Planning and Control of Stable Walking for a 3D Bipedal Robot

Abstract

This paper presents a time-invariant feedback controller that simultaneously regulates the ZMP (zero-moment point) position and the joint configuration of a 3D biped in order to achieve an asymptotically, periodic walking gait for a 3D bipedal robot with feet. The cyclic walking gait is composed of a successive single-support phase and an impulsive impact with full plane-contact between the feet and the ground. The biped robot has 10 DOFs (degrees of freedom) in the single-support phase and 10 actuators. In order to avoid the unexpected rotation of the supporting foot, the position of the ZMP in the horizontal plane has to be controlled. It is also desired that the feedback controller tracks a parameterized reference trajectory to achieve walking stability. We use the method of virtual constraints previously implemented for controlling point-feet bipedal robots to create a set of parameterized reference walking trajectories. By creating the hybrid zero dynamics, an orbital stability study with Poincaré map is evaluated in a reduced space. We then design a supplemental event-based feedback controller to enhance walking stability. The walking gait has an average walking speed of 0.76m/sec (or 0.72 body lengths per second) in the simulation study.