Asymptotic Stabilization of Aperiodic Trajectories of a Hybrid-Linear Inverted Pendulum Walking on a Vertically Moving Surface

This paper presents the analysis and stabilization of a hybrid-linear inverted pendulum (H-LIP) model that describes the essential robot dynamics associated with legged locomotion on a dynamic rigid surface (DRS) with a general vertical motion. The H-LIP model is analytically derived by explicitly capturing the discrete-time foot placement and the continuous-phase dynamics associated with DRS locomotion, and by considering aperiodic DRS motions and variable H-LIP continuous-phase durations. The closed-loop tracking error dynamics of the H-LIP model is then established under a discrete-time feedback footstep control law. The stability of the closed-loop H-LIP error dynamics is analyzed to construct sufficient conditions on the control gains for ensuring the asymptotic error convergence. Simulation results of the proposed H-LIP walking on a vertically moving DRS confirm the proposed control law stabilizes the H-LIP model under various vertical, aperiodic DRS motion profiles and variable H-LIP step durations.