Global-Position Tracking Control of 3-D Bipedal Walking via Virtual Constraint Design and Multiple Lyapunov Analysis
This work addresses a safety-critical challenge in legged locomotion for robotics, offering a method to improve trajectory tracking in complex hybrid systems, though it appears incremental as it builds on existing control and analysis techniques.
The paper tackles the problem of enabling 3-D bipedal robots to accurately track desired time-varying position trajectories, termed global-position tracking, by introducing a nonlinear control approach that achieves asymptotic tracking through virtual constraint design and Lyapunov analysis, with simulations and experiments on a 20-joint robot confirming its validity.
A safety-critical measure of legged locomotion performance is a robot's ability to track its desired time-varying position trajectory in an environment, which is herein termed as "global-position tracking". This paper introduces a nonlinear control approach that achieves asymptotic global-position tracking for three-dimensional (3-D) bipedal robot walking. Designing a global-position tracking controller presents a challenging problem due to the complex hybrid robot model and the time-varying desired global-position trajectory. Towards tackling this problem, the first main contribution is the construction of impact invariance to ensure all desired trajectories respect the foot-landing impact dynamics, which is a necessary condition for realizing asymptotic tracking of hybrid walking systems. Thanks to their independence of the desired global position, these conditions can be exploited to decouple the higher-level planning of the global position and the lower-level planning of the remaining trajectories, thereby greatly alleviating the computational burden of motion planning. The second main contribution is the Lyapunov-based stability analysis of the hybrid closed-loop system, which produces sufficient conditions to guide the controller design for achieving asymptotic global-position tracking during fully actuated walking. Simulations and experiments on a 3-D bipedal robot with twenty revolute joints confirm the validity of the proposed control approach in guaranteeing accurate tracking.