A higher order partial feedback linearization based method for controlling an underactuated hopping robot with a compliant leg

This paper considers control techniques for a planar model of an underactuated hopping robot. Our focus is on tracking trajectories for center of body and body angle, given a single point of support on the ground, with the goals of having stable and robust gaits and of switching among reference trajectories to achieve variable stride lengths on potentially rough terrain. Having a control framework capable of generating and tracking feasible body movements for an underactuated compliant hopper in the presence of ground collisions and uneven terrain is a challenging problem. In this work we provide a robust solution by extending partial feedback linearization (PFL) techniques. We investigate the problem of having a passive spring element in the leg and attempting partial feedback linearization based control, and show that while this cannot be achieved for instantaneous control of the CoM accelerations, it is possible to linearize the instantaneous CoM jerk and develop suitable control laws.