Energy-preserving control of a passive one-legged running robot

Fast and energy-efficient control is an increasingly important and attractive area of research in legged locomotion. In this paper, we present a new simple controller for a planar onelegged passive running robot having a springy leg and a compliant hip joint. The most distinctive advantage of the controller over previously proposed ones is it does not require any pre-planned trajectories nor target dynamics. Instead, it utilizes exact non-linear dynamics. Our results are summarized as follows. First, we propose an energy-preserving control strategy for energy-efficient and autonomous gait generation. This strategy is successfully implemented as a new touchdown controller at the flight phase. Simulation results show that the robot can hop from a wide set of initial conditions. Moreover, the running gaits generated are found to be quasi-periodic orbits, which can be seen in Hamiltonian systems. Since the controlled running gaits exist for every admissible energy level, they have some robustness against disturbances. Next, it is shown that an adaptive control of the touchdown angle, which is similar to a delayed feedback controller for a chaotic system, can asymptotically stabilize these quasi-periodic gaits to the periodic ones of the desired period, with some limitations. In particular, for one-periodic gait, by using some additional adaptive controllers, the robot eventually hops without any control inputs. Since our energy-preserving strategy is clear and implementation of the controller is straightforward, we believe it can be easily applied to a wide class of legged mechanisms.