Exponential Stabilization of Fully Actuated Planar Bipedal Robotic Walking with Global Position Tracking Capabilities

Abstract

This paper focuses on the development of a model-based feedback controller to realize high versatility of fully actuated planar bipedal robotic walking. To conveniently define both symmetric and asymmetric walking patterns, we propose to use the left and the right legs for gait characterization. In addition to walking pattern tracking error, a biped's position tracking error in Cartesian space is included in the output function in order to enable high-level task planning and control such as multi-agent coordination. A feedback controller based on input-output linearization and proportional-derivative control is then synthesized to realize exponential tracking of the desired walking pattern as well as the desired global position trajectory. Sufficient stability conditions of the hybrid timevarying closed-loop system are developed based on the construction of multiple Lyapunov functions. In motion planning, a new method of walking pattern design is introduced, which decouples the planning of global motion and walking pattern. Finally, simulation results on a fully actuated planar biped show the effectiveness of the proposed walking strategy.