving parts as a ﬂying microrobot. This section will attempt to outline some of the advantages and disadvantages of using EHD force for propulsion versus the two most popular mechanisms at this scale, spinning rotors and ﬂapping wings. Comparisons of these mechanisms in theory and in implementation are shown in Table 1.1 and Table 1.2, respectively.

Table 1.1: Qualitative comparison between actuation candidates for centimeter-scale ﬂight based on theory. X = Worst, XXX = Best

Mech. Complexity Control Complexity Mech. Eﬃciency Thrust-to-weight Robustness

Propellers Flapping Wings

XX XXX XX X X

X X XXX XX XX

EHD Thrust
XXX XX X XXX XXX

“Pico” air vehicles [95, 16], under 5cm and 500mg, sit in a unique aerodynamic position compared to typical man-made ﬂying vehicles. While everything larger than a bird (Re > 10,000) can take advantage of the high lift to drag ratios possible due to the dominance of inertial forces, the scale and ﬂight speed of a pico air vehicles places it much closer to a fully laminar region ( Re < 2,500). Viscous drag begins to dominate, lift to drag ratio decreases drastically, and new “unsteady” dynamics become possible for ﬂight. In nature this manifests itself as a stark transition between a soaring ﬂight mode found in the majority of birds and the ﬂapping wing mechanism used by insects.
The quadcopter is by far the most popular archetype for modern autonomous ﬂying robots. Typical quadcopters are on the order of a meter in size, but consumer models as small as 5cm exist (e.g. the CX10). Reynolds number of the propeller airfoil tips for a typical centimeter-scale quadcopter is on the order of 10,000, right around the turbulent to laminar transition ﬂow region [64]. Although even small quadcopters demonstrate impressive performance, they suﬀer from extremely short ﬂight time (on the order of minutes) and extreme fragility. Using actuator disk theory, thrust from a propeller can be expressed as:

T = ktρn2D4

(1.1)

where kt is the thrust coeﬃcient (a function of propeller design and geometry), ρ is the ﬂuid density, n is the propeller angular velocity, and D is the propeller diameter. Even a naive approach to scaling therefore shows that as critical dimension of the propeller decreases,

CHAPTER 1. INTRODUCTION

5

Table 1.2: Quantiative comparison between actuation candidates for centimeter-scale ﬂight. It should be noted that in some cases, data for the comparison chart on the right has been estimated or derived with some assumptions from published work.

Type
Nano-quad, coreless DC Fixed-wing, EHD Flapping, piezo Flapping, electrostatic Flapping, electromag. Ionocraft, EHD

Source bitcraze

Meas. Force [N]
0.55

Thrust [N/m2]
86.5

Thrust Eﬀ. [N/W]
0.039

Thrust- Largest Mass

to-

dim. [mg]

weight [cm]

2.04

13.7

27000

[96]

3.2

3

0.005

500

[94]

1.14e-3 5.7

0.03

1.9

3

60

[51]

7.92e-5 0.4

0.05

0.16

5.6

50

[52]

1.17e-4 0.39

0.13

3

90

[17]

1.2e-3 7.6

0.002 4

2

30

rotational speed must increase dramatically to maintain the same thrust levels. This problem is further compounded by the decreased lift coeﬃcient of airfoils (i.e. the propeller section) at low Reynolds numbers regimes [5] and the fact that viscous drag is proportional to the speed of rotation. Miniature brushless DC motors capable of the RPM required by centimeterscale propellers (typically on the order of 50,000) are fragile and more ineﬃcient than larger versions [64].
As we scale increasingly smaller, ﬁghting against the physics doesn’t make sense; we can instead turn to nature for a solution. Flapping wing micro air vehicles (FMAVs) represent a biologically inspired mechanism for centimeter scale ﬂight. Signiﬁcant progress has been made, including: controlled ﬂight of a ﬂapping wing robot with a piezoelectric actuator [94]; takeoﬀ of a robot with an electromagnetic actuator [99]; measured thrust using an electrostatic actuator [51]; and even wireless takeoﬀ using an external laser pointed at a high voltage PV cell on a piezo-actuated ﬂier [36]. Nevertheless, biomimetic ﬂiers are diﬃcult to design, build, and control. Engineers face a constant tradeoﬀ between size, mass, and eﬃciency of mechanical motion, as the ﬂapping wing mechanism functions increasingly well at smaller Reynolds numbers (and worse at higher Reynolds numbers). Incorporating all the system components necessary for an autonomous robot, while maintaining the scale and therefore Reynolds number regime of a ﬂying insect, will test the limits of packaging, electronics, and actuation in even the most optimistic case. A notable exception to this constraint of scale is

CHAPTER 1. INTRODUCTION

6

the hummingbird, which has evolved an extremely complicated mechanical transmission able to produce fast wing motions (Re > 7000) that allow it to ﬂy like an insect while massing about ﬁve grams. While the systems engineering eﬀorts of nature are worthy of aspiring to, it may not be the path of least resistance.
Electrohydrodynamic thrust is a propulsion mechanism that is silent, has no mechanical moving parts, is mechanically trivial to design, and theoretically simple to use for controlled ﬂight. It has unparalleled potential for robust construction, a high thrust-to-weight ratio, and retaining functionality through a wide range of Reynolds numbers. The thrust itself is scale invariant, indicating a favorable scaling to low-mass systems. Just as importantly, the mechanism is relatively underexplored for propulsion; I believe that the future is ﬁlled with important discoveries that will further increase the advantages of EHD while diminishing the downsides (e.g., high voltage operation, lower mechanical eﬃciency than wings).
Contributions
The summarized contributions of my dissertation work are as follows:
• Elucidation and exploration of the scaling of corona discharge based electrohydrodynamic force. Related work at the millimeter or submillimeter scale typically relies on incomplete or inconsistent theoretical backing, empirical models with decreasing relevance at this scale, or simplifying assumptions that simply do not apply. I believe that I provided one of the more thorough (and candid) investigations of the physics of corona discharge based EHD at this size scale.
• Novel proof of concepts demonstrating implementation possibility of meso- and microscale EHD systems. It has been decades since the last large wave of serious academic eﬀort devoted to electrohydrodynamic force based propulsion. I believe that by demonstrating the viability of systems created with both standard commercial materials and rapid prototyping techniques, as well as techniques speciﬁc to the semiconductor industry, others will be encouraged to study EHD for meso-scale and smaller propulsion applications.
• Exploration of geometric eﬀects and assembly techniques speciﬁc to MEMS-based electrodes. Although on one hand modern photolithography aﬀords tremendous freedom for design, on the other there are signiﬁcant constraints imposed by planar MEMS subtractive manufacturing. I have investigated various designs for electrode sets as well as various assembly methods for their integration. I believe that both my quantitative as well as qualitative results are valuable for future researchers on this topic.
• Design, fabrication, and characterization of a centimeter-scale ﬂying robot with no precedent and no natural analogue. The ionocraft is the smallest EHD-powered ﬂying robot to ever exist. It has a relatively high thrust to weight ratio compared to other pico air vehicles; this lets it carry state of the art commercial sensors for control. The

CHAPTER 1. INTRODUCTION

7

fabrication is simple and amenable to batch processes that could result in an extremely low unit cost. Although comprised of many discrete components, the assembly process is mechanically simple and could be performed by a commercial pick and place machine.
• A research roadmap towards the creation of a future autonomous ionocraft. I use my accrued domain knowledge to chart out some future directions for researchers seeking to use EHD for propulsion, as well as to provide some design guidelines for a future autonomous system.

1.2 Electrohydrodynamic Force for Propulsion, In
Brief
What follows is a colloquial explanation of corona discharge-based electrohydrodynamic force:
Assume two electrically conductive structures are separated by a dielectric ﬂuid, in this case air at atmospheric pressure. An applied voltage between geometrically asymmetric electrodes will result in a non-uniform electric ﬁeld, with higher relative magnitude in the proximity of the electrode with a higher surface charge density (e.g., one with a small radius of curvature). Given a suﬃciently high ﬁeld strength, an initial ambient electron will gain enough kinetic energy to ionize a neutral molecule of air, “freeing” another electron. Assuming that the electric ﬁeld magnitude is high enough for this electron to regain enough kinetic energy for another impact ionization event before its next collision (or recombination with the electrode surface), this eﬀect will continue, growing the number of generated ions geometrically. At some distance r from the surface of the electrode, the electric ﬁeld will decrease below the criterion for continued ionization events between collisions; electrons will instead recombine with ions or attach to neutral air. As a result, with the applied voltage constant, a stable bipolar plasma region is formed around the “sharp” electrode. Outside the plasma region, a unipolar drift region is established between the two electrodes as ions are ejected. A closed circuit of ion current is formed between the two electrodes — collectively, this stable atmospheric plasma (the “corona”) and the ion current (the “discharge”) form the phenomenon known as corona discharge (see Figure 1.1).
Electrohydrodynamic (EHD) force refers to the kinetic energy transfer between charged particles and a neutral ﬂuid. In the case of corona discharge, the energy transfer occurs via collisions between the ions in the discharge and the neutral air molecules occupying the electrode gap. It is worth noting that negligible net force is produced from the collisions occurring within the bipolar plasma region. Momentum transferring collisions occur in a speciﬁc direction, resulting in a net vertical acceleration of neutral air evacuating the gap. As pressure decreases, new air is pulled into the system, eﬀectively creating a ﬂuid accelerator much like a propeller or jet engine. Viewed one way, EHD is a direct transduction of electrical input power to output mechanical work in the form of accelerated air; viewed another, it is instead a conversion from the mechanical work of the moving ions to mechanical work of

CHAPTER 1. INTRODUCTION

8

Figure 1.1: Schematic depiction of the cross-sectional view of an emitter wire and collector grid electrode pair. Thrust is produced when ions, drifting in the applied electric ﬁeld, collide with neutral air molecules and impart momentum. Bipolar ions are generated in the corona plasma region localized at the sharp tips of the emitter electrode, but only positive ions (mainly N2+) will drift towards the collector grid.
moving air. Although similar in some ways, EHD force is not electrostatic in the same way as a standard MEMS actuator; the ion discharge results in a DC current, and the electric ﬁeld strength is a function of the space charge distribution of the ions themselves until a steady state (i.e., space charge limited) current is reached.
1.3 A Brief History and Modern Applications of Corona Discharge and EHD
This section is intended not as a comprehensive survey of the ﬁeld of electrohydrodynamics, but instead as a succinct overview of the scientiﬁc study (and when possible, general scholarly perception) of EHD force through its history. Although more complete reviews exist (see end of section), it is worth repeating if only due to the number of incredible minds (and far-ﬂung ideas) which have populated the ﬁeld. It should be noted that within the majority of literature, EHD and corona discharge are used almost interchangeably. Technically, the

CHAPTER 1. INTRODUCTION

9

corona discharge is only the ion source that leads to the resultant electrohydrodynamic force; alternate mechanisms for ion generations, and their implications on EHD performance, are discussed in later sections.
Accelerated air resulting from EHD force was recorded as early as 1709, when Francis Hauksbee of the Royal Society reported a blowing sensation by holding a charged tube to his face. Interestingly, in investigating this eﬀect he also ended up recording some of the ﬁrst notes on electrostatic precipitation (i.e., removal of ﬁne particles from air using an electrostatic charge). This ﬁnding was later replicated by both Isaac Newton and Benjamin Franklin; the former endowing the phenomenon with its ﬁrst name, the “electric wind”, in 1718. It is also worth noting that as early as 1750, Wilson of the Royal Society proved that this eﬀect only occurred in the presence of air. As is a common thread in the history of EHD, this knowledge was either lost or forgotten by the many researchers who labored to demonstrate EHD force in vacuum at the end of the 20th century. It is especially ironic in light of Robinson’s note of surprise in [76] regarding the seemingly inadequate communication between scientists of the previous century leading to many independent “discoveries” of the electric wind.
Both Faraday (1838) and Maxwell (1873) also contribute to the history of electrohydrodynamics. The former was among the ﬁrst to attribute the “electric wind” to kinetic energy transfer between charged and uncharged particles. Maxwell took the theory further by qualitatively describing the corona plasma region and correctly attributing the source of ions to a breakdown of air due to a suﬃcient electron energy. Neither man was able to fully explain the phenomenon, largely because the gaseous ion was not discovered until later in 1896. It is interesting that, although Maxwell had seemingly explained the phenomenon with remarkable precision (given the additional knowledge of gaseous ions to his description), researchers in the 20th and even 21st century continued to attribute some degree of mystery to the electric, or later, ion wind.
Thomas Brown, in collaboration with Paul Biefeld, ﬁled a 1960 patent for an “Electrokinetic Apparatus” that kicked oﬀ a new frenzy of interest in EHD force. Brown wrongly attributed his “discovery” of EHD force to some kind of antigravity eﬀect despite a severe lack of evidence, and it is unfortunate that this belief persisted among both hobbyists and the occasional researcher alike for over 50 years. The “Biefeld-Brown eﬀect” was investigated for use in aircraft in the early 1960s, even being featured on the front cover of Popular Mechanics in August 1964. At the time of the Popular Mechanics article, the most successful demonstration of EHD thrust was with the “lifter” model now popular with students and hobbyists. The lifter is on the order of 0.1 to 1 square meter, typically constructed from balsa wood and aluminum foil, and can take oﬀ when connected to a high voltage (30 kV) power supply. These supplies can be easily sourced from standard microwaves or older (e.g. CRT) televisions and monitors, but are heavy and quite dangerous.
Important fundamental research from investigators including Christenson, Moller, and Robinson realigned this eﬀort with previous investigations of electrohydrodynamic force in the mid to late 1960s. Ultimately, the eﬀect was deemed to have too low of a thrust aerial density and too low of an eﬃciency for human-scale ﬂight [77, 12]. The theoretical framing

CHAPTER 1. INTRODUCTION

10

as well as many of the fundamental governing equations for EHD force found in these works are correct. Nevertheless, uncertainty surrounding the thrust persisted until much later; a NASA technical report was commissioned in 2004 after researchers in the Army Research Lab concluded that “at present, the physical basis for the Biefeld-Brown eﬀect is not understood” — in 2002. Unsurprisingly, they concluded that the thrust could only be attributed to electrostatic forces on ions causing momentum transferring collisions [7]. More recent theoretical work has seemingly conﬁrmed earlier conclusions that electrohydrodynamic thrusters are not well suited for human-scale propulsion applications [71, 30]. The ﬁrst wireless EHD propelled ﬁxed wing vehicle was recently demonstrated [96]. Generating suﬃcient lift to carry the power supply unit necessary for the 40kV thrusters (around 600W) required a wingspan of ﬁve meters; no other useful payload was demonstrated. While an important achievement in systems engineering and as a proof of concept, it still indicates, to me, that we are better oﬀ looking towards miniaturization as the prime use case for EHD.
Modern applications of corona discharge based electroydrodynamics can be broadly separated into two categories: ones that take advantage of corona discharge speciﬁcally as an ion source mechanism, and ones that primarily utilize the resulting EHD airﬂow. Corona discharge in air has been found to be a relatively stable, repeatable, and high current ionization source for ion mobility spectrometry [83], industrial electrostatic precipators [97], photocopiers and jet printers, surface treatment systems [78], and ozone producers [81]. Microfabricated corona discharge based devices have shown promise as portable airborne particle analyzers and separators [13]. The largest current driver of miniaturization of corona discharge based EHD devices is for thermal management applications (IC cooling). A review of this research can be found in [90]. It should be noted that millimeter-scale devices are rare. Ong et al. demonstrated microfabricated devices with onset voltages around 1.1kV, but their low current makes them unsuitable for thruster applications [68]. The important metric of thrust to weight ratio is also unique to thruster applications and is relatively unexplored in literature.
Further reading: Myron Robinson, one of the ﬁrst investigators to rigorously study the eﬀect, also reviewed the history [76]. Interestingly, Robinson references an even earlier historical review paper by Lehman in 1897 summarizing the knowledge up until the turn of the century, but the paper itself is not archived. A more recent and thorough review on the history as well as contemporary applications of EHD force (speciﬁcally resulting from corona discharge) can be found in [29]. It is a testament to the intriguing nature of the eﬀect that it has generated so much scholarly interest, over such an extended time period, without (yet) ﬁnding a signiﬁcant foothold in an industry sector.

11
Chapter 2
Theoretical Framework and Numerical Modeling
This chapter attempts to provide a basis for understanding the fundamentals of corona discharge and electrohydrodynamics. While the material is suﬃcient for understanding the experimental work in later chapters, it is by no means complete. When possible, I have inserted nearby references to the best related material I have come across. The chapter concludes with an investigation of a uniﬁed numerical model, coupling corona discharge and electrohydrodynamics through a commercial multiphysics software package (COMSOL). While I make no strong claims as to whether this model in and of itself constitutes a research contribution, I have both attempted to make the model easily replicable and have pointed out shortcomings and room for improvement. Research questions to answer:
• Where and why do standard models for corona discharge begin to fail? • What typical simplifying assumptions for EHD fail or change at the meso- to micro-
scale? • Can a numerical model be developed that would actually serve as a useful design aid
for EHD propulsion?
2.1 Corona Discharge
The most common method of atmospheric ion generation for EHD thrust is through the atmospherically-stable corona discharge phenomenon. Corona discharge is characterized by a self-sustained plasma localized around a charged conductor, the “emitter”, and ionic current ﬂowing to a second electrode, the “collector”. The magnitude of the discharge is typically space-charge limited, with the polarity determined by whether positive voltage is

CHAPTER 2. THEORETICAL FRAMEWORK AND NUMERICAL MODELING 12
Figure 2.1: Schematic depiction of positive and negative polarity corona discharges in a point to plane conﬁguration. Relative species concentrations and device geometries have been exaggerated for clarity.
applied to the so-called emitter (“positive corona discharge”) or the collector (“negative corona discharge”) [8].
Positive Versus Negative Corona Discharge
Polarity in a corona discharge process refers to the sign of the emitter electrode relative to the collector; a positive corona discharge will have a positive bias applied to the emitter, and vice versa. This is a non-trivial distinction that has ramiﬁcations on everything from ignition voltage to resultant EHD force. A schematic depiction of both polarities is shown in Figure 2.1. Excellent summaries of the two corona discharge polarities can be found in [10, 9].
In a positive corona discharge, ionization occurs due to inelastic collisions between electrons and neutral gas molecules. These impact ionization events release free electrons which are subsequently accelerated by the electric ﬁeld, leading to further ionization events (an “avalanche” eﬀect). The secondary electron source for sustaining the plasma is from photoionization of neutral gas via high energy photons emitted during de-excitation of ions following impact ionization. The primary mechanism for negative ion formation would be electron attachment, but the rate coeﬃcients are small compared to those for impact ionization at the electron energies present within the plasma region; the corona plasma region can therefore be assumed to be a bipolar mixture primarily composed of positive ions and free electrons. Naturally occurring free electrons in the inter-electrode gap provide the seed for initial formation of the plasma.
A negative corona discharge has a more complicated plasma region, as there is both a layer composed of positive ions generated by impact ionization alongside free electrons as well as an electron attachment region where the bulk of the negative ions are formed prior to

CHAPTER 2. THEORETICAL FRAMEWORK AND NUMERICAL MODELING 13

unipolar drift. The primary source of secondary electrons used to sustain the plasma is via photoemission from the emitter electrode surface, which is a function of the work function of the material. Naturally occurring ionization events (e.g. photoionization) provide the seed for initial formation of the plasma. Negative corona discharge has been widely reported as a less qualitatively uniform phenomenon, with plasma appearing as discrete points or “tufts” along the emitter.
There are numerous reasons to use a positive corona discharge for propulsion applications, including: reduced ozone generation compared to negative corona discharge, which makes future systems safer to operate indoors in large quantities; the lower ion mobility of positive ions (N2+) compared to negative (O2−) in air leading to higher force output (see Section 2.2); reduced corona ionization region thickness, leading to an increased unipolar drift region length and hence output force; reduced dependence on electrode material selection due to not using the electrode itself as a secondary electron source for sustaining the plasma, opening up the design space; and improved plasma uniformity near the ignition voltage for greater predictability of performance. Throughout the remainder of this section (and throughout my research eﬀorts) I have used a positive corona discharge. Although I will not include data, I have periodically validated this choice during device characterization; negative corona has performed worse in every trial.

Empirical Models and Simplifying Assumptions for Corona Discharge
The vast majority of literature taking advantage of corona discharge relies on a largely empirical/phenomenological theoretical foundation. An equation of the form shown below, sometimes referred to as “Townsend’s relation,” has been experimentally conﬁrmed over a wide range of geometries and is assumed true for space-charge limited discharges such as corona [77].

I = CV (V − Vc)

(2.1)

Where Vc is the corona inception voltage and C is a constant with units of A/V 2 that depends on a combination of device geometry and ion mobility. Analytical values for C exist for a few simple geometries, e.g. concentric cylinders [26], but are typically extracted from experimental data.
Peek provided solutions for the critical surface ﬁeld to initiate corona discharge for var-

ious geometries [70]. Peek’s experiments were carried out with centimeter- to meter- scale electrode gaps and millimeter- to centimeter- radius emitter wires. For example, the empirically calibrated equation for the critical ﬁeld (the electric ﬁeld necessary to initiate a corona discharge) in a parallel wire electrode geometry is:

c

Ec

=

E0δ(1

+

√) δr

(2.2)

CHAPTER 2. THEORETICAL FRAMEWORK AND NUMERICAL MODELING 14

Peek derived this critical ﬁeld from the critical potential for corona onset, which between two symmetrical conductors is given as:

S

√

S

Vc = Ecrln( r ) = E0δr(1 + c/

δr)ln( ) r

(2.3)

Where S is the distance between the wire centers in centimeters, c is an empirical dimensional constant equal to 0.301cm1/2 for parallel wires, r is the wire radius in centimeters, δ is a density correction factor N/N0, where N0 = 2.5 × 1025m−3 at STP, and E0 is the bulk breakdown ﬁeld strength in air (approximately 30kV /cm).

This equation is widely used in literature and consistently produces predicted voltages

accurate to within about 10%. The pressure correction term is typically minor a√nd ignored. Peek further stated that the radius of the plasma region would be equal to c r, as that

is the distance from the wire surface where the bulk breakdown ﬁeld will be reached. The

portion of Equation 2.3 which does take into account the gap is from a simpliﬁed version of

the wire to plane electric ﬁeld equation which assumes d is much larger than r.

Peek derived the complete equation for the electric ﬁeld along the center axis between

two parallel wires in [70] as below:

E(x) =

√ V S2 − 4r2

(r

+

x)(S

−

2r)ln(

S 2r

+

(

S 2r

)2

−

1)

(2.4)

Where r is the radius of the wire and S is the distance between the centers of the wires, S = d + 2r. Assuming that S >> r, this equation then simpliﬁes to:

VS

V

E(x)

=

(r

+

x)S

ln(

S 2r

+

S 2r

)

=

(r

+

x)ln(

S r

)

(2.5)

Th√en solving for the critical potential, deﬁned as the voltage where the electric ﬁeld at x = c r is equal to the breakdown ﬁeld:

√ E(c r)

=

E0

=

r

+

√Vc c rln(

S r

)

√

S

sS

S

Vc = (r + c

r)E0ln(

r

)

=

E0r(1

+

√ )ln( r

r

)

=

Ecrln(

r

)

(2.6) (2.7) (2.8)

The c term was empirically derived by Peek; because the electric ﬁeld between the electrodes is a function of both radius and distance it is clear that this empirical relationship, which depends only on the electrode geometry (e.g. wire to wire vs sphere to sphere), cannot hold true for all values of the ratio d/r.

CHAPTER 2. THEORETICAL FRAMEWORK AND NUMERICAL MODELING 15

For our devices we are interested in a wire to plane solution, not the electric ﬁeld between parallel wires (for Peek, the latter was interesting due to high voltage transmission lines). Th full parallel wire equation 2.4 is equivalent to an image charge solution to a wire-to-ground plate problem with twice the distance S between conductors (see Figure 2.2). Substituting into Equation 2.4, we ﬁnd the electric ﬁeld between a wire and a ground plane:

E(x) =

√ V 4S2 − 4r2

(r

+

x)(2S

−

2r)ln(

S r

+

(

S r

)2

−

1)

Assuming that S >> r, this equation then simpliﬁes to:

(2.9)

V

V

V

E(x)

=

(r

+

x)ln(

2S r

)

=

(r

+

x)ln(

2d+4r r

)

=

(r

+

x)ln(

2d r

)

(2.10)

Figure 2.2: Schematic depiction of the wire to plane versus wire to wire geometries, and how the image charge method can be used to derive the former from a solution to the latter.
The geometry and relevant parameters are shown and labeled in Figure 2.3. Electric ﬁelds in the vicinity of the emitter wire as calculated by (2.10) versus the full version (2.9) can deviate by as much as 50% for d/r ratios less than 20. These shortcomings may help explain why research exploring sub-millimeter corona discharge with d/r ratios on the order of 15 have seen greater divergence from Peek’s formulas [85]. While Peek stated that corona discharge would occur at d/r ratios down to about 3, Peek (and others [85]) have seemingly been unable to measure corona discharge before sparkover below a ratio of about 10.
Analytic Models for the Corona Plasma Region
A fully analytic model for corona discharge would allow for more accurate onset voltage prediction at the scales where Peek’s empirical formula break down, as well as more accurately predict resultant EHD force production due to a better accounting of both plasma region thickness as well as space charge interactions.

CHAPTER 2. THEORETICAL FRAMEWORK AND NUMERICAL MODELING 16

Figure 2.3: Schematic depiction of the wire to plane two dimensional geometry, with parameters relevant to calculating the electric ﬁeld labeled.

Most work focuses on either the discharge initiation, e.g., the kinetics and sustaining reactions of the corona plasma, or the development of subsequent ion current with space charge eﬀects taken into account. In the latter case, inception voltage and some current trends are typically taken from experimental data. A method of solving for the corona inception voltage as a function of electrode geometry outside the usable range of Peek’s criterion would be a valuable tool for design; unfortunately, existing analytic models are typically conﬁrmations of Peek’s equations for simple geometries (e.g. concentric cylinders [26]) at >mm gaps. An interesting exception is [61], which claims greater accuracy for their analytical model at small gaps and for small emitter radii, although still only for concentric cylinder geometries.
A widely used method to determine the corona inception voltage for complex geometries is to arbitrary deﬁne a plasma radius, r0, and then iteratively solve for electric ﬁeld magnitude at this distance from the emitter electrode until it reaches a breakdown ﬁeld magnitude, typically E = 3M V /m. This electric ﬁeld magnitude, however, is not the true breakdown ﬁeld strength at all electrode distances and conditions.
A more satisfying method of determining onset voltage is through the eﬀective ionization criterion deﬁned as:

αeff = αi − η

(2.11)

where αi is the ionization rate coeﬃcient and η is the electron attachment rate coeﬃcient. A αeff = 0 would signify the boundary of the bipolar corona plasma region as free electrons would all be consumed [9].
One method of using this method is through arbitrarily deﬁning a plasma radius, r0, and then iteratively solving for αeff , where both rate coeﬃcients are functions of the reduced

CHAPTER 2. THEORETICAL FRAMEWORK AND NUMERICAL MODELING 17

electric ﬁeld. When the electric ﬁeld at r0 is found to make this eﬀective rate equal to zero then the critical inception voltage has been found.
It is obviously not satisfying to deﬁne a corona plasma radius a priori. Another method uses the integral:

r0
αeff (r)dr = K
0

(2.12)

Where K is a dimensionless parameter known as the “ionization integral.” Values of K have been empirically determined in the range of 5-20 [53]. Solving for the corona inception voltage for complex geometries would then be a process of iteratively integrating this quantity until it matches the a priori determined K. Unfortunately, K has only been analytically determined for simple geometries [65].

The Limits of Corona
At the extreme limit of scaling, as the inter-electrode decreases to some smaller multiple of the electron mean free path in air (about 200 nm at low electron energies [92]), sustained Townsend avalanche breakdown ceases to be the dominant charge generation mechanism. At some point, the required electron energy (and therefore electric ﬁeld) required for impact ionization will become larger than the required electric ﬁeld for a new mechanism to take place: ﬁeld emission. This phenomenom and its potential for use in EHD is discussed more in Section 5.5.

2.2 Electrohydrodynamic Force

Electrohydrodynamics (EHD), sometimes referred to as electro-ﬂuid-dynamics, electrokinetics, or ion drag pumping, refers to the motion of ﬂuids with diﬀuse charged species under the inﬂuence of an applied electric ﬁeld.
A one dimensional model for electrohydrodynamic thrust based on the Coloumb electrostatic force on a volume of ions leads to an expression for force in terms of ion current, I, distance the ions travel d, and the ion mobility, µ. Here V is the applied potential and A is the ion volume cross-sectional area. This assumes all ion current is due to applied drift ﬁeld as opposed to bulk ﬂuid motion, an assumption [77] proved accurate for the 3m/s maximum air velocities measured in this work versus ion velocity that is on the order of 100m/s.

Id V

Id

F = ρEdV = ρEAdx =

Adx =

µV A d

µ

(2.13)

This represents the theoretical maximum force from an EHD thruster. The fundamental electrostatic force given in (2.13) is proportional to ion drift distance; if the ratio of ionization

CHAPTER 2. THEORETICAL FRAMEWORK AND NUMERICAL MODELING 18

radius to gap distance is signiﬁcant, then simply using the electrode gap to determine theoretical force is incorrect. This ratio is typically small for high d/r ratio devices and is safely ignored. However, Vuhuu and Comsa experimentally measured ionization radii on the order of hundreds of micrometers [89], which would be a signiﬁcant fraction of a sub-millimeter discharge. For consistency with literature I have maintained d as the full inter-electrode gap when using this equation and reporting deviations from theoretical maximums. The relative ratio of ionization region to drift gap can be encompassed in a “loss factor,” β:

Id F =β
µ

(2.14)

Future investigations would do well to separate the factors out for analysis.

The Mott-Gurney law for space charge limited current density (2.15), which assumes

that only one type of charge carrier is present in the drift ﬁeld, that the carrier material

is not conductive, and that carrier mobility (actually, a weak function of electric ﬁeld) and

permittivity are constant throughout the device, is assumed valid for a corona discharge based

in-air system. Based on the Mott-Gurney law, the equation for the electrohydrodynamic

force derived for the 1D simplifying case can instead be expressed in terms of applied drift

ﬁeld E and air permittivity 0:

I = 9 0µAV 2 8d3
F = Id = 9 0 AE2 µ8

(2.15) (2.16)

Note that this is force acting on the ions; direct translation of this to thrust requires that all momentum is transferred in the preferred thrust direction by ion-neutral collisions. Deviation from this assumption is also encompassed in the β factor of Equation 2.14. Assuming applied voltage is the same as the drift ﬁeld potential and that ion current is the only current ﬂow, this yields a thrust eﬃciency in terms of N/W of:

P

= IV

=

9 8

0

A d3

µV

3

Fd 1 ==
P µV µE

(2.17)

Note that this thrust eﬃciency also has a dependence on freestream air velocity, v, in its full form:

F

1

=

P µE + v

(2.18)

which indicates that thrust eﬃciency of an EHD thruster will, unlike a jet or turbofan,

become less eﬃcient at higher speeds (i.e., as v approaches µE). For the projected drag-

limited airspeeds of a centimeter-scale ionocraft (i.e., 1-10 m/s) this is largely not an issue;

CHAPTER 2. THEORETICAL FRAMEWORK AND NUMERICAL MODELING 19

ion drift speed will range from approximately 100m/s at a ﬁeld of 5 × 105 V/m to 600m/s at a drift ﬁeld of 3 × 106 V/m, corresponding to an eﬃciency deviation of about 1%.
Power eﬃciency, however, in terms of produced mechanical power per input electrical power, has been shown to increase with freestream air velocity in experiment from less than 1% to 7.5% at freestream velocities of 50 ms−1 [4]. To directly compute the output mechanical power requires integration of the velocity distribution over the local electric force density. For simpliﬁcation we can assume an equation of the form below, although it will overestimate eﬃciency:

Pout = F (v + vacc) = v + vacc Pin F (µE + v) µE + v

(2.19)

where v is the freestream air velocity and vacc accounts for accelerated outlet velocity. Assuming a standard commercial airplane cruising velocity of 240 m/s, a thruster operating with a 5×105 V/m drift ﬁeld for higher eﬃciency, a 300% increased ion mobility due to being

at 10km altitude [3], and that vacc is 10 m/s, power eﬃciency would reach approximately 46%.

Ion Mobility
Ion mobility is a key factor in determining the thrust eﬃciency of EHD (Equation 2.17). The ion species, ambient air pressure and temperature, and relative humidity all aﬀect mobility. A summary of these eﬀects is shown in Table 2.1.
Table 2.1: How varying environmental factors aﬀect ion mobility.

Pressure (Pa)

Value
⇑

⇑ Temperature (K)

Humidity (%)

⇑

Mobility
⇓ ⇓ ⇓

Notes
Thrust eﬃciency will decrease by 80% from 0km to 25km due to this change [30] Complicated dependency, < 10% change from 87C to 250C [41] Decreases by approximately 10% from 70% RH to 80% RH [28]

It is also worth noting that N2+ mobility is approximately 70% that of O2− [25] in air. A consistent challenge when evaluating EHD systems is in deciding on an ion mobility
constant to use in analysis. Direct measurement at test time is not feasible, and literature values for positive ions in air range from 1.6×10−4m2V −1s−1 to 3.0×10−4m2V −1s−1 [86,
62, 71]. Determining a thrust loss factor with any accuracy is therefore nigh-impossible

CHAPTER 2. THEORETICAL FRAMEWORK AND NUMERICAL MODELING 20
between diﬀerent experimental setups and conditions; it implies that only measurements taken in the same location, at about the same time, can be trusted for any precision. It is interesting to note that corona discharge is actually a stable enough plasma mechanism for use in ion mobility spectrometry given a controlled instrument environment [83]. Lacking such a controlled environment, a closed loop feedback controller for an EHD thruster would likely beneﬁt from real-time recalibration of the voltage-force transform using active current measurement.
2.3 FEA for Corona-discharge Based Electrohydrodynamics
Motivation and Description
A large amount of work has been performed simulating corona discharge-based EHD systems. The typical approach combines the critical ﬁeld criterion established by Peek with the Kaptsov hypothesis [40], which stipulates that the electric ﬁeld on the corona emitter surface remains constant at Peek’s critical value even as applied voltage increases; the ionization region radius is typically ignored or assumed a constant (e.g. the same as emitter diameter). Surface charge density and subsequently the space charge region can then be solved for, yielding a numerical solution for ion current due to drift. Typical simulation performed in this manner agrees to within about 10% with experimental values [1]. Combining this approach with a diﬀuse species collision model and a ﬂow model yields a simulated measure of air ﬂow as a result of EHD ion-neutral collisions; this approach has also been veriﬁed experimentally [98]. Although there are obvious limitations with this approach as an a priori design tool for corona discharge, there are still possibilities for FEA to make an impact. I believe that two promising areas are in investigations of ion ﬁeld path shape as a vertical thrust “loss” mechanism, and in design of mass- and ﬂow- eﬃcient collector electrodes.
The canonical expression for electrohydrodynamic force, where output force is directly proportional to ion current, assumes one-dimensional momentum transfer and ducted ﬂow. In reality, ions will typically be traveling with some horizontal momentum at time of impact. This component of the momentum transfer is therefore, at least partially, lost as useful vertical thrust. Ion and electron beam systems in other applications often contend with this problem, going to great lengths to collimate their beams (i.e., minimize those undesired path components). Many of these approaches, such as external electromagnets or physical grates, are unfeasible for a mass-limited propulsion system. It may turn out that an important aspect of EHD thruster design is proper placement and shaping of the electrodes, not just to aﬀect corona ignition properties, but also to shape the shape charge distribution and resultant ﬁeld paths in order to maximize vertical momentum transfer. Concretely, a question that could be asked is, for a system with multiple emitter wires per collector grid, is there an emitter wire spacing that actually impinges the “interior” space charge region ﬂow, creating more of a “jet” proﬁle? Finite element analysis provides an answer.

CHAPTER 2. THEORETICAL FRAMEWORK AND NUMERICAL MODELING 21

Previous work has noted that collector electrode geometry signiﬁcantly aﬀects both corona current and the resultant ﬂow rate, with grid electrodes performing better than rings [63]. Literature on airﬂow through micromeshes on the size scale relevant for centimeterscale ionocraft is extremely sparse. A further consideration is how the micromesh geometry aﬀects the electric ﬁeld proﬁle of the device. Maxwell claimed that at gap distances equal to or greater than the grid separation, the grid will look virtually identical to a solid plane at the emitter wire [57]. If this holds true for corona discharge devices, decreasing gap distance will necessitate a decreased grid separation and therefore presumably a higher drag coeﬃcient. A multiphysics simulation model would allow for designers to view both the expected ﬂow properties (e.g., coeﬃcient of drag) of their systems as well as minimize the chance of “reverse corona” (e.g., if the grid pitch is too high, the grid wires will look like corona emitters of the opposite polarity). Key challenges include properly designing the simulation geometry, and inserting proper boundary conditions, such that the ﬂow properties can be trusted. For example, right angles (e.g., the edge of a rectangular simulated geometry) have dramatic eﬀects on ﬂow, dramatically enhance electric ﬁeld, and are likely non-physical.

Methods: COMSOL Multiphysics Simulation
The ﬁnite element method (FEM) is a computationally tractable way of solving a complex group of partial diﬀerential equations given a set of boundary conditions. This method, which organizes a system into a “mesh” where each mesh boundary represents a system of equations to be solved, is known as ﬁnite element analysis (FEA) when applied. COMSOL Multiphysics is a commercial FEA and simulation tool which includes multiple physics modules (e.g. electrostatics, ﬂuid ﬂow) that can be explicitly and implicitly coupled during FEM solving. Although many groups have applied numerical methods to corona discharge and electrohydrodynamics (e.g. [6]) using tools such as OpenFOAM, COMSOL is probably the most widely used FEA tool for this purpose [37]. Its graphical interface, active community, and large amount of documentation make it relatively straightforward to use. As always, a solid grasp of the theory prior to jumping in to the modeling is recommended.
Momentum-transferring interactions with neutral molecules can be modeled as an external force (i.e. Coulomb force) in the Navier-Stokes ﬂow equation. This modeling assumes that the electrostatic force on the ions is exactly equal to the kinetic energy transfer to the neutral molecules. Coupling the electrostatics module with diﬀuse species ﬂow and ﬂuid ﬂow models results in ion current density, j, as a sum of three diﬀerent contributing terms:

j = qNi(µE + v) − qD∆Ni

(2.20)

where D is the diﬀusion rate related to ion mobility and temperature, T , through Einstein’s relation. These terms correspond to drift due to electric ﬁeld, advection in a ﬂuid media, and diﬀusion through the carrier ﬂuid. For most arrangements, it is expected that ion current will be dominated by the drift term. A common challenge when modeling corona discharge is handling the charge injection mechanism. Here, I have assumed a uniform initial

CHAPTER 2. THEORETICAL FRAMEWORK AND NUMERICAL MODELING 22

charge distribution on the emitter electrode corresponding to the inception ﬁeld. This assumption seems plausible if the Kaptsov assumption and the assumption that plasma radius is negligible compared to drift distance hold, but is an obvious failure source for miniaturized devices or ones with more complicated electrode geometries. Nevertheless, as long as the model is not being used as a predictor of voltage-current transforms or inception voltage, this simplifying assumption represents a ﬁne initial path.
Table 2.2 shows the physics modules, most relevant governing equations within each module, and the boundary conditions used for this COMSOL coupled model. Alone, this is not enough to generate a coupled simulation; without coupling parameters speciﬁed, the physics modules will either be solved independently, giving false solutions, or will solve to zero due to under speciﬁed initial conditions. The mass transport and ﬂuid ﬂow models are coupled via convection, i.e. the movement of ions in the free airstream. The mass transport and electrostatics modules are coupled through the “migration in electric ﬁeld” option as well as by setting the space charge density explicitly equal to the concentration of dilute species. The electrostatics module is tied to the ﬂuid ﬂow model by adding a volume force to the ﬂuid ﬂow equivelant to ρE. Screenshots of relevant input ﬁelds in COMSOL are shown in Figure 2.4. Excluded in my model is the thermal domain; some prior work has attempted to model it, coupling with Joule heating due to the ion current and buoyancy volume forces produced via temperature gradients [6]. It is uncertain how much thermal eﬀects change the results, and while it may be a vital domain to cover for heat transfer applications, it is unclear how much it matters for propulsion.

Table 2.2: Overview of Multiphysics FEA Setup: Modules

Physics Description COMSOL Module Governing Equ.

Boundary Conds.

Electrostatics

Electrostatics

Gauss, Poisson

Mass Transport

Transport of Dilute Nernst-Planck Species

Fluid Flow

Laminar Flow

Navier-Stokes

DC voltage at emitter, ground at collector Concentration at emitter surface, outﬂow at collector surface No slip at all surfaces, outlet (zero pressure/stress) at model bottom

Geometry and Mesh Deﬁnition
For the fully coupled simulations I have used a 2D model in the interest of convergence, time per simulation, and ease of use. Simulations with the level of mesh reﬁnement required

CHAPTER 2. THEORETICAL FRAMEWORK AND NUMERICAL MODELING 23
Figure 2.4: Screen captures of the exact COMSOL ﬁelds in which coupling between the physics modules is achieved.
for well-behaved coupled electrostatic and ﬂuid ﬂow modules are extremely ineﬃcient when performed on a consumer PC. The geometry of my ion thrusters is largely axi-symmetric, and edge eﬀects (e.g. ﬂow around the collector grid “frame”) can still be captured in two dimensions. Other authors have shown transferability of their 2D models to experimental results in the past. As corona discharge inception is not the focus of this modeling eﬀort, a circular geometry is used for the emitters to simplify convergence. As ﬂuid ﬂow models have diﬃculty converging for ﬂat planes and right angles, circular geometries are also used for the collector grid lines. This is obviously non-physical; more rigorous experimental validation would be needed to properly assess a radius of curvature to use for rectangular wire geometries.
Convergence of the electrostatic and ﬂuid ﬂow modules requires reﬁnement around ﬂow boundaries as well as the charge injection point, i.e., the collector grid and emitter wires (Figure 2.5). There is an additional trade-oﬀ between model boundary size and convergence time. Too small of a model boundary and the conditions speciﬁed at the walls (e.g., outlet or no ﬂow) will unduly inﬂuence behavior; too large, and convergence will take extremely long as the solver works on “useless” nodes. Unfortunately, I think that the compromise must be found largely on a case-by-case basis.
Results and Discussion
Simulations investigating the eﬀect of emitter spacing were performed (Figure 2.6 and 2.7). Although I am hesitant to make statements about the validity of these results without experimental validation, I believe the method is sound to allow for some qualitative comparison. Note that an emitter separation of 500µm is nearly enough to isolate the resulting ﬂow regions for an inter-electrode gap of 750µm. This may indicate agreement with analytic models developed by Gilmore et al in [30] which state that optimal emitter wire spacing is at roughly 70% of the inter-electrode gap.
Simulations were also performed that investigate the eﬀect of emitter point alignment with the collector grid (Figure 2.8). Consider a series of emission points above a mesh; given perfect assembly, a designer has the choice of aligning each point above either grid crosspoints

CHAPTER 2. THEORETICAL FRAMEWORK AND NUMERICAL MODELING 24
Figure 2.5: Meshing strategy for COMSOL multiphysics coupled FEA. Reﬁnement around the emitters and around ﬂow barriers such as the collector grid is critical for convergence.
Figure 2.6: Plots of the space charge distribution given a static applied voltage, assumed to be above the corona ignition voltage. The spacing between both emitter wires and collector grid lines are varied, although only the former is assumed to be signiﬁcant electrostatically. It is clear that emitter wire neighbor spacing aﬀects space charge distributions of both the interior and exterior wires; although closer spacing may impinge interior ﬂow and create a more uniform vertical “jet”, it also creates an elongated horizontal distribution at the exterior (clearly visible in the plotted white ﬁeld lines).

CHAPTER 2. THEORETICAL FRAMEWORK AND NUMERICAL MODELING 25
Figure 2.7: Plots of the resultant ﬂuid velocity at a given applied voltage, assumed to be above the corona ignition voltage. The spacing between both emitter wires and collector grid lines are varied. For the closer wire pitch, impinged ﬂow case, recirculation patterns are evident at the collector electrode.
Figure 2.8: Plots of the resultant ﬂuid velocity at a given applied voltage, assumed to be above the corona ignition voltage. In this case, the alignment between the emitter wires (i.e., whether emitters fall directly over grid crosspoints or over open spaces) is varied. The assumption would be that the former is “better” electrostatically, while the latter is better for aerodynamic drag. The latter result seems supported by the simulation results (i.e., the wires present less of a ﬂow boundary and there is less of a drag “bubble” underneath them), but would require experimental validation.

CHAPTER 2. THEORETICAL FRAMEWORK AND NUMERICAL MODELING 26

or open areas. Obviously, doing so would prohibit certain emitter point spacings and emitter wire densities; simulation should be able to provide some indication of whether drag beneﬁts are worth this choice. Unfortunately, although simulation shows a large qualitative diﬀerence between the two cases, imperfect assembly techniques made experimental validation diﬃcult without more focused eﬀort.
A three dimensional model was also created to study purely the aerodynamic drag through the collector grid. O’Hern and Torcyznski measured drag coeﬃcients on the order of 1-5 from photoetched meshes with wire widths of 50 µm, thickness of 50 µm, and separations of 318 µm at similar Reynolds numbers to those expected in EHD microrobots [67]. Computational values for drag coeﬃcient from this work were found to be sensitive to mesh wire cross section, and later experimental results showed a strong dependence on wire separation, with drag coeﬃcient increasing by about 50% for a 20% lower open area fraction (i.e., more of the total grid area is solid).
Concretely, using the results of Figure 2.9 (e.g., averaging the pressure below the grid), solutions for drag coeﬃcient and Reynolds number could be computed:

Re = ρU Dwire µ ∆p
cd = 0.5ρU 2

(2.21) (2.22)

Where ρ is the air density of 1.225kg/m3 and µ is the dynamic viscosity of 1.82 ∗ 10−5kg/ms. For the geometry shown, computed drag coeﬃcient is approximately 4.0, which is well in line with literature values for similarly sized micromeshes. This indicates potential for 3D FEA to be used as a design tool for collector electrodes.

Figure 2.9: Plots of the resultant ﬂuid velocity through a three-dimensional microgrid given an inlet at the top of the model. Although the ﬂow would be ducted by the boundary conditions of the model sides, they are placed far enough to not aﬀect the grid ﬂow. Not shown is the associated pressure plot from which drag coeﬃcient can be extracted.

CHAPTER 2. THEORETICAL FRAMEWORK AND NUMERICAL MODELING 27
Contributions and Conclusions
I believe that this section could serve as a strong starting point for someone looking to perform FEA of corona discharge based electrohydrodynamics. Personally, I struggled with properly coupling the multiphysics modules in order to get proper convergence, and this section would have helped me. I think that, unfortunately, FEA is not yet a true a priori design tool for EHD propulsion, and needs extensive experimental validation with each use — hopefully someone will take it a step further in the future.
I do think that some conclusions can be drawn from this work with a decent amount of conﬁdence, namely: it is possible to explore the eﬀect of space charge region impingement due to neighboring emitters as a function of electrode spacing with FEA; FEA could serve as a tool for investigating mass optimization of electrodes (e.g., when do extra grid wires only add more drag and mass); and FEA gives reasonable estimates for drag through a micromesh in 3D, pointing to future success as a design tool.

28
Chapter 3
Experimental Scaling Validation and Proof of Concepts
While on paper electrohydrodynamic thrust scales well enough to justify its use for insectscale ﬂight, this conclusion was completely lacking in experimental validation when I started my graduate career. My initial eﬀort focused on, essentially, proving that this was an idea worth pursuing. Although there existed some prior work on sub-millimeter corona discharge and some prior work on heat transfer using the resultant EHD ﬂow, the question remained as to whether a propulsion system (e.g. a free-standing device with directed air acceleration) could be created. Additionally, prior work had largely looked at static measurements; there was an open question about the possibility of feedback control of an EHD system, especially with high enough frequency for stability at the centimeter scale. Research questions to answer:
• Is corona discharge a reliable eﬀect at the millimeter- and sub-millimeter- scale for producing directed EHD force?
• Can thrust-to-weight ratio be increased by aggressively scaling electrode dimensions, without inﬂuencing the produced force?
• How does electrode geometry and separation aﬀect corona discharge and EHD force production at the sub-millimeter scale?
• Is it possible to implement real time feedback control of an EHD thruster?
3.1 A Rapidly Prototyped Meso-scale EHD Flier
Some of this work was presented at the Robot Makers (RoMa) workshop at the Robotics: Science and Systems 2014 conference.

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Motivation and Brief Description

The ﬁrst step in investigating EHD for insect-scale robots was to experimentally verify scaling relationships at the meso scale. The standard “hobby model” ionocraft uses balsa wood, aluminum foil, and magnet wire as components, and is cut and assembled by hand. If the force is indeed electrostatic and scale invariant, then shrinking the size of the model could only help in thrust-to-weight ratio. Hand fabrication at the centimeter scale is diﬃcult, so we turned to rapid prototyping techniques. Using laser cutters and 3D printers allowed us to quickly make and test design modiﬁcations as well as achieve some degree of fabrication precision.

Methods
Accurately measuring changes in mass to within 0.1 mg would typically require the use of an enclosed digital scale, but available tools were found to be inaccurate in the presence of high electric ﬁelds. To combat these issues, a 3D printed testing apparatus was developed. With this setup, the forces on the craft could be measured accurately and easily. The 3D printed system is made up of two separately printed pieces: an ionocraft frame and a measurement base (Figure 3.1).

Figure 3.1: A fully assembled testing aparatus used to determine ionocraft output force. It is comprised of two 3D printed components: a serpentine spring frame and a square base.

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The ionocraft frame functions as the internal structure and support. The capability for rapid iteration provided by the 3D printer allows for testing of the relationship between geometry and output force. Two notched posts allow for suspension of a wire across them while the curved bottom section allows for a bottom electrode or “skirt”, in this case made of aluminum foil, to be stretched across it. The three main parameters then varied are wire to skirt distance as controlled by the post height, skirt radius, and skirt length. The ionocraft frame has long folded springs that are inserted into the measurement base. This suspends the ionocraft frame in the air so the balance of forces between its weight and produced thrust can be measured. These 3D printed springs were found to be linear in the desired region of operation and to have a total spring constant between 1-2 N/m.
A test setup was developed to measure the current consumption as well as the output force of the ionocraft. A resistor was connected in series with the ionocraft to measure current, and a high resolution camera was used to measure output force. The two long beams that extend axially from the 3D printed device shown in Figure 3.1 are used to measure the displacement of the ionocraft that has been assembled at the center. This is accomplished by placing one of these beams directly in front of a repeated black and white striped pattern of known period. The experiment is performed by increasing the voltage across the ionocraft in discrete increments. For each voltage value, the voltage across the 2MΩ series resistor is measured to determine the current, and an image is taken.
To determine the force output from the ionocraft, the displacement of the long beam must be determined. This beam can be located precisely by ﬁtting a Gaussian proﬁle to a ﬁltered form of the image shown in Figure 3.1 (inset). This ﬁlter ampliﬁes the purple signal of the beam while ﬁltering out the black and white lines. Once this beam’s location is known relative to the image, the black and white periodic signal is used to determine the absolute displacement of this location from the beam’s original location. This displacement is then multiplied by the previously measured spring constant to ﬁnd the ionocraft output force.
With experimental results demonstrating the feasibility of electrohydrodynamic ﬂight at this scale, the next step was to fabricate a full, free-standing ionocraft with minimal total mass. Balsa wood was chosen for the frame material due to its extremely low density and ability to function as an electrical insulator. However, even though balsa is typically considered an easy material to work with, the required sub-millimeter precision necessary for these craft was not attainable with hand tools. The solution was to use a laser engraving machine, allowing fabrication of designs starting from computer drawings reproducibly, quickly, and in batches. Additionally, a wet etchant was used to decrease the mass contribution of the aluminum “collector.” Combining these methods yielded ionocraft prototypes with total mass under 100mg (see Figure 3.2).
For control, a microcontroller (GINA [58]) containing a 9-axis IMU was used to determine the angular displacement in real time and transmit the data wirelessly. A PD controller was implemented using the PWM output voltage of the microcontroller as the control signal in conjunction with the high-voltage control circuit; the full system diagram is shown in Figure 3.3. Measurements from a three-axis gyroscope are used with a quaternion transformation to ﬁnd the current angle of the ionocraft. Because the device geometry aﬀords only

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Figure 3.2: Fabricated meso-scale ionocraft. Components: Tungsten wire (50µm diameter), aluminum mesh, balsa wood frame. one degree of freedom for thrust, it was necessary to constrain the other axes with a simple “seesaw” test setup.
Figure 3.3: Full system block diagram.

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Results and Discussion

In the fabricated device there is not a uniform 2D body of charge as assumed in the standard EHD force equation. However, agreement between the theoretical and experimental force curves in Figure 3.4 implies the device is generating thrust at a magnitude approaching the theoretical limit. As the characterized device masses about 75mg, generated force of roughly 0.75mN is the minimum for tethered ﬂight; the peak measured force exceeds a thrust to weight ratio of 1.5:1, indicating controllable ﬂight is possible.

Figure 3.4: Plot showing measured force and current versus supply voltage for ionocraft with a 4mm gap between electrodes.
The system was modelled in MATLAB for design of the feedback controller. Model parameters were ﬁrst tuned to ﬁt empirical data. Despite the linearization of multiple system blocks, the experimental step input response was similar to the simulated performance, as can be seen in Figure 3.5. Attitude-based feedback control was successfully demonstrated. Nonlinearities in the physical test setup led to more repeatable performance when the system was underdamped. The presence of steady state error indicates an integrator term should be incorporated in future versions of the controller.

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Figure 3.5: Simulated and actual system responses with PD controller implemented. The presence of ringing and a signiﬁcant settling time in the experimental data indicate the system is underdamped. Kd = 0.183, Kp = 0.43.
Contributions and Conclusions
Succinctly, the contributions of this work were:
• The smallest, lowest voltage EHD-powered ﬂier to demonstrate repeated takeoﬀ.
• The ﬁrst documented feedback control of an EHD-powered ﬂier in a constrained environment.
The largest challenge was with repeatable operation. There was a good deal of device variation stemming from both fabrication and assembly. For example, if the emitter wire was not properly tensioned, it would be electrostatically attracted towards the collector and create a failure point wherever it was lowest. Surface breakdown along the balsa wood dielectric standoﬀs was a signiﬁcant problem, as they seemed to pick up static charge worse than expected. Oxidation of the tungsten emitter wire was evident over time; although it could be (carefully) cleaned by hand, this limited experimentation time. Overall, the conclusion was that while this was a strong indicator that we would be successful in scaling an EHD-powered ﬂier down to the centimeter-scale, we would require signiﬁcant advancements in electrode fabrication and robot assembly.

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3.2 An EHD Thruster Using Microfabricated Silicon

Electrodes

This work was published and presented at the 2017 International Conference on Micro Electro Mechanical Systems (MEMS) [20].

Motivation and Brief Description
If, in theory, EHD electrodes are only required to be electrically active and not used structurally, then we should be able to produce devices with a high thrust-to-weight ratio by using very thin planar geometries. Given a positive corona discharge, material choice should not actually matter (See Section 2.1). Standard MEMS techniques allow for the deﬁnition and release of planar structures ranging in thickness from a single to dozens of microns.
Prior work had identiﬁed the need for extremely uniform electrodes, ideally without the need for external ﬁxtures for tensioning/stretching. Prior work had also demonstrated that even 40µm thick silicon (SOI device layer) was remarkably simple to handle with tweezers. Microfabricating individual electrodes and assembling a millimeter-scale thruster by hand seemed like a natural evolution given the research group’s expertise in SOI wafer processing.
Electrical characterization was performed to analyze the eﬀect of inter-electrode gap and emitter electrode width on corona discharge and compare ﬁndings to simulation; this would be an important test of microfabricated silicon as a replacement for more standard electrode materials.

Methods
Devices are fabricated in a two mask SOI process and individually plasma diced. The corona emitter wires have cross sections ranging from 10µm × 40µm to 50µm × 40µm. The collection grids were typically 6mm squares, with 50µm wires on 500µm centers, a compromise between smooth electric ﬁelds (approximating a point-plane system) and lower air ﬂow resistance.
For electrical characterization, glass cover slips are used to vary the inter-electrode distance (Figure 3.6). High voltage was supplied to the emitter wire by a Gamma High Voltage 10kV supply and current was measured by a benchtop ammeter connected to the collector grid. The power supply is current limited to protect the ammeter. Contact is made with tungsten probe tips.
Outlet air velocity measurements were performed using a TSI AVM430 hot wire anemometer placed two millimeters below the collector grid.

Results and Discussion
The presented data is from a range of fabricated devices, replaced when failure during testing caused obvious damage (e.g. arcing events).

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Figure 3.6: Electrical testing was performed at a probe station. Glass cover slips were used to vary the inter-electrode distance and contact was made via tungsten probe tips. The collector grids were elevated from the probe station chuck by glass slips.
Electrical Characterization
Figure 3.7 shows measured voltage versus current relationships for devices with three diﬀerent inter-electrode spacing. A 50µm wide emitter wire is used for each. Figure 3.8 shows measured IV curves from devices with a constant inter-electrode spacing and varying emitter wire widths.
Plotting I/V as a function of V allows us to relate this gathered electrical data to the Townsend relationship (Equation 2.1). The value of C can be found from the slope, while the intercept represents the corona onset potential. Onset potential found by this method, through the simulation method described previously (Section 2.3), and by Peek’s analytical formula are shown in Table 3.1. It is important to note that both the Peek’s equation and the simulation method treated the emitting wire as having a circular cross section equal to the wire width instead of the actual rectangular cross section.
The results show that scaling the rectangular wire width does not strongly correlate with a decreased corona inception voltage as would be predicted from our circular cross section approximation. The experimental results for varying gap distance of the 50µm wire agree with simulated and analytic results within 10%. Lack of agreement for the 10, 20, and 30µm values indicate that scaling the wire width does not change the critical radius of curvature that ampliﬁes the local emitter ﬁeld.

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Figure 3.7: Current versus voltage for varying inter-electrode gaps: 50µm wide wire, 6mm × 6mm grid.

Figure 3.8: Current versus voltage for varying emitter wire widths: 2mm inter-electrode gap, 6mm × 6mm grid

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Table 3.1: Corona inception voltage (in kV) calculated by three diﬀerent methods for varying electrode geometries.

Width (µm) Gap (mm)
Peek’s Sim. Exp.

10 20 30

2

2

2

1

50

2

3

1.45 1.89 2.21 2.31 2.67 2.89 1.50 2.00 2.35 2.50 2.85 3.25 2.76 2.75 2.85 2.51 2.99 3.28

Thrust Measurements
Thrust produced by the engines was ﬁrst characterized indirectly by the outlet air velocity as measured by hot wire anemometer. The results for 2mm and 3mm electrode gaps with a 50µm wide wire over a 6mm grid are shown in Figure 3.9.

Figure 3.9: Air velocity versus voltage for varying inter-electrode gaps: 50µm wide wire, 6mm × 6mm grid.
Using the grid without its surrounding frame as the control area, thrust can be deduced

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from the simple mass ﬂow equation, with A representing the ﬂow outlet area, ρ the density of air, and ve the outlet ﬂow velocity:

F = mae = ρAve2

(3.1)

Thrust was then measured directly by assembling a thruster on the end of a roughly onemeter long balsa wood pendulum with a pin pivot at the top. With the total mass and center of mass known, observing the angular deﬂection at the tip of the rod and solving the torque balance equation determined the output force. The resulting rod deﬂection for various data points is shown in Figure 3.10. Tests were performed with a 50µm wide wire and a 2mm electrode gap.

Figure 3.10: Direct thrust measurements by deﬂection of a physical pendulum. Current and voltage information was collected alongside video and then still frames were extracted to take individual data points.

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The forces, measured directly by the deﬂection of the pendulum and indirectly by the outlet air velocity, are compared to the theoretical electrostatic force to ﬁnd the geometric loss factor (Equation 2.14). The two methods agree to within 20% and yield an average loss factor of 48% (β = 0.52). These results are shown in Figure 3.11. Possible sources for this loss factor include drag on the grid wires, horizontal force vector components due to electrode asymmetry, and atmospheric conditions aﬀecting ion mobility.

Figure 3.11: Plotting theoretical electrostatic force versus experimentally measured force for extraction of the geometric loss factor.
Outputs were stable over a roughly ten second period per each data point during the mass ﬂow experiments. Devices could be retested with consistent results after the thirty-minute experiment was complete.
Assembly
Dielectric standoﬀs as tall as the desired inter-electrode gap are necessary to produce a low-mass free-standing device with the microfabricated electrodes. Re-designed structures include an attachment mechanism consisting of guiding slots and locking cantilevers. Coated silica capillary tubes with 450µm OD and 25µm wall thickness were inserted into these points and then secured with UV-cured epoxy applied by probe tip. This process leads to the type of device shown in Figure 3.12, with a total mass of 2.5mg.

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Figure 3.12: The microfabricated silicon components and silicon capillary tubes were assembled by hand. This roughly 100 cubic millimeter device has a mass of about 2.5mg. Inset: Attachment mechanism with guiding slot and locking cantilevers.
Contributions and Conclusions
Succinctly, the contributions of this work were:
• A feasibility proof for hand-assembly of microfabricated silicon electrodes for use in a standalone EHD device.
• A roughly 100 cubic millimeter, 2.5mg thruster was assembled with a thrust to weight ratio exceeding 20. This is the smallest, highest thrust-to-weight ratio standalone EHD thruster ever demonstrated.
• Electrical characterization and direct force measurement from microfabricated silicon EHD thrusters, the latter being a novel measurement.
This work was a suﬃcient demonstration of EHD from microfabricated silicon electrodes to warrant further investigation. There was still a distinct need to improve operating voltage, device assembly, and to further investigate thrust eﬃciency loss mechanisms. In particular, the fact that operating voltage was not a function of drawn emitter wire “width” showed that the naive approach to improving the emitter geometry would not work. The various failure modes stemming from poor design choices (e.g. not rounding the emitter wire “handling tabs”) were all important to keep in mind for future work.

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3.3 Pushing the Limits of Corona Scaling for

Microfabricated Silicon Electrodes

This work was published in the journal Micromachines as an invited contribution to the Microplasmas special issue [19].

Motivation and Brief Description
Prior work had shown that there is a limit to the operating voltage scaling of microfabricated silicon electrodes by simply altering drawn width. Moving forward, there are two main avenues to explore: decreasing operating voltage strictly through inter-electrode distance scaling, and decreasing operating voltage via more complex alteration of the geometry of the emitter wire. As SOI wafer scale fabrication is a relatively simple and scalable technique, we would prefer to make any design changes compatible with this process.
In this work, an array of hybrid wire-needle and grid electrode geometries were fabricated and characterized to attempt to minimize both corona discharge onset voltage and thrust loss factor. Statistical analysis of this dataset was performed to screen for factors with signiﬁcant eﬀects. An optimized emitter electrode decreased onset voltage by 22%. Loss factor was found to vary signiﬁcantly (as much as 30%) based on collector grid geometric parameters without aﬀecting discharge characteristics.

Methods
Electrode Design and Fabrication
Devices are fabricated in a two mask silicon-on-insulator process and individually plasma diced, as described in [18]. The corona emitter wires have nominal cross sections of 40 µm by 40 µm. The silicon resistivity ranges from 1 to 100 Ω·cm.
Emitter wires with periodic protrusions of various shapes and collector grids with varying wire separation and width were fabricated. Figure 3.13 depicts both of these types of geometries. Table 3.2 shows the range of swept features. They include tip angle, spine separation and height, and whether the wire is populated with spines on one or both sides.

Characterization Setup
A Gamma High Voltage supply with 10 kV maximum voltage and 500 µA maximum current is used for electrical testing. A HP benchtop multimeter with a resolution of 100 nA is used for current measurements. A TSI AVM430 hot wire anemometer with a resolution of 0.01 m/s is used for air velocity measurements. The edge of the anemometer inlet is placed within a millimeter of the grid, while the actual hot wire is approximately 2 mm away axially. The anemometer inlet width is about 5 mm, meaning it should collect the full grid outlet airﬂow without needing to take measurements at multiple points along the

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Figure 3.13: (a) The emitter wires have triangular protrusions (“spines”). The distance between spines, height, and tip angle are all varied. Some wires are created with spines only along one half of the wire, while others are fully populated. In all cases the cross section of the rectangular portion of the wire is 40 µm by 40 µm; (b) Silicon collector grids have varied separation and wire width. The grids are designed to keep the total interior area constant at 25 mm2. Because the wire width is also controlled, the separation is scaled around the set point to accomplish this. In all cases the thickness of the grid is 40 µm.

Table 3.2: The electrode geometric factors and their values that were investigated in this work.

Emitter Wires

Collector Grids

Separation Height Angle Fill Separation Width

250

250 15

Half 250

10

500

500 30

Full 500

25

750

-

45

-

750

50

1000

-

-

-

1000

-

-

-

-

-

1250

-

channel. A depiction of the test setup is shown in Figure 3.14. Velocity measurements are internally ﬁltered by the anemometer using a moving average with ﬁve second time constant. During testing both the current and velocity were allowed to settle (between 5 and 10 s) before recording the data point.
Output force is calculated using simple momentum theory, where F = m˙ ve = ρAve2. The entire interior area of the collector grid (5 mm×5 mm) is used as the outlet area. This assumes a negligible inlet velocity and a uniform outlet velocity (Ve). Previous EHD research showed severe overestimation of thrust by using outlet air velocity as opposed to a scale [62], noting that a single velocity proﬁle is insuﬃcient to accurately calculate the volumetric force. We expect this problem to be less signiﬁcant both for thrusters of the scale shown here, where the outlet is on the order of the measurement apparatus inlet, and for our test setup, where the outlet ﬂow is ducted by the dielectric standoﬀs. Previous research

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has shown fair agreement between mass ﬂow calculations and more direct methods of thrust measurement for similar electrode arrangements [20].

Figure 3.14: (a) A pair of fabricated electrodes next to a U.S. one cent coin for scale; (b) A schematic view of the characterization setup. The entire setup is contained within a probe station. Distance between the electrodes is set by glass cover slips. The electrode set is elevated oﬀ the probe station chuck by glass spacers so that the conductive chuck does not interfere with measurements and so that the hot wire anemometer can be placed underneath the outlet. Not shown is the second tungsten probe tip which makes electrical contact with the collector grid and the third tungsten probe tip which makes mechanical contact with the other side of the wire to keep it stable during testing.
Results and Discussion
The presented data is from a range of fabricated devices. Statistical analysis was performed using JMP by SAS Institute.
Corona Inception Voltage and Current
A total of 21 diﬀerent electrodes were characterized. In all cases a 500 µm grid separation was used. Electrodes were exchanged when catastrophic failure occurred (see Figure 3.21).
Corona inception voltages and C coeﬃcient were calculated by plotting Equation (2.1) in terms of I/V . This method, as opposed to the method of ﬁnding the critical voltage with a µA transition, was deemed more reliable given the current resolution of the test setup. The C coeﬃcient can be used as a rough quality factor when designing for high current discharge devices as long as the breakdown voltage does not decrease signiﬁcantly between electrodes. R2 vales above 95% were found in the linear ﬁt for all cases.
Commercial software was used for modelling signiﬁcance of the varied factors on two eﬀects, Vcrit and C. An ideal electrode has a low inception voltage and a high C. The

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dataset was ﬁt to the models using a standard least squares regression analysis. The results of these ﬁts are shown in Figure 3.15.
Angle, ﬁll (half or full rank of spines), and separation were all found to be statistically signiﬁcant (p < 0.05 ) factors aﬀecting inception voltage, with tip angle being the dominant factor. Spine height was found to be statistically insigniﬁcant. For C, emitter ﬁll and separation were found to be the only two signiﬁcant factors. These models allow us to generate prediction plots for the quantitative eﬀect of the various factors on the response; these are shown in Figure 3.16.

Figure 3.15: Response models generated by least squares regression analysis of the 21 run dataset. A p value below 0.05 generally represents a statistically signiﬁcant factor (rejection of the null hypothesis). (a) The regression model for corona inception voltage; (b) The regression model for C coeﬃcient.
By following these trends we can identify the two geometries that should independently have the lowest inception voltage and the highest C. This is conﬁrmed experimentally as shown in Figure 3.17. The lowest measured inception voltage is 1453 V and the highest measured C is 5.65 ×10−11 A/V2, as compared to the bare wire’s 1981 V and 7.30 ×10−11 A/V2. Noting that tip angle is the dominant driver of inception voltage and does not signiﬁcantly aﬀect C we can select an “optimized” design. At this point no weighting has been attached to the responses for a true optimization problem to be set up. The electrical characteristics of this geometry compared to the bare wire are also shown in Figure 3.17.
Loss Factor
Loss factor can be determined by plotting the theoretical electrostatic force (Equation (2.13)) versus the force measured using the grid outlet air ﬂow. The slope of this line represents

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Figure 3.16: Response prediction proﬁles for the four factors varied in this experiment based on regression analysis for corona inception voltage (top) and for C (bottom). These plots in conjunction with the signiﬁcance proﬁles from Figure 3.15 can be used to select an optimized geometry.
Figure 3.17: All tests performed with a gap distance of 500 µm and a collector grid separation of 500 µm. (a) The current-voltage characteristics of the lowest inception voltage conﬁguration, highest C conﬁguration, and a bare wire; (b) The current-voltage characteristics of the “optimized” wire, with separation of 750 µm, tip angle of 15◦, height of 250 µm, and full ﬁll. This electrode had an inception voltage of 1542 V and a C of 5.63 ×10−11 A/V2.
the fraction of theoretical force being produced as measured output force in the preferred direction. An ion mobility of 2 × 10−4 m2·V−1·s−1 and the nominal electrode gap distance were used in the theoretical force equation in all cases. Although that means loss factor in this case will also include deviation in ion mobility from this value, that error will presumably be a static oﬀset and it is still a useful tool to examine trends. This method was previously explored in [20], where a loss factor term β was introduced to Equation (2.13).
Grid wire separation is directly related to open area fraction. As shown in Figure 3.18, loss factor was found to be aﬀected by this value without a change in discharge electrical

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Figure 3.18: (a) Changing the grid wire separation from 500 µm to 250 µm had an insigniﬁcant eﬀect on discharge characteristics with a bare wire at a 1 mm gap distance; (b) Decreasing the wire separation changed the loss factor by over 30%. Because there is no change in IV characteristics the increased losses can presumably be attributed to increased drag.
characteristics for some values of separation. For a 1 mm electrode gap, discharge with a 750 µm wire separation grid was inconsistent and sparkover occurred before discharge for all larger separations. For a 500 mm gap, however, discharge was consistently measured using 500 µm wire separations. At this time it is unclear what causes this discrepancy in stable gap-separation ratio.
Grid wire width was found to have a signiﬁcant eﬀect on loss factor. For a 500 µm wire separation grid, the open area fraction is about 91% for a 25 µm wire width and about 83% for a 50 µm width. This 8% change in open area fraction resulted in a 20% increase in measured loss factor, as shown in Figure 3.19.
Loss factor was found to be a strong function of electrode gap, as shown in Figure 3.20. With all other factors constant a 50% decrease in electrode gap increased loss factor by over 30%.
Failure Modes
Once the electric ﬁeld reaches a critical magnitude dielectric breakdown occurs. The high voltage supply used during characterization has a current limit of 500 µA, which is typically reached during these sparkover events. The two most common catastrophic failure modes are for (1) the emitter wire to “pop” and break somewhere in the vicinity of the center or (2) for the collector grid to be physically damaged in the vicinity of the sparkover point. The latter case is shown in Figure 3.21.
The fact that tip angle does not have a statistically signiﬁcant eﬀect on current generation seems to indicate that the corona plasma is highly localized; this is supported visually by the visible corona plasma being conﬁned to the tips, as shown in Figure 3.22. This contrasts with [24], which noted an eﬀect of the tip angle used for emission on corona discharge

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Figure 3.19: Both of these ﬁgures are for 500 µm grid wire separations with a bare wire as the emitter electrode. (a) Changing the grid wire width from 25 µm to 50 µm at a 1 mm electrode gap increased loss factor by about 20% without a signiﬁcant eﬀect on discharge current; (b) Changing the grid wire width from 25 µm to 50 µm at a 0.5 mm electrode gap increased loss factor by about 19% without a signiﬁcant eﬀect on discharge current

Figure 3.20: (a) Changing the electrode gap distance from 1 mm to 500 µm with all else held constant increased loss factor by over 30%. Test performed with a bare wire, a 500 µm grid wire separation, and a 25 µm wire width; (b) Measured outlet air velocity versus applied voltage for the two electrode gap distances. As expected by combining Equations (2.13) and (2.15) with the mass ﬂow equation, the voltage-velocity relationship is linear above the corona onset voltage.
current. Further analysis of the dataset shows that there is a signiﬁcant correlation (p = 0.01) between the number of tips and C. Because the height of the spines did not have a clear eﬀect on either the inception voltage or the discharge current, it may be possible to design a new geometry that increases C without aﬀecting onset potential; for example, a move from triangular spines to a triangle-on-a-post.
Increased corona inception voltage for small tip separation may be explained by a shielding eﬀect similar to that noted in both ﬁeld emission array literature and in multiple-needle

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Figure 3.21: A typical failure mode of an electrode set. Permanent damage is sometimes observed following sparkover from a wire tip to the collector grid. This may be due to the relatively high current density following dielectric breakdown causing rapid Joule heating in the grid wires, or due to physical ablation during the high current breakdown. After a destructive event such as this, both electrodes were replaced despite there being no visible damage to the emitter wire.

Figure 3.22: The corona discharge is characterized by a purple/violet glow visible in low light conditions. With the probe station door shut during electrical testing it was possible to take still images capturing the corona plasma. The ﬁrst pane is the device with the light turned on, before testing. In the middle pane the device is at about 2500 V applied potential, where the plasma is clearly localized to the spine tips. The third pane is a still frame taken during a sustained breakdown event after the device had failed around 3000 V.
corona discharge studies. Although we expect to see some coupling between minimum separation to avoid shielding and height of the tips, there is no evidence of that with the currently fabricated device geometries.
Although positive corona discharge is primarily driven by geometry and electrode material choice is unlikely to strongly aﬀect operating voltage, the catastrophic failure mode sometimes exhibited may be related to material properties (e.g., resistivity). Metal emitter electrodes in sub-millimeter corona devices have their own unique failure modes, including mechanical yield [85]. Therefore, instead of switching materials entirely, a ﬁrst step would be to investigate the eﬀects of silicon doping concentration on device performance. Regardless, in an autonomous microrobot it is unlikely that the power circuitry would be able to supply

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current far in excess of the maximum operating point, perhaps negating this issue. Holding all other factors constant and decreasing the electrode gap distance increased the
loss factor by around 30%. We attribute this increase to two related primary reasons: increase in the ionization region to drift region ratio, and increase in the percentage of collisions imparting horizontal momentum components. The former will inﬂuence the eﬀective d of Equation (2.13) and the latter will break the assumption that all collision energy generates force in the preferred direction.
As electrode gap is decreased the grid wire separation must also decrease to prevent them from inﬂuencing the emitter ﬁeld. Decreasing the grid wire separation from 500 µm to 250 µm was found to increase loss factor by about 30%. Interestingly, this is roughly the same decrease in open area fraction (about 10%) that caused a 20% loss factor change when grid wire width was varied. This would imply that edge eﬀects at the grid wires and not just obstructed area plays a role in drag through the grid; this theory is supported by literature, where drag through a micromesh decreased when edges were beveled [67].

Contributions and Conclusions
Succinctly, the contributions of this work were:
• Demonstration that simple lithographically-deﬁned asperities can signiﬁcantly decrease the operating voltage of SOI silicon electrode corona discharge devices.
• A statistical analysis of the geometric factors aﬀecting corona discharge inception voltage as well as subsequent ion current for microfabricated silicon emitters.
• An investigation of the eﬀect of collector electrode geometry on EHD loss factor for various interelectrode distances, which may serve as a design tool for future researchers.
In conclusion, we have explored a method to lithographically deﬁne features that can be used to decrease operating voltage without unduly inﬂuencing discharge current. Further, we have attempted to test the limits of collector grid geometry scaling, demonstrating changes in loss factor of around 30% with no change in discharge current. Although the hybrid wireneedle design presented herein was successful in decreasing corona onset voltage, the current setup is not optimized for ﬂow through the grid. Future work will investigate the limits of the scaling trends for lithographically deﬁned emitter features in an eﬀort to decrease operating voltage below 1000 V at an acceptable force loss factor; these electrodes will then be incorporated into future designs of ﬂying ionocraft.

50
Chapter 4
Design and Realization of a Flying Microrobot
A robot must have the capacity for controlled motion. An EHD-powered ﬂying robot will require thrusters in a conﬁguration that allows for attitude and trajectory control, the ability to modulate the thrust, the ability to sense its environment, and the computation power to close a control feedback loop.
A design inspired by the success of the quadcopter, replacing the rotors with EHD thrusters, allows us to sidestep some of the unfavorable scaling laws of propellers while maintaining the ability to transfer domain knowledge from the rich world of quadcopter design and control. Without an aerodynamic control surface (e.g. a propeller or wing) we have eﬀectively decoupled our force output scaling from the characteristic size of the robot. Research questions to answer:
• Can a quad-thruster be designed with low enough airframe overhead for takeoﬀ, ideally maintaining a high thrust-to-weight ratio?
• Can attitude control be demonstrated using similar control methods to a standard quadcopter?
• Can full robots be assembled reliably enough, and can device lifetime be extended long enough, to make control experimentation possible?
• Can an ionocraft carry a sensor payload that allows for stable ﬂight without external sensing?

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4.1 First Takeoﬀ of a Centimeter-scale EHD Quadthruster
This work was published and presented at the 2017 International Conference on Manipulation, Automation, and Robotics at Small Scales (MARSS) [18].

Motivation and Brief Description
With prior work demonstrating the viability of an EHD thruster composed of microfabricated silicon electrodes, the next step was to design a system with the capacity for controlled ﬂight. Assuming that the thrust can be modulated by changing the voltage applied to the emitter wires, the collector grids of four individual thrusters can be biased together. This is the key for creating the simplest feasible quad-thruster ionocraft; the collector grids make up the bulk of the airframe, with connections only for structural support.

Methods
Electrode geometries were chosen based on a combination of lessons learned from previous eﬀorts to create meso-scale EHD thrusters (e.g. limits of repeatable gap scaling for a given emitter radius), availability of a stable fabrication process with the given wafer properties, and feasibility of hand assembly (e.g. minimum size to handle with tweezers). Devices are fabricated in a two mask silicon-on-insulator (SOI) process and individually plasma diced. The active electrode material is all device-side silicon, allowing for a high thrust to weight ratio as the force is a predominantly two dimensional eﬀect. The process ﬂow is depicted in Fig. 4.1. After the backside deep reactive ion etch, the devices are physically removed from the wafer with tweezers and etched with vapor HF to clear the buried oxide layer. Corona discharge is a strong function of electrode geometry; care must be taken in designing the electrodes to prevent early breakdown, reverse corona (where a plasma is formed around the collector), and wasted area. Exterior corners are ﬁlleted and only rounded shapes are used in non-functional area, e.g. near the dielectric standoﬀ attachment points.
Fused silica capillary tubing with an inner radius of about 400µm and a wall thickness of 25µm is used for the dielectric posts that set the distance between the two electrodes. The device is designed so that they can be fabricated in a stack - a rendered depiction of the device assembly is shown in Fig. 4.2. An aluminum jig is used during the assembly process to assist with placement and alignment of the silica tubes. An assembled ionocraft is about 10mg and 1.8cm by 1.8cm (see Fig. 4.3). It takes roughly thirty minutes to assemble by hand.
During electrical characterization the quad-thruster is weighted down by glass cover slips so it remains stable. High voltage was supplied to the emitter wire by a Gamma High Voltage 10kV supply and current was measured by a benchtop ammeter connected to the collector grid. The power supply is current limited to protect the ammeter.

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Figure 4.1: The simple two mask silicon-on-insulator (SOI) process to fabricate the silicon electrodes. First the 40µm device silicon is patterned. The wafer is ﬂipped and loosely bonded to a handle wafer using a thermally conductive grease. The 500 µm handle silicon is aligned, patterned, and then etched to plasma dice the individual devices. Finally, tweezers are used to physically remove the electrodes, breaking the buried oxide in the process. The electrodes are placed into a vapor HF etcher to clear the remaining oxide.
Figure 4.2: Fused silica capillary tubes are inserted vertically through slots in the microfabricated silicon electrodes and secured with UV-curable epoxy applied via probe tip. A machined aluminum ﬁxture (far right) provides help with alignment and stability. Tabs on the emitter wire and collector grid (latter not shown) provide a place to attach the power connections using silver epoxy applied via probe tip.
Results and Discussion
The results are shown in Fig. 4.4 for both a full quadthruster, for two grids, and for one grid of the same device. Using Equation 2.13 with the loss factor for a similar electrode

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Figure 4.3: These “quad-thrusters” are made of microfabricated silicon electrodes and fused silica capillary tubes and assembled by hand. They are 1.8cm x 1.8cm, 10mg, with four individually addressable electrode sets, and a 1mm electrode gap. They should be capable of producing around 1mN of force for a thrust to weight ratio of about 10.
geometry found in [20] of 50%, a peak force for the quad-thruster of about 1mN is expected, corresponding to a thrust to weight ratio of 10.
Using 60µm diameter copper wires as the power connections the device was actuated in front of a high speed camera. At about 2400V the ionocraft took ﬂight, reaching a peak altitude of around 5cm before the instability of its attitude caused a power wire to touch the collector grid. This ﬂight is shown in Fig. 4.5. From this video a peak acceleration of about 2 gravities can be calculated, corresponding to a force of about 200µN , far below the theoretical maximum force these devices should be able to provide. During the video the voltage was being slowly increased by hand and, due to the high thrust to weight ratio, the device took oﬀ and subsequently crashed before the voltage could be increased to the levels used to measure the maximum thrust point.
The goal of using four individually addressable electrode sets is to allow for attitude control similar to that of a quadcopter. As an initial feasibility test, only two of the four thrusters were actuated. As shown in Fig. 4.6, this created a moment around the center axis and the ionocraft ﬂipped over as predicted. The question of how to control yaw remains open. A traditional quadcopter controls yaw by coupling torque from its rotors to produce a net moment around only one axis; the EHD thruster presented here has no analagous torque component. One possibility is to angle the emitter electrode along the vertical axis in order to produce horizontal force, although this would lead to decreased vertical force.
Contributions and Conclusions
Succinctly, the contributions of this work were:

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Figure 4.4: Electrical characterization of a quad-thruster with number of actuated wires varied. Calculated corona onset voltage is 2309V with a standard deviation of 50V. Measured currents agreed with geometric prediction (e.g. one wire produces one fourth the current of four wires at a given voltage) to within about 5% on average. Tests concluded when an arc occurred, destroying the wire.
Figure 4.5: Takeoﬀ of a microfabricated ionocraft captured at 1000fps. At about 2400V it took ﬂight silently. The ﬂight ended in around a second when the power connection became tangled with the collector grid, leading to an arc.
• The ﬁrst takeoﬀ of an EHD powered, centimeter-scale “robot” (as in, has the capacity for controlled ﬂight).
• A feasibility proof for a quad-thruster design with minimal airframe mass overhead,

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Figure 4.6: By applying voltage to only two of the four grids we can control roll/pitch of the robot. In this video, captured at 1000fps, the ionocraft ﬂips over its center axis when the two rear thrusters are actuated at about 2400V.
enabling the highest thrust-to-weight centimeter-scale ﬂier to date.
• A feasibility proof of using a quad-thruster design for attitude control.
The viability of the quad-thruster design had been proven, but there were major challenges with this iteration. The operating voltage was still too high; lessons learned in lithographic asperity deﬁnition for the emitter wires had yet to be incorporated into the design. The assembly was diﬃcult and not very repeatable; having to use a separate spacer to deﬁne the inter-electrode spacing led to issues during assembly with uniformity and device survival. The design was fundamentally ﬂawed; having a planar emitter leads to surface breakdown along the dielectric posts and makes it diﬃcult to attach the power tethers without harming performance. All of these problems would have to be solved before it was worth pushing towards controlled ﬂight of an ionocraft.
4.2 Improved Assembly, Lifetime, and Payload Capacity
This work was published and presented at the 2018 Transducers Research Foundation Microsystems Workshop at Hilton Head (HiltonHead).
Motivation and Brief Description
While the initial results of the quad-thruster ionocraft were promising, there was signiﬁcant room for improvement in terms of thrust density, operating voltage, device lifetime, and assembly repeatability. In this work, a 13.6mg, 1.8cm by 1.8cm ionocraft is shown to take oﬀ while carrying a 40mg Flex PCB with 9-axis IMU and associated passives while tethered to a power supply. A new emitter electrode design decreased corona onset voltage by over 30% and takeoﬀ voltage by over 20% from previous eﬀorts. Ease of assembly is an important metric for a future microrobotic platform, as it may be a key driver of scalability and unit

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cost. The reﬁned assembly process shown in this work has decreased time per robot to about half an hour, with nearly a 100% success rate, in a process that could easily be automated thanks to its mechanical simplicity. Additionally, a key actuator performance degradation issue, inherent to the energetic plasma of the corona discharge eﬀect, is remedied in a simple and scalable manner (i.e. through a single thin ﬁlm deposition).
Methods

Figure 4.7: Photograph of the assembled ionocraft. With four individual addressable thrusters, it is about 1.8cm by 1.8cm and masses 13.6mg. It is comprised of 13 individual components connected by a combination of mechanical slots and UV-curable epoxy. The design includes various tabs for handling and connection to power tethers.
Silicon electrodes with lithographically deﬁned asperities to decrease corona onset voltage are fabricated in plane, fully released, and then rotated and assembled out of plane. The fabrication process previously reported at MARSS 2017 [18] is adapted to a single mask SOI process in this work to increase device yield and decrease number of fabrication steps. An improved assembly method (Fig. 4.8) diﬀers from prior work in that it: allows the electrodes to be designed for mechanical robustness (to survive assembly); separates the power tether connection point from the collector grid by a lithographically deﬁned amount to prevent surface breakdown along the dielectric post; and allows the inter-electrode gap to be controlled semi-lithographically.
The new emitter electrode design for out of plane rotation requires inserting silicon “shanks” into the silica dielectric standoﬀ tubes. Typically, capillary tubes are cut by hand using a small ceramic tool; while macroscopically these cuts are smooth, they actually often leave jagged or ragged edges. Inserting wires into a poorly cut capillary tube could either

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Figure 4.8: 3D model renders of the assembly process. Pre-cut silica tubes are inserted into slots in a CNC-milled aluminum jig. The ionocraft frame is slid down the guiding posts. The emitter wires are rotated out of plane and tapered guides are inserted into the silica tubes. The inter-electrode distance is now determined by a combination of lithography, slot depth, and tube length.
be impossible or result in potential misalignment/non-uniformity of the emitter. A new, surprisingly rare tool was procured to get around this issue. It consists of a mechanical clamping mechanism with a manual set-screw and a diamond cutter mounted on a rotary wheel. Capillary tubes are inserted, the diamond cutter is brought into contact with the surface, and the entire cutter is manually rotated. This results in highly uniform, repeatable cuts. This tool (see Figure 4.9) is also the secret as to why the emitters are shaped with their particular “elbow,” and how emitter-collector gap is able to be set semi-lithographically. By setting the tool on a level surface and sliding the capillary tube through until it makes contact prior to clamping and cutting, tubes of 5.67 ± 0.02 mm are made (n=10, measured by digital micrometer). Various attempts to modify the setup in order to cut shorter tubes have negatively aﬀected uniformity and repeatability.
A Flex PCB board (Fig. 4.10) has been fabricated containing a commercial 9-axis IMU,

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Figure 4.9: Left: The rotary blade capillary tube cutter allows for more uniform, repeatable cuts. Center: A new tube is shown on the left while a typical edge on one of the old is shown on the right. This was key in the transition towards enabling perpendicular (i.e., emitters pointed towards the collector grids) electrode design. Right: The standard ceramic cutting tool used for capillary tubes.
the InvenSense MPU-9250, as well as three associated passives and bonding pads. The board’s 5mm by 5.5mm footprint allows it to be placed in a designated central region of the robot airframe without interfering with the surrounding thrusters. The total board mass of about 40mg (including all components) is within the expected payload capacity reported in prior work.
To measure output force, the device under test is mounted on a threaded nylon post ﬁxed directly to a Phidgets 100g Micro load cell. For full quad-thruster ionocrafts there is a dedicated region in the center of the airframe for mounting; single thrusters are mounted using one of the unused silica tube slots along the grid frame. Multiple instruments are controlled via GPIB for synchronized force-current-voltage sweeps.
Results and Discussion
The presented data is from a range of fabricated devices; unless otherwise noted, collected data is from the ﬁrst trial using each device to reduce the eﬀect of lifetime performance degradation (device lifetime discussed in Section 4.2). There was signiﬁcant noise in the strain sensor used for force measurement for the values used in this work; presented data is ﬁrst passed through a low pass ﬁlter in the Phidgets data hub and then averaged over 3 seconds of collection (11 data points) for each measurement.
Electrode Geometry
In a widely-used empirically derived equation for corona onset voltage formulated by Peek [70] (discussed further in Section 2.1), for point-to-plane geometries it is found that V0 ∝ ln(d). Decreasing the electrode gap from 500µm to 250µm (Fig. 4.11) was shown to decrease the onset voltage, as found by the 0-intercept of the curve ﬁt to Eq.2, by approximately 400V,

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Figure 4.10: Flex PCB IMU board on a U.S. penny. The board is about 5mm by 5.5mm and masses 40mg including all components. It contains an InvenSense MPU-9250 9-axis IMU and three associated passives.
a larger change than predicted by this trend. Although related work already shows deviation from Peek’s equations in sub-millimeter corona discharges, this greater deviation at even smaller gaps bears further investigation. The factor relating ion current after corona ignition to the input voltage, C, was shown to increase by about 230%; because current must double to produce the same output force at half the drift distance, this would ideally correspond to a smaller required operating voltage swing for the same force production range.
The 250µm gap device has an extracted β via linear ﬁt of current-force data of 0.33, 44% lower than the extracted value of 0.59 for the 500µm gap, 5-degree device. Although the absolute value of this factor may be incorrect due to likely variation in ion mobility from the assumed 2cm2/V s, the trend is expected from prior work and likely largely due to the eﬀect of aerodynamic drag on the smaller spacing of the 250µm collector grid. Further, device failure (i.e. arcing) occurred before the same maximum force could be produced by the smaller electrode gap, indicating that emitter tip radius, r, should be decreased in an eﬀort to increase the d/r ratio critical for corona discharge.
The onset voltage was not found to change signiﬁcantly between 5-degree and 10-degree drawn emitter tip angle wires. This could indicate some limit in dimensional scaling following DRIE and current lithography methods, as asperity drawn angle was shown to have a strong eﬀect on onset voltage in prior work [4].

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Figure 4.11: Current and force versus voltage curves for thrusters with diﬀerent electrode gaps or diﬀerent drawn emitter tip angles. The current-voltage data from MARSS2017 [2] is a 20µm by 40µm cross section silicon “wire” with no lithographically deﬁned asperities at an electrode gap of 1mm. The 250µm electrode gap device uses a collector grid with 250µm spacing. The plotted lines in the force-voltage plot are 2-degree polynomial ﬁt lines.

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Thrust Density
Adding more emitter wires per collector grid should have the eﬀect of increasing both C and thrust-to-weight ratio at the cost of additional assembly time. Experiments show that corona discharge current scales approximately linearly with number of emitter wires (Fig. 4.13) at a wire spacing of 3mm for the 2-wire case and 1.5mm for the 3-wire case. Going from one emitter wire per collector grid to three increases C by about 250%, while β decreases from 0.59 to 0.53. The fact that current did not scale linearly may be attributable to assembly or device degradation nonuniformity, and the decrease in beta is within the measurement error for the strain sensor used in this work. As discussed in Section 2.3, we would actually expect β to improve with more emitter wires (given correct neighbor spacing) due to space charge region interactions.
The mass of an additional emitter wire and two silica posts is only 1.5mg while the maximum thrust is increased by approximately 100µN (10mg) per set, showing a large potential boost to thrust-to-weight ratio. Prior work in FEA simulation indicates that the space charge region developed from a single emitter wire’s corona discharge spans a horizontal radius approximately equal to the electrode gap distances. This indicates that wire neighbor spacing can be decreased from 1.5mm to 1mm and the maximum number of emitter wires per collector grid could double to 6 without signiﬁcant neighbor interactions; although this would certainly continue to provide an aerial thrust density and thrust-toweight ratio beneﬁt, assembly complexity would be prohibitive with the current design.
Device Lifetime
Performance of a corona discharge based EHD thruster can be expected to degrade over time, largely as a result of interactions of the bipolar plasma region with the emitter electrode. Initial experiments saw rapid loss of discharge current over time with a constant applied voltage (Fig. 4.14). Scanning electron micrographs showed large amount of physical damage to the emitter wires, localized to the tips themselves, with a damage radius of around 60µm. With the hypothesis that this damage is a result of energetic ion ablation in the bipolar plasma (a plasma radius of 50µm is often assumed in literature), the tips were sputtered with a 100nm titanium nitride layer, turned over, and sputtered with another 100nm layer (Fig. 4.14, bottom). Subsequent testing saw no degradation of performance in the same time period. It is expected that the new failure mode will be through oxidation of the tips, enhanced by the energetic oxygen plasma.
Takeoﬀ with Sensor Payload
Current ﬂying microrobots are typically payload constrained; either they fail to lift the weight of their own actuators and airframe, or must seek to develop novel sensing schemes and platforms to optimize for mass. The relatively high thrust-to-weight ratio of the ionocraft means that it may be possible to use standard commercial sensors, simplifying development and

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implementation. To prove the feasibility of future controlled ﬂight using a commercial sensing package we developed a 40mg FlexPCB with 9-axis IMU as discussed above, attached it to a designated central region in the ionocraft airframe with UV-curable epoxy, and demonstrated take oﬀ (Fig. 4.12). This single-emitter design had an unladen takeoﬀ voltage of about 2000V (2100V with IMU); this number should decrease by using multiple emitter wires per thruster, but with the assembly jig used in this work it was diﬃcult to reliably assembly such a version.

Figure 4.12: An ionocraft with assembled 40mg Flex PCB IMU board attached to the airframe center pad. At about 2100V, the ionocraft is able to take oﬀ from the table; the power and ground wires prevent the ionocraft from going any higher. There is only one high voltage line attached here, with connections between the emitter wires done on the ionocraft itself. The IMU board is not wired or active during takeoﬀ in this particular work (see Section 4.3).

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Figure 4.13: Current-voltage and force-voltage curves produced by varying the number of emitter wires in a thruster. Tests are for 5-degree emitter tips, an electrode gap of 500µm, and a collector grid spacing of 500µm. The plotted lines in the force-voltage plot are 2-degree polynomial ﬁt lines.

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Figure 4.14: Device lifetime quantiﬁed by measured ion current versus time at a constant operating voltage. Bare silicon emitter wires saw immediate performance degradation during testing, while wires coated by about 100nm of sputtered TiN had stable performance up to the measured 1000s of operation. Devices are 10-degree tips at a 500µm gap with 1800V applied.

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Contributions and Conclusions
Succinctly, the contributions of this work were:
• Demonstration of improved thrust density of EHD actuators via a simple increase in number of emitter wires.
• Signiﬁcantly decreased operating voltage of a centimeter-scale ionocraft from prior work.
• An improved assembly method for quad-thruster ionocraft that signiﬁcantly improved repeatability and decreased time per experiment.
• An identiﬁcation of a limiting factor for device lifetime and a simple, scalable solution.
• First demonstrated takeoﬀ of a centimeter-scale ionocraft while carrying a useful sensor payload.
Although we have validated the use of multiple emitter wires as a way to increase device performance, with the current design each new emitter wire requires both its own pair of silica posts (with associated epoxy) and electrical connection to its neighbors, decreasing beneﬁt to thrust-to-weight ratio. Future work will explore new methods, for example designing mechanical interlocks into the components themselves, to overcome these challenges. As electrode gap continues to decrease in an eﬀort to decrease operating voltage, the eﬀect of decreasing electrode d/r ratio on minimum drift ﬁeld strength, and therefore eﬃciency, becomes more pronounced. The devices in this work have eﬃciencies that range from 2 mN/W to 1 mN/W over their operating range, unacceptably low for a truly autonomous ﬂying robot with any useful mission time; see Section 1.1 for comparisons with existing technology. It may be necessary to increase emitter tip sharpness beyond what is possible with standard lithographic techniques, for example with thermal oxide sharpening, in order to operate ionocraft in higher eﬃciency regimes by trading oﬀ output force.

4.3 Towards Controlled Flight of the Ionocraft
This work was published in the journal Robotics and Automation: Letters [17]. It was made as a dual contribution to the 2018 IEEE International Conference on Intelligent Robots and Systems (IROS), and was presented there.
Motivation and Brief Description
With the validation of the quad-thruster conﬁguration and the various improvements to thrust density, assembly, and lifetime, the next step in creating an autonomous ionocraft was to demonstrate the possibility of closed-loop control. The robot and assembly jig were

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both redesigned to incorporate some of the improvements. A high voltage control circuit had to be prototyped to attempt to measure the dynamic response to a time varying signal instead of the standard steady state value previously measured.
For the ﬁrst time, attitude and acceleration data is continuously collected from takeoﬀ and sustained ﬂight of a 2cm x 2cm, 30mg “ionocraft” carrying a 37mg 9-axis commercial IMU on FlexPCB payload, with external tethers for power and data transfer. The ionocraft’s steady state thrust versus voltage proﬁle, dynamic response to a time-varying signal around a high voltage DC bias point, and aerodynamic drag at incident angles around 90 degrees were measured. These experimental measurements, as well as measured IMU sensor noise, were inserted into a Matlab Simulink simulation environment. Simulation shows controlled hovering and planned ﬂight in arbitrary straight trajectories in the X-Y plane.
Methods

Figure 4.15: An assembled ionocraft next to a United States quarter. The ionocraft itself is approximately 2cm by 2cm and masses 30mg. Also shown is the 37mg FlexPCB board with 9-axis IMU and associated passives attached to the center of the airframe. The ionocraft is built from 41 discrete components, each connected by a combination of mechanical slots and UV-curable epoxy. Inset: A single emitter electrode. The 500µm long, 5deg tip angle lithographically deﬁned asperities are aligned with the grid and used to reduce operating voltage.
The robots (Figure 4.15) are made using active electrodes fabricated in standard MEMS wafer-scale silicon processes as well as commercially available silica tubing. A silicon-oninsulator wafer with 40µm device thickness forms the substrate for a single-mask deep

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reactive ion etch and subsequent vapor-phase hydroﬂouric acid release etch. Thin tether structures are broken manually to yield fully released, 40µm thick emitter and collector electrodes that can be removed from the wafer surface for assembly. Fused-silica capillary columns, typically used for gas chromatography, are the dielectric standoﬀs between the electrodes.
Assembly of the robots (Fig. 4.16) involves standard surface-mount technology (SMT) practices performed under a dissection microscope. Electrodes are moved and placed by a combination of a small diameter vacuum wand and tungsten micromanipulator probes. Mechanical connections and alignments are handled by a combination of geometric tolerances and UV-curable epoxy applied via a micromanipulator probe. Electrical connections are formed by silver epoxy applied via a pneumatic ﬂuid dispensing system and cured on a hot plate. A CNC-milled aluminum ﬁxture is used to keep the device in place and provide alignment aid for various components.

Figure 4.16: 3D model renders of the assembly process. (1) Pre-cut silica tubes are inserted into slots in a CNC-milled aluminum jig. (2) The ionocraft airframe is slid down the guiding posts. (3) The emitter wires are rotated out of plane and tapered guides are inserted into the silica tubes. The distance between the emitter wires and collector grid is now determined by a combination of lithography, the length of the silica tubes, and the depth of the guide slots milled into the jig. (4) Silicon “jumpers” are lowered onto guide posts on the emitter wires. These both help with alignment between adjacent emitter wires and serve as electrical connection points after application of silver epoxy.

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A Flex PCB board was designed to contain a commercial 9-axis IMU, the InvenSense MPU-9250, as well as three associated passives and bonding pads. The board’s 6mm by 6.5mm footprint allows it to be ﬁxed in place via UV-curable epoxy in a designated central region of the robot airframe without interfering with the surrounding thrusters.

Results and Discussion

Actuator Response

To measure output force, the ionocraft is mounted on an acrylic post ﬁxed directly to a Phidgets 100g Micro load cell. Multiple instruments are controlled via GPIB for synchronized force-current-voltage sweeps.
The canonical expression for electrohydrodynamic force based on an ideal 1D model together with a constant factor, β, is given in (4.1) and discussed in Section 2.2, where d is the ion drift distance and µ is the ion mobility in air (approximately 2e-4 m2/V s for N2+ in dry air). The β factor accounts for losses in the system that arise as a combination of indirect ion ﬁeld paths (loss of vertical output force to horizontal momentum transfer), ratio of plasma sheath size to drift gap, and aerodynamic drag on the collector grid,

Id F =β
µ

(4.1)

Sets of emitter wires with both 5 and 10 degree nominal tip angles (tips visible in Fig. 4.15 inset) were fabricated. Decreasing the lithographically deﬁned tip angle from 10 to 5 degrees was shown to decrease corona discharge onset voltage by about 100V without a signiﬁcant aﬀect on the IV relationship following plasma ignition (Fig. 4.17). Prior work has measured a loss factor of about 50% (β = 0.5) using similar microfabricated silicon electrodes [20]. Direct measurement of output force as a function of applied voltage and ion current (Fig. 4.17) in this work yield a β of approximately 0.8 for the 5 degree emitter tips and 0.7 for the 10 degree emitter tips.
A 1mN total output force from four 6mm x 6mm collector grids corresponds to a thrust density of about 7N/m2, a similar value to prior work despite an increased emitter wire density. It is possible that the emitter wire spacing of approximately 1.5mm is too high and should be brought to a value between 40% and 80% of the electrode gap distance (500µm) for an optimal thrust density increase, as shown in work on larger electrode gap EHD systems [30].
A high voltage ampliﬁer circuit (Fig. 4.18) was created for testing the dynamic response of the ion thrusters. First, a positive DC voltage above the corona discharge initiation is applied to the emitter electrode with the collector electrode held at ground. Next, a 2Vpp sine wave produced by a function generator at the input of the ampliﬁer is transformed by the ampliﬁer gain of 100 into a high voltage (200Vpp) signal.
The ionocraft was shown to successfully track sine wave inputs with frequency up to 10Hz (Fig. 4.19). Signiﬁcant measurement noise, with magnitude higher than the forces

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Figure 4.17: Plots showing measured current (left) and measured output force (right) of the ionocraft as a function of its input voltage. The upper horizontal line shows the current (left) and force (right) required for hovering with the IMU onboard. The lower line shows the current and force needed for takeoﬀ without the IMU. While collecting this data, all four of the thrusters were electrically connected. Tip angle refers to the nominal apex angle of the lithographic asperities on the emitter wires.
attempted to be resolved, precluded experimentation without the load cell’s custom-built data capture accessory (PhidgetBridge). The sampling frequency limitations of this accessory made experiments at frequencies above 10Hz impossible. Future work will develop a more stable testing platform for >100Hz dynamic response characterization that can resolve forces on the order of 10µN .
Tethered Flight with Onboard Sensor
Takeoﬀ while streaming attitude and acceleration data from the on-board 9-axis IMU was demonstrated (Fig. 4.20). Liftoﬀ occurred at approximately 2000V — over 20% lower than prior work which did not contain an onboard sensor package [18]. There are a total of seven external wires: two high voltage lines to the emitter wires (the two other thrusters are connected internally); power, ground, and two data wires to the IMU FlexPCB; and a separate ground connection to the airframe. A common issue in the ﬁeld of microrobotics is that the spring force of the external tethers required for power and control tends to overpower the system due to the robot’s relatively low mass and output force, preventing

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Figure 4.18: Circuit schematic of the actuator dynamic response test setup. A high voltage op-amp is used to modulate the control inputs around a DC bias point by raising and lowering the voltage of the collector grid.

movement. The external wires in this case confer a degree of stability during open-loop ﬂight that prevents an immediate failure like twisting in its own tethers, but the robot is still both unstable (high body angle oscillations) and able to return to landing on the ground when power is no longer applied. Although future work will strive to decrease the number of external tethers and therefore their contribution to body dynamics, the ﬁrst instances of controlled ﬂight will certainly be under tethered power; this demonstration of takeoﬀ despite the external tether forces is encouraging.
The open-loop ﬂight is synchronized with the streaming sensor readings during postprocessing. Takeoﬀ and landing cycles were repeated up to ﬁve times with a single robot without failure, although the IMU had to be restarted after a landing where the ionocraft had ﬂipped completely over before touching down.

Aerodynamic Drag

A miniature low-speed wind tunnel, designed using ANSYS FEA software and constructed

from a combination of laser cut and 3D printed parts, is used to characterize aerodynamic

drag on the ionocraft. The full tunnel is about 1.5 meters long, with a 10cm x 10cm x 20cm

test chamber. A manually controlled variable-speed fan is calibrated using a TSI AVM430

hot wire anemometer inserted through an inlet in the test chamber. The ionocraft is mounted

on an adjustable acrylic sting using epoxy applied to the center pad of the airframe. The

sting attaches directly to a Phidgets 100g Micro load cell.

Experimental measurements of drag force FD versus wind speed v and angle of incidence θ are ﬁt to a hyperplane, as shown in Fig. 4.21. The region of measurements collected are

v

∈ [0, 10)

(m/s)

and

φ = 1−θ

∈

[0,

π 6

)

radians.

We

model

the

drag

at

this

wind

speed

as

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Figure 4.19: The output force from an ionocraft with a 1800V DC bias applied to the emitter wires and a 200V peak-to-peak, 10Hz sine wave applied to the collector grids. The data is collected with a sampling period of 16 ms. Top: Measured output force with DC bias force (approximately 0.22mN) and weight of the ionocraft subtracted, then ﬁltered by a digital 20Hz cutoﬀ low pass ﬁlter. Bottom: A Fourier transform of the zero centered, unﬁltered strain data shows the distinct 10Hz peak.

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Figure 4.20: Open-loop, uncontrolled takeoﬀ of the ionocraft while carrying an InvenSense MPU-9250, a state of the art 9-axis IMU. The IMU is reporting accelerations and Euler angles at roughly 100Hz, the latter of which is calculated using InvenSense’s proprietary MotionFusion algorithm on-board the IMU. Each image of the ionocraft was taken at the time corresponding to the black line below it. Erratic transient response from the IMU at the time of high voltage application indicates that further electromagnetic shielding may be necessary.

being of the form

FD(v) = av2 + bv [mN ]

(4.2)

where the constants a and b are parameters of φ, resulting in the drag function FD(v, φ). Fitting the a and b to a ﬁrst order polynomial to match the common approximations sin(φ) = φ, cos(φ) = 1 − φ for 0 ≤ φ 1, we get a parametric function of the form:

FD(v, φ) = (a1φ + a2)v2 + (b1φ + b2)v [mN ]

(4.3)

Fitting with ordinary least squares returns the following parameters:

a1 = −.0558 b1 = −.0201 a2 = .1305 b2 = .6275
The drag ﬁt yields a maximum vertical (90 degree angle of incidence) airspeed of 1.26 m/s; this corresponds to a drag force of 1mN, which is equal to the maximum thrust the

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Figure 4.21: Plot of the wind tunnel drag data shown with a ﬁtted hyperplane using (4.3). The upper left diagram shows the deﬁnition of angle of incidence.
Figure 4.22: Left: A simulated ﬂight of the ionocraft over a 4 second ﬂight about a square. The square is navigated by supplying sinusoidal proﬁles as desired states to pitch and roll controllers independently, and the trajectory of its center of mass is shown in the dotted black line. Right: Control inputs and state variables for the simulated ﬂight. Note that global Z position is only for evaulating simulation performance, and is not a variable being controlled. The pitch and roll measurements have noise, but the magnitudes are substantially lower than the controlled movement.

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ionocraft is capable of producing. The measured values used to create the hyperplane are above 3 m/s due to the diﬃculty of reliably generating low speed laminar ﬂow in the wind tunnel.

Dynamics Model

The dynamics of a quadcopter are well studied and understood [2, 54]. A quadcopter’s four individually controllable thrusters each generate a force Fi resulting in a body ﬁxed-frame z-axis thrust, T , and body ﬁxed-frame torques τx, τy, and τz, as shown in (4.4). The constant c is a coupling factor between the motor forces and the τz. The parameters lx and ly are deﬁned as the distance from the thruster’s center to the body ﬁxed-frame’s center of mass in the x and y directions, respectively. We use a north-west-up axis orientation.
Because a quadcopter’s four thrusters are propeller based, and therefore generate angular momentum, the coupling factor c is non-zero. It can then be seen that the matrix in (4.4) is full rank, and therefore control of Tz, τz, τy, and τx are decoupled.

 Tz   1 1 1 1   F1 

  

τz τy

 

=

 



−c −lx

c −lx

−c lx

c   F2 

lx

 

F3

 

τx

−ly ly ly −ly

F4

(4.4)

The ionocraft model is the same as the quadcopter model, with one important exception — the ionocraft uses ion thrusters instead of propeller based thrusters (i.e., the ionocraft thrusters do not generate angular momentum) and therefore the coupling constant c is equal to 0. Accordingly, the matrix in (4.4) is not full rank and control authority of τz (i.e. yaw control) is lost.
The ionocraft thrust forces, assumed to be point forces at the corners of the robot, along with drag, are the only forces applied in the model; the tether wires are not incorporated in the dynamics. The assumption of thrust being a point force holds when the force distribution over the collector grid is uniform; in reality, the EHD force is not axisymmetric but instead expected to decrease with distance from the emitter wires (i.e., in the x direction if the wires are assumed to lie along the y axis) as some function of the device electrostatic solution.

Controller Design

Hovering and basic open loop trajectories only require data streamed from the 9-axis IMU.

To hover, the controller regulates z¨, pitch, and roll to zero. The equilibrium input for each

individual

thruster

is

Feq

=

mg 4

.

The

outputs

uz¨, uθ,

and

uφ

of

the PID

controllers

(shown

in Fig. 4.23) are used to drive the system to desired vertical acceleration, desired pitch, and

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 z¨d   θd 
φd +
−
 zˆ¨   θˆ 
φˆ

PIDz¨

PIDθ

+

PIDφ

Sensor Noise

Convert

xt Dynamics

Figure 4.23: Overall structure of the control scheme. The errors between the estimates of vertical acceleration, pitch, and roll (zˆ¨, θˆ, and φˆ, respectively) and the desired states z¨d, θd, and φd are fed through three PID controllers. The outputs of the controllers are then converted into a vector input as shown in (4.5). Not shown is a saturation block that prevents
the thrusters from trying to apply more force than the maximum value before breakdown
(approximately 0.25 mN per thruster).

desired roll, respectively, where F is the vectorized input containing all four thruster forces.

 Feq   1   −1   1 

F

=

 



Feq Feq

 

+

 



1 1

 

uz¨

+

 



−1 1

 

uθ

+

 



−1 −1

 

uφ



Feq

1

1

1

(4.5)

Each thruster has a maximum force it can provide (approximately 0.25mN); this saturation makes each thruster nominally non-linear. The PID controllers are tuned around equilibrium so that the controlled forces stay well away from saturation within tested operation.
Yaw actuation can be achieved by quick, repeated sequences of “pitch and then roll.” Simulation demonstrates this approach achieving a yaw rate of up to ±10 deg/s while still maintaining stable hover. This method comes at the cost of up to 10 cm/s X-Y drift because of the lack of simultaneous decoupled control of x¨ and y¨. Future formalization of this “pitch and roll” method with Lie brackets (as in [47]) could lead to a closed-loop nonholonomic yaw controller.

Flight Simulation
The experimental drag data and voltage to force mapping, as well as the sensor noise discussed below, are included in the simulation model. The simulation dynamics time-step is 10µs. This is suﬃcient, because if the ionocraft rolls or pitches by applying the maximum thrust that it is capable of producing (approximately 0.5 mN by ﬁring two of its thrusters simultaneously and leaving the other two oﬀ), it would change roll or pitch angles by fewer than 10−4 degrees within one simulation time-step. The measurement and hand-tuned PID

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control blocks update at 100Hz, which is the sample rate used when collecting experimental ﬂight data with the MPU-9250 9-axis IMU with the Motion√Fusion algorithm on [66]. The documented noise power from the IMU on x¨, y¨, z¨ = 300µg/ Hz. The noise power on the Euler angles is undocumented for the Digital Moti√on Processing unit. Direct measurement of the noise power of a stationary signal is 25nrad/ Hz. During the simulation, we increase the Euler angle noise power by a factor of 40x as well as increase the accelerometer noise power by a factor of 10x. These increases provide overestimates of the noise signals in order to better prepare for future controlled ﬂight of a fabricated device outside a laboratory setting.
Open loop maneuvers have been encoded to demonstrate the future potential of controllability over arbitrary shapes in the X-Y plane. The simulation results, shown in Fig. 4.22, shows a square ﬂight pattern, control input, noisy states, and true state variables. Because direct measurements of the global positions X, Y , and Z are unavailable, the global positions drift over time. The raw accelerometer data for z¨ provides a reference for maintaining altitude. However, the global Z position is only controlled by the local z¨ reading, so it does not exactly track gravity when pitch and roll are non-zero. This global Z drift is compensated for by controlling to a desired state of z¨ = .015 m/s2.
Disturbance characterization of the system is not included because the currently collected drag data does not account for resultant body torques. Without characterizing these moments, any planar disturbance will only cause drift and will not test roll or pitch stability; subsequent drift recovery is not possible with the current implementation due to the lack of global position data.
Separate simulations with variation in force produced by each thruster (e.g. from fabrication variation) at a given controller-outputted input voltage show loss of X-Y controllability above 1% variation and loss of hover functionality at 10% force variation. This is due to the hand-tuned PID controllers and could be improved with either more robust controllers or an in-line calibration method prior to takeoﬀ.
Contributions and Conclusions
Succinctly, the contributions of this work were:
• Force-voltage characterization, both static and dynamic, of the highest thrust density ionocraft to date.
• Aerodynamic drag characterization of a centimeter-scale ionocraft using a low-speed wind tunnel.
• Repeated ﬂight with streaming IMU data and individually addressable thrusters, opening the door for a feedback loop to be closed for the ﬁrst time.
• Simulated controlled ﬂight of a ionocraft in arbitrary X-Y trajectories using largely empirically derived values for performance.

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Validation of using a high voltage time varying signal in tandem with an applied DC bias above the corona discharge initiation point to modulate thrust indicates that a future low mass power and control circuit could use a similar topology to Karpelson et al [44][45]. A low mass optical ﬂow sensor similar to one fabricated in [23] could be used in conjunction with IMU data to stabilize absolute position as well as attitude. Assuming a single Flex PCB could be shared for the 9-axis IMU, control ASIC, driver circuit, and optical ﬂow sensor, a total mass budget on the order of 100mg could be expected. This should be well within the capabilities of future ionocraft designs, opening the door for controlled ﬂight of a 2cm by 2cm microrobot with only high voltage DC bias, low voltage (for ICs), and ground wires, with no external sensors.
The aerial thrust density measured in this work is still far below the theoretical maximum. Further, while increasing the number of emitter wires per thruster improved the maximum force output compared to prior work, it did not come with a large beneﬁt to thrust-to-weight ratio. Future designs should look to maximize thrust density by increasing the number of emitter tips per collector grid and optimizing the tip spacing; they should also include mechanical aﬀordances to decrease the number of required adhesive joints and additional components per emitter wire. Process development to further enhance the electrode geometric asymmetry (e.g., by creating tips with lower radii of curvature) should both decrease the required voltage for ﬂight as well as allow for operation in a higher eﬃciency regime at the cost of output force.

78
Chapter 5
A Path to Power Autonomy and Other Future Directions
I believe that the future is ﬁlled with important discoveries that will further increase the advantages of EHD while diminishing the downsides. In this section, I will point future researchers in a number of directions that I see as having great potential. Research questions to answer:
• What near-term possibilities are there for continued scaling of corona-discharge based EHD force?
• What would an autonomous ionocraft system design look like in terms of energy and mass breakdown?
• What major alternative approaches remain relatively underexplored despite their promise?
5.1 A Preface on Eﬃciency
Theory dictates, from Equations 2.17 and 2.16, that thrust eﬃciency should scale inversely with thrust in an EHD system. In terms of robot design, this represents a tradeoﬀ in necessary battery energy and power density versus necessary size to produce the required lift force. For example, at an eﬃciency of 2 mN/W, projected maximum thrust is on the order of 100 N/m2. Neglecting any mass besides the battery for this simple calculation, this would require storage with a density of at least 5 kW/kg and, for a 250 mg total robot mass, a thruster area of at least 25 square millimeters. At 10 mN/W, a reduction in electric ﬁeld from 3×106 V/m to 5×105 V/m, a 1 kW/kg power density is required; the resulting maximum thrust of 2.5 N/m2 requires 1000 square millimeters to lift 250 mg. Noting the comparisons with other mechanisms in Section 1.1, and due to the fact that thrust scales proportionally to the square of the electric ﬁeld and eﬃciency scales only linearly, it would

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seem that EHD systems make the most sense when they can take advantage of the highest possible power density storage.
The reality of current designs (e.g., those shown in Chapter 4) is that even 2 mN/W is diﬃcult to achieve in practice for an aggressively scaled ion thruster. Current designs operate in the range between 1 mN/W and 2 mN/W at takeoﬀ. The cause for this is rooted in the d/r ratio discussed in Section 2.1. Even with lithographically deﬁned silicon asperities, the drift ﬁeld outside the ionization region is relatively high following corona ignition. As the maximum breakdown ﬁeld increases between the two electrodes as a function of decreasing distance, the theoretical “minimum” thrust eﬃciency becomes even lower. Ultimately, the only path forward for corona discharge based EHD thrusters is in new emitter designs with much smaller radii of curvature. This may not actually require moving entirely away from DRIE-deﬁned processes in silicon; there are a few reports of “high” aspect ratio silicon nanopillar deﬁnition using DRIE (e.g., [11]), although the resultant structure height is probably not large enough for use with an EHD thruster that has a cathode-anode distance in the hundreds of microns. Independently, I have seen silicon wires formed post-DRIE with aspect ratios on the order of 800 (Figure 5.1). Ensuring device lifetime for structures such as these (see Section 4.2) would require careful process development.

Figure 5.1: Silicon wires remaining post-DRIE, with aspect ratios on the order of 800. It is possible these wires are a result of etching and subsequent redeposition of the oxide hard mask in this process; they demonstrate the possibility of producing structures with high enough aspect ratio and low enough tip radius for potential increase in d/r ratio of an EHD thruster.
5.2 Future Power System Design
High Voltage Circuitry
For future corona discharge based thrusters we will assume that a high voltage DC bias is applied to the common collector electrode such that corona discharge is already initiated. Operating in this manner should be more eﬃcient, as the plasma sustaining voltage is lower than the inception voltage; this indicates that energy is lost in “striking the plasma.” In

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this case, only a dynamic voltage range corresponding to the useful operating swing of the thrusters is required. For typical electrode geometries this is a range of approximately 300V. Simulation in [17] showed that controlled ﬂight is possible with a thrust modulation bandwidth of 100Hz. Suddenly, the “big, scary” question of how to control a robot using such high voltages has become much more tractable, and it turns out we can borrow from the (quickly growing) body of literature on miniature, low mass drive circuits for piezoelectric actuators.
The ﬁrst step is to generate the high voltage DC bias. Recent work on high voltage DC conversion, speciﬁcally for ion thrusters, has shown impressive power densities [96] (1.2kW/kg) with a step-up ratio of roughly 200 from an initial 200V. Their design consisted of three stages: a full-bridge resonant inverter, a high voltage transformer, and a six-stage Cockcroft-Walton voltage multiplier. Miniaturization of this design would require high voltage CMOS, a low mass transformer, and high voltage diodes. The X-Fab XDM10 process provides high voltage transistors and trench-isolated high voltage diodes (>350V breakdown), and extremely high eﬃciency DC-DC converters up to 400V have been previously demonstrated in the process [79]. Hand-wound low mass transformers have been demonstrated with a combination of laser cut steel cores and high-gauge wire [45].
Piezoelectric actuators, previously demonstrated for both ﬂying and walking microrobots, require signiﬁcant electric ﬁelds and, especially in the case of the former, high power densities. The Harvard Microrobotic Fly, for example, uses piezoelectric actuators requiring drive voltages in the range of 200-300V [44], in line with what we may expect a future ionocraft to require. Batteries and solar cells with energy densities suitable for microrobots generate output voltages below 5V, and stacking these in series in order to generate high voltage signals may not be possible due to packaging overhead and eﬃciency degradation (e.g., due to “weaklink” cells). Step-up ratios on the order of 10-100 are therefore required in most conceivable implementations. A large number of circuit topologies can deliver these ratios; selection requires speciﬁcally assessing the ability to miniaturize (both in terms of mass and eﬀects on eﬃciency) and fabricate the circuit. Promising candidates include the tapped-inductor boost converter and bidirectional ﬂyback converter. Steltz et al and Karpelson et al provide overviews of power system design choices for piezoelectric actuators [82], and for ﬂapping wing microrobots more speciﬁcally [42]. Implementations for FMAVs with experimental results are given in [44, 43, 45].

Candidate Battery and Solar Cell Technologies
A battery technology can be evaluated based on its speciﬁc energy (typically in W h/kg, or J/cc), with some caution towards ensuring that required discharge rates are feasible for the chosen chemistry and won’t signiﬁcantly degrade lifetime. A large challenge in evaluating batteries is their amenability to miniaturization; for most, it is not immediately clear how scaling will impact performance or packaging overhead percentage when looking at most papers. Thin ﬁlm batteries being developed for wearable applications share many of the

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design constraints as those for microrobots, including high (areal) energy densities, variable and often high potential discharge rates, simple fabrication, and long-term rechargability.
Flexible (i.e., thin ﬁlm) batteries with high energy densities have been demonstrated; for example, >1 Wh/kg lithium ion [48] as well as 6.98 mWh/cm2 and over 100 Wh/kg for other lithium ion (graphite and lithium cobalt oxide) batteries [69]. Some of these thin ﬁlm battery technologies lack proper current densities and discharge rates for use in ionocraft (e.g. about 100µA/cm2 1C discharge for [48]), but cutting edge batteries approach 2 mA/cm2 [69]. While the latter case presents an almost ideal candidate for ﬂying microrobots, there is a remaining challenge of fabricating small active area batteries without undue packaging overhead; the impressive performance listed is extracted from a much larger battery. Duduta et al [22] recently demonstrated a thin ﬁlm lithium-ion battery using laser micromaching techniques that achieved a 2 mAh capacity while massing only 140 mg (roughly 2 cm by 1 cm active area, about 43 Wh/kg density), with a power density on the order of 1 kW/kg. The authors note they have also tested a 0.1 mAh, 14 mg battery with similar power densities.
Carbon nanotube-based thin ﬁlm supercapacitors are an additional exciting active research topic, with demonstrations of extremely high power densities and reasonable energy densities (on the order of 50 kW/kg and 6 Wh/kg, respectively) [39]. These devices have the beneﬁt of relatively high potential discharge rates (over 1mA/cm 2 shown). Lithium-air batteries also represent a promising future direction due to extremely high theoretical energy densities [74].
We can set up a toy problem for a high level evaluation. Assume that ionocraft are deployed with the goal of ﬂying for 5 minutes before recharging. Assuming a drag-limited ﬂight speed of 5m/s this corresponds to, roughly, a maximum travel distance of 1.5 km. With a simple model for EHD eﬃciency as κ/µE, where κ is some term accounting for loss in power transmission between the battery and the propulsion system, we can derive the required energy and power densities of the battery as a function of applied electric ﬁeld. Assuming energy storage can account for only half of the total robot mass adds an additional factor of 0.5 to the eﬃciency equation. We will assume thrust is equal to Equation 2.16, with no deviation from the ideal maximum. The results are shown in Table 5.1. Note that the battery from [22] is only on the edge of feasibility for a centimeter-scale (e.g. <100 cm2) EHD ﬂier, but the battery presented in [69] could enable minutes of ﬂight depending on packaging mass overhead.

Solar Power Area Optimization
EHD represents a direct transduction of electrical power to useful mechanical work; it would be an extremely elegant solution to power the device entirely from solar energy. Wireless takeoﬀ of a ﬂapping wing centimeter-scale robot was recently demonstrated using an external 976 nm laser shining at a high voltage solar cell with 200-suns intensity [36]. It turns out that, on paper, operation at one-sun illumination is not outside the realm of possibility, although it will require progress on quite a few fronts. Multi-junction silicon solar cell arrays fabricated on SOI wafers alongside CMOS circuits have been demonstrated with eﬃciencies