Nonlinear Analysis of an Indirectly Controlled Sliding Locomotion Robot

Abstract

With the purpose of achieving stable and energy efficient locomotion on the slippery road surface, a sliding locomotion robot without joint torque but indirectly controlled by an active wobbling mass is recently proposed. In this paper, we deepen the analysis of the mechanism of the indirectly controlled sliding locomotion for further optimization and generalization. First, we derive the equations of dynamics and control. Second, we estimate the natural frequency of the robot, the moving speed and energy efficiency are also evaluated with respect to forcing amplitude and frequency of the wobbling mass. Third, the Arnol'd tongue is introduced to analyze the relationship between achieving efficient locomotion and being entrained. In addition, phase oscillation and synchronization phenomenon are analyzed via hysteresis plot to further interpret the unusual shapes of the Arnol'd tongues. Finally, we analyze the entrained, however, inefficient locomotion by reconfirming the rolling constraints from the mechanical energy dissipation point of view. Our results help better understanding of the indirectly controlling mechanism, and the methods can be applied to other indirectly controlled locomotion robots.