Stable walking control of a 3D biped robot with foot rotation

Abstract

SUMMARYIn order to obtain a more human-like walking and less energy consumption, ait foot rotation phaseis considered in the single support phase of a 3D biped robot, in which the stance heel lifts from the ground and the stance foot rotates about the toe. Since there is no actuation at the toe, a walking phase of the robot is composed of a fully actuated phase and an under-actuated phase. The objective of this paper is to present an asymptotically stable walking controller that integrates these two phases. To get around the under-actuation issue, a strict monotonic parameter of the robot is used to describe the reference trajectory instead of using the time parameter. The overall control law consists of a zero moment point (ZMP) controller, a swing ankle rotation controller and a partial joint angles controller. The ZMP controller guarantees that the ZMP follows the desired ZMP. The swing ankle rotation controller assures a flat-foot impact at the end of the swinging phase. Each of these controllers creates two constraints on joint accelerations. In order to determine all the desired joint accelerations from the control law, a partial joint angles controller is implemented. A word “partial” emphasizes the fact that not all the joint angles can be controlled. The outputs controlled by a partial joint angles controller are defined as a linear combination of all the joint angles. The most important question addressed in this paper is how this linear combination can be defined in order to ensure walking stability. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincaré map of the hybrid zero dynamics. Finally, simulation results validate the effectiveness of the control law even in presence of initial errors and modelling errors.