On Stabilization Mechanism of a Hopping Robot Utilizing Weakness of Actuator

Abstract

This paper is concerned with nonlinear analysis of a 1-d.o.f. vertical hopping robot, composed of its body, foot and a DC motor with crank mechanism. We show that its hopping motion under a constant voltage converges into a stable limit cycle, through physical experiments and numerical simulations. We then clarify this stabilization mechanism based on a simplified mathematical model, by showing that the negative torque-velocity correlation (weakness) of DC motors plays as a feedback law for stabilization. We also show that the limit cycles exhibit period-doubling bifurcation as the applied voltage increases, and the corresponding bifurcation diagram is affected by the weakness parameter of the DC motor.