A periodic solution for friction drive microrobots based on the iteration perturbation method

The friction drive principle, which is based on the superposition of two synchronized perpendicular vibrations at the interface of the robot and the work floor, plays a fundamental role in the locomotion of miniaturized robots. In this paper, the iteration perturbation method proposed by He is used to generate a periodic solution for this type of friction drive microrobot. The equation of motion for the system reveals a parametrically excited oscillator with discontinuity, the elastic force term for which is proportional to a signum function. The obtained solutions are in excellent agreement with those achieved from numerical integration and experiments reported in the literature. Results show that for a wide range of variation of system parameters, a phase shift near 90°between the perpendicular vibrations leads to the maximum achievable velocity of the slider. Besides, we have shown that driving frequency and the relative amplitude of vibrations are the best parameters for the control purposes of this type of microrobot.