A multiple-mode dynamic model is developed for a piezoelectrically-actuated micro-robot with multiple legs. The motion of the micro robot results from dual direction motion of piezoelectric actuators in the legs, while the complexity of micro robot locomotion is increased by impact dynamics. The dynamic model is developed to describe and predict the micro robot motion, in the presence of asymmetrical behavior due to non-ideal fabrication and variable properties of the underlying terrain. The dynamic model considers each robot leg as a continuous structure moving in two directions derived from beam theory with specific boundary condition. Robot body motion is modeled in six degrees of freedom using a rigid body approximation. Individual modes of the resulting multimode robot are treated as second order linear systems. The dynamic model is tested with a meso-scale robot prototype having a similar actuation scheme as micro-robots. In accounting for the interaction between robot and ground, the dynamic model with first two modes of each leg shows good match with experimental results for the mesoscale prototype, in terms of both magnitude and the trends of robot locomotion with respect to actuation conditions.

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