Hopping with Nearly-Passive Flight Phases

The paper presents a novel method which generates hopping gaits for an articulated single leg. Inspired by human running, the flight phase is assumed to be nearly-passive. Consequently, the initial joint velocities of the flight phase can be solved by using a static optimization procedure, provided that the boundary joint angles have been picked in advance. The two hopping phases can then be dynamically optimized, with the velocity jumps of the joints predicted by a simple collision model. The direct single shooting method solves the nonlinear constrained optimization problem. Ground reaction forces and the zero-moment-point serve as constraints. Simulation results show that the proposed approach produces energy-efficient hopping gaits.