The spring loaded inverted pendulum (SLIP) model is commonly used to describe the dynamics of hopping robots. Based on this model, the control of hopping robots has been widely investigated. A fundamental limitation of the model is that it fails to account for impact with the ground, and this is due to its single degree-of-freedom in the vertical direction. A more accurate representation of the hopping robot is proposed using a two mass model and inelastic impact with the ground. A control scheme is developed to converge the maximum jumping height of the robot to a desired value. The control scheme utilizes feedback linearization in continuous time and updates a control parameter in discrete time to achieve the control objective. Simulation results are presented to show the efficacy of the control scheme.

Bipedal robots have the potential to provide robust locomotion over uneven terrain and its dynamic stability has been shown to be analogous to that of a spring loaded inverted pendulum (SLIP). The SLIP model is fundamentally limited in its ability to accurately represent legged locomotion since it does not take into account the impulsive dynamics of foot ground interaction. In this paper we investigate the control of a four-link hopping robot based on the complete dynamics of the system. Using partial feedback linearization to control the configuration in continuous time, and discrete parameter variations the control object of apex height control of the robot is achieved. Simulation results are presented to show the efficacy of the control scheme.