Global-Position Tracking Control of 3-D Bipedal Walking via Virtual Constraint Design and Multiple Lyapunov Analysis

TL;DR

This paper presents a nonlinear control method for 3-D bipedal robots that ensures accurate global-position tracking during walking by combining impact invariance and Lyapunov stability analysis, validated through simulations and experiments.

Contribution

It introduces impact invariance conditions for hybrid robot models and a Lyapunov-based stability analysis for global-position tracking control, addressing complex hybrid dynamics and planning challenges.

Findings

Successful asymptotic global-position tracking demonstrated in simulations.

Experimental validation confirms the effectiveness of the control approach.

Decoupling of planning and control reduces computational complexity.

Abstract

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.