Adaptive Non-linear Centroidal MPC with Stability Guarantees for Robust Locomotion of Legged Robots

TL;DR

This paper introduces an adaptive nonlinear centroidal MPC approach with stability guarantees, enhancing robustness and stability in legged robot locomotion under disturbances and parameter uncertainties.

Contribution

It provides a systematic reformulation of centroidal MPC with stability certificates inspired by adaptive control and Lyapunov functions, applicable to humanoid and quadruped robots.

Findings

Validated on humanoid and quadruped robots demonstrating robustness.

Provided stability guarantees for the closed-loop system.

Enhanced disturbance rejection capabilities.

Abstract

Nonlinear model predictive locomotion controllers based on the reduced centroidal dynamics are nowadays ubiquitous in legged robots. These schemes, even if they assume an inherent simplification of the robot's dynamics, were shown to endow robots with a step-adjustment capability in reaction to small pushes, and, moreover, in the case of uncertain parameters - as unknown payloads - they were shown to be able to provide some practical, albeit limited, robustness. In this work, we provide rigorous certificates of their closed loop stability via a reformulation of the centroidal MPC controller. This is achieved thanks to a systematic procedure inspired by the machinery of adaptive control, together with ideas coming from Control Lyapunov functions. Our reformulation, in addition, provides robustness for a class of unmeasured constant disturbances. To demonstrate the generality of our approach, we validated our formulation on a new generation of humanoid robots - the 56.7 kg ergoCub, as well as on a commercially available 21 kg quadruped robot, Aliengo.