Hybrid Trajectory Tracking for a Hopping Robotic Leg

Reference-spreading based trajectory tracking is a recently introduced control strategy for hybrid systems with state-triggered jumps that allows to handle the time mismatch between nominal and closed-loop impact times. In this paper, we demonstrate that the approach can handle even the change in state dimension corresponding to, e.g., the activation of a unilateral contact constraint occurring when dealing with mechanical systems experiencing inelastic impacts. We demonstrate the effectiveness of the approach by means of simulations, addressing a trajectory tracking problem for a two-link robotic leg performing a hopping motion. The robot leg is modeled as a hybrid system possessing two different dynamic phases (stance and flight) with different state dimensions. Robustness of the approach, in particular to inexact measurement of robot height with respect to the ground, is also discussed.