Apex height control of a two-mass robot hopping on a rigid foundation

The spring loaded inverted pendulum (SLIP) model is commonly used to describe the dynamics of hopping robots. A fundamental limitation of the SLIP model is that it fails to account for impact with the ground; this is due to the fact that the leg is modeled as a massless spring. Assuming that the ground is rigid, a two-mass model with inelastic impact is proposed for more accurate description of hopping dynamics. A control scheme is developed to converge the maximum jumping height of the center-of-mass of the robot to a desired value. The control scheme utilizes feedback linearization in continuous time and update of a control parameter in discrete time. Simulation results are first presented to show the efficacy of the control scheme. Experimental results based on a voice-coil actuator show good match with simulation results despite actuator saturation.