Simulation of a one-legged hopping robot with phase plane stability

Abstract

This paper presents numerical simulation of a Spring-loaded Inverted Pendulum (SLIP) for analyzing the stability of robot hopping. In general, the SLIP is extensively used when the most simplified model is considered for a running animal or robot. It is because the conceptual model captures the essential hopping behavior in the sagittal plane. In the case of this paper, the conceptual model is adopted for the stability study for a robotic hopping machine. Due to the dynamical complexity of the hopping machine, the most simplified model is desired. Furthermore, the equations of motion are not integrable and analytical solutions cannot be obtained under the dynamical condition that the robot's leg is in contact with the ground. To avoid these mathematical problems, therefore, numerical simulation is performed. The phase plane and space plots of the vertical position of the SLIP are obtained using simulation results, and the stability of robot hopping is discussed in the context of the limit cycle.