Continuous cyclic stepping on 3D point-foot biped robots via constant time to velocity reversal

This paper presents a control scheme for ensuring that a 3D, under-actuated, point-foot biped robot remains balanced while walking. It achieves this by observing the center of mass (COM) position error relative to a reference path and re-planning a new reference trajectory to remove this error at every step. The Prismatic Inverted Pendulum Model (PIPM) is used to simplify behavioral analysis of the robot. We use phase space techniques to plan the COM trajectories and foot placement. While obtaining a stable path using this simplified model is easy, when applied to a real robot, there will usually be deviation from the expected path due to modeling inaccuracies. Although fully-actuated robots can reduce the deviation with relatively simple feedback control loops, when working with under-actuated robots, it is challenging to design such a feedback control loop. Our approach is based on continuous re-planning. By planning the path of the next step based on the observed initial error, we can find the proper landing location of each step. For each step we allocate sufficient time to avoid disturbances from the moment induced by the moving leg, which is not modeled in the PIPM. Our control scheme relies on the PIPM instead of the Linear Inverted Pendulum Model (LIPM) to enable non-planar COM motion, which is essential for rough terrain locomotion. We show simulation results that include full multi-body dynamics, friction, and ground reaction forces.