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Research Papers

Dynamic Structural and Contact Modeling for a Silicon Hexapod Microrobot

[+] Author and Article Information
Jinhong Qu

Vibration and Acoustics Laboratory,
Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: jinhongq@umich.edu

Jongsoo Choi

Vibration and Acoustics Laboratory,
Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: jongs@umich.edu

Kenn R. Oldham

Mem. ASME
Vibration and Acoustics Laboratory,
Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: oldham@umich.edu

1Corresponding author.

Manuscript received April 12, 2017; final manuscript received August 11, 2017; published online September 18, 2017. Assoc. Editor: Larry L. Howell.

J. Mechanisms Robotics 9(6), 061006 (Sep 18, 2017) (12 pages) Paper No: JMR-17-1106; doi: 10.1115/1.4037802 History: Received April 12, 2017; Revised August 11, 2017

This paper examines the dynamics of a type of silicon-based millimeter-scale hexapod, focusing on interaction between structural dynamics and ground contact forces. These microrobots, having a 5 mm × 2 mm footprint, are formed from silicon with integrated thin-film lead–zirconate–titanate (PZT) and high-aspect-ratio parylene-C polymer microactuation elements. The in-chip dynamics of the microrobots are measured when actuated with tethered electrical signal to characterize the resonant behavior of different parts of the robot and its piezoelectric actuation. Out-of-chip robot motion is then stimulated by external vibration after the robot has been detached from its silicon tethers, which removes access to external power but permits sustained translation over a surface. A dynamic model for robot and ground interaction is presented to explain robot locomotion in the vibrating field using the in-chip measurements of actuator dynamics and additional dynamic properties obtained from finite element analysis (FEA) and other design information. The model accounts for the microscale interaction between the robot and ground, for multiple resonances of the robot leg, and for rigid robot body motion of the robot chassis in five degrees-of-freedom. For each mode, the motions in vertical and lateral direction are coupled. Simulation of this dynamic model with the first three resonant modes (one predominantly lateral and two predominantly vertical) of each leg shows a good match with experimental results for the motion of the robot on a vibrating surface, and allows exploration of influence of small-scale forces such as adhesion on robot locomotion. Further predictions for future autonomous microrobot performance based on the dynamic phenomena observed are discussed.

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Figures

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Fig. 1

Photo of (left) a silicon die containing tethered hexapod microrobots; and (right) sample hexapod microrobot detached from its wafer; the coordinate system for dynamic model is also labeled; with the z-direction pointing out of plane

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Fig. 2

Side view of nominal robot foot motion when ground is present; the foot remains stationary with respect to the ground for a certain period of time when actuated downward and moves in air when actuated upward

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Fig. 3

(Left) the compliant structure of a sample robot leg with a high aspect ratio link connecting the hip and knee actuators; also shown are the COMSOL-simulated mode shapes of the first lateral mode of the leg (middle), originating in pivot about the hip actuator, and the first vertical mode of the leg (right), originating in bending of knee actuators

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Fig. 4

Photo of the experimental setup: (left) LDV measuring in-chip dynamics; (right) robot out-of-chip measurement with shaker

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Fig. 5

Resonance measurement of three different locations on the microrobot: body (pink dash line), hip (blue dotted line), and knee (black solid line) indicate mode shapes associated with the hip near 438 Hz, uniformly generated on the body near 830 Hz, and most strongly associated with the knee near 3.4 kHz

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Fig. 6

Frequency sweep results of a detached hexapod microrobot: (left) the absolute velocity of the robot body; (right) the velocity of robot body (pink dotted line), robot hip (blue dashed line), and robot knee (black solid line) relative to the tray motion

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Fig. 7

Hexapod microrobot location at (left) time = 0 s and (right) time = 1 s when the tray is externally vibrated by the shaker at 240 Hz

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Fig. 8

The relationship between shaker frequency and average robot speed; the simulations are shown as the black dashed line, and the experimental results are shown as individual red data points with error bars

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Fig. 9

The vertical motion (velocity and displacement) of robot knees measured with the LDV at different legs, with commonly observed motion patterns: (top left and top right) firm-contact pattern with constant foot–ground contact, (bottom left) partial firm-contact pattern with extended adhesion mode but eventual detachment from ground, and (bottom right) jumping pattern with long time in-air mode. The red line in the bottom right is a sample tray motion beside the measured location on the body. The shaker is actuated at 2 V (top left), 4 V(top right), 6 V (bottom left), and 8 V (bottom right), respectively.

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Fig. 10

The vertical motion of the robot knee (dashed red) and tray (solid black), measured with the LDV when the shaker is actuated with 4 V input voltage

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Fig. 11

Robot leg vertical motion simulated with the proposed dynamic model: (top left) firm-contact pattern, (top right and bottom left) partial-contact and an intermediate, semi-periodic, pattern, and (bottom right) the jumping pattern. Red dashed line in all plots is the tray motion in simulation. The shaker is actuated at 2 V (top left), 4 V (top right), 6 V (bottom left), and 8 V (bottom right), respectively.

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Fig. 12

Robot leg vertical motion simulated with the dynamic model under different hypothetical microscale forcing scenarios: (left) simulated without squeeze film damping force for neither robot leg nor body; (right) simulated without adhesion force between robot foot and ground. Robot leg motion is shown with the black solid line, and ground motion is shown with the red dashed line.

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Fig. 13

Simulated relation between robot mass and microrobot motion when actuated with PZT actuators at 1.8 kHz (first vertical resonance in simulation); Robot mass is about 0.33 mg with structure and actuators

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Fig. 14

Simulated microrobot motion when actuated with PZT actuators at different frequency around the first lateral resonance (438 Hz) with same voltage amplitude (20 V)

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