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Research Papers

Modeling Legged Microrobot Locomotion Based on Contact Dynamics and Vibration in Multiple Modes and Axes

[+] 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

Clark B. Teeple

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

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 10, 2016; final manuscript received January 30, 2017; published online April 24, 2017. Assoc. Editor: Jeffrey F. Rhoads.

J. Vib. Acoust 139(3), 031013 (Apr 24, 2017) (10 pages) Paper No: VIB-16-1498; doi: 10.1115/1.4035959 History: Received October 10, 2016; Revised January 30, 2017

A dynamic model is developed for small-scale robots with multiple high-frequency actuated compliant elastic legs and a rigid body. The motion of the small-scale robots results from dual-direction motion of piezoelectric actuators attached to the legs, with impact dynamics increasing robot locomotion complexity. A dynamic model is developed to describe the small-scale robot motion in the presence of variable properties of the underlying terrain. The dynamic model is derived from beam theory with appropriate boundary and loading conditions and considers each robot leg as a continuous structure moving in two directions. Robot body motion is modeled in up to five degrees-of-freedom (DOF) using a rigid body approximation for the central robot chassis. Individual modes of the resulting multimode robot are treated as second-order linear systems. The dynamic model is tested with two different centimeter-scale robot prototypes having an analogous actuation scheme to millimeter-scale microrobots. In accounting for the interaction between the robot and ground, a dynamic model using the first two modes of each leg shows good agreement with experimental results for the centimeter-scale prototypes, in terms of both magnitude and the trends in robot locomotion with respect to actuation conditions.

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References

Figures

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Fig. 1

Schematic of a generic microrobot with 2n elastic legs connected to a rigid body. The motion of each foot in the y- and z-directions is modeled by two separate mass–spring–damper systems. (Color figure can be viewed online)

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Fig. 2

Photo of (a) a silicon micromachined millimeter-scale microwalking robot and (b) legs detail of the microrobot [11] (Color figure can be viewed online)

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Fig. 3

Photograph of both centimeter-scale walking robot prototypes with schematics of leg construction for each. The 80 mm prototype (top) uses a single-beam leg design with a misaligned PZT actuator, and the 30 mm prototype (bottom) uses a double-beam leg design with a PZT actuator on one beam and the other beam left unactuated. (Color figure can be viewed online)

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Fig. 4

Finite element analysis (FEA) illustration of leg displacement in Y- and Z-direction of 30 mm centimeter-scale prototype (bottom) and 80 mm centimeter-scale prototype (top) (Color figure can be viewed online)

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Fig. 5

Frequency response of 80 mm robot body (solid line) and two legs (dashed lines) with different actuation phases under same boundary conditions, without ground contact (Color figure can be viewed online)

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Fig. 6

Sample experimental (black solid line) and simulated (pink dash line) time response of the 80 mm robot prototype vertical leg motion at different actuation voltages (20/30/40 V) (Color figure can be viewed online)

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Fig. 7

Vertical body motion of the 30 mm prototype actuated with a 1400 Hz square wave with 15 V amplitude on a wood surface: measurement (lower) and simulation (upper)

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Fig. 8

Fast Fourier transform of vertical body motion of the 30 mm prototype (1400 Hz square wave, 15 V amplitude, wood surface): measurement (black solid line) and simulation (red dotted line) show similar distributions of frequency content, with large body “bouncing” motion at lower frequency than leg actuation (Color figure can be viewed online)

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Fig. 9

The relationship between actuation frequency and average robot velocity (80 mm robot, wood surface, 30 V actuation amplitude); black solid line is the measurement and red dash line is simulation. The average robot velocity was measured by recording videos of the robot's motion, tracking the position of the robot in each frame, and then finding the average numerical derivative between frames. Supplementary Video S1, which is available under the “Supplemental Materials” tab on the ASME Digital Collection, shows a representative sample of robot walking and subsequent velocity measurements for both prototypes. (Color figure can be viewed online).

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Fig. 10

The relationship between actuation voltage and average robot velocity of large robot prototype (80 mm robot, metal surface, 140 Hz actuation frequency); black solid line is the measurement, red dashed line is the simulation with multiple modes, and lowest blue dotted line is the simulation with first resonance only (Color figure can be viewed online)

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Fig. 11

The relationship between payload mass ratio and average robot velocity at 130 Hz, 30 V actuation on the wood surface; black dash line is the measurement, red solid line is the simulation with six legs under nominal gravity load, and lowest blue dotted line is the simulation with four legs under nominal gravity load (Color figure can be viewed online)

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Fig. 12

Simulated relationship between the ratio of y- and z-direction motion on average robot velocity (80 mm robot, 140 Hz actuation frequency, metal surface); average ratio is 10 from measurement (Color figure can be viewed online)

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Fig. 13

Simulated relationship between coefficient of friction (CoF), coefficient of restitution (CoR), and average robot velocity (80 mm robot, 120 Hz); experimentally validated coefficient range is indicated (Color figure can be viewed online)

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