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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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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