Hybrid Lyapunov-based feedback stabilization of bipedal locomotion based on reference spreading

TL;DR

This paper introduces a hybrid Lyapunov-based feedback control method for bipedal robot walking, using a novel model that triggers foot switches based on the center of mass, enhancing stability and eliminating pre-set footstep timings.

Contribution

It develops a hybrid model with reference spreading, stabilizes the error dynamics with convex optimization, and provides stability proofs and practical simulation results.

Findings

Local asymptotic stability of the tracking error.

Certified basin of attraction estimate.

Superior performance compared to standard model predictive control.

Abstract

We propose a hybrid formulation of the linear inverted pendulum model for bipedal locomotion, where the foot switches are triggered based on the center of mass position, removing the need for pre-defined footstep timings. Using a concept similar to reference spreading, we define nontrivial tracking error coordinates induced by our hybrid model. These coordinates enjoy desirable linear flow dynamics and rather elegant jump dynamics perturbed by a suitable extended class ${\mathcal K}_\infty$ function of the position error. We stabilize this hybrid error dynamics using a saturated feedback controller, selecting its gains by solving a convex optimization problem. We prove local asymptotic stability of the tracking error and provide a certified estimate of the basin of attraction, comparing it with a numerical estimate obtained from the integration of the closed-loop dynamics. Simulations on a full-body model of a real robot show the practical applicability of the proposed framework and its advantages with respect to a standard model predictive control formulation.