Velocity Decomposition-Enhanced Control for Point and Curved-Foot Planar Bipeds Experiencing Velocity Disturbances

Abstract

This paper extends the use of velocity decomposition of underactuated mechanical systems to the design of an enhanced hybrid zero dynamics (HZD)-based controller for biped robots. To reject velocity disturbances in the unactuated degree-of-freedom, a velocity decomposition-enhanced controller implements torso and leg offsets that are proportional to the error in the time derivative of the unactuated velocity. The offsets are layered on top of an HZD-based controller to preserve simplicity of implementation. Simulation results with a point-foot, three-link planar biped show that the proposed method has nearly identical performance to transverse linearization feedback control and outperforms conventional HZD-based control. Curved feet are implemented in simulation and show that the proposed control method is valid for both point-foot and curved-foot planar bipeds. Performance of each controller is assessed by (1) the magnitude of the disturbance it can reject by numerically computing the basin of attraction, (2) the speed of return to nominal step velocity following a disturbance at every point of the gait cycle, and (3) the energetic efficiency, which is measured via the specific cost of transport. Several gaits are analyzed to demonstrate that the observed trends are consistent across different walking speeds.