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We apply nonsmooth multibody dynamics to describe the motion of a microrobot which is driven by the wireless resonant magnetic microactuator. We first analyze the robot using a simplified analytical model, which allows us to derive characteristic and nondimensional parameters that describe its dynamics. We then perform a numerical study to analyze the nonlinearities. We predict several nonintuitive phenomena, such as switching of the direction of the velocity with changing excitation frequency, and show that both erratic and controlled motions occur under specific conditions. Our numerical results are qualitatively consistent with experimental observations and indicate that previous speculations on the motion mechanism were incorrect. The modeling method is general and readily applies to other microrobots as well.