Stability Analysis and Design of Momentum-based Controllers for Humanoid Robots

TL;DR

This paper analyzes the stability of momentum-based controllers for humanoid robots, revealing potential instabilities and proposing modifications to ensure asymptotic stability validated through simulations and experiments.

Contribution

It identifies instability issues in current momentum-based control strategies and introduces simple modifications to achieve stable zero dynamics in humanoid robots.

Findings

Unstable zero dynamics can occur with existing momentum-based controllers.

Proposed control modifications stabilize the zero dynamics.

Experimental validation confirms the effectiveness of the new control approach.

Abstract

Envisioned applications for humanoid robots call for the design of balancing and walking controllers. While promising results have been recently achieved, robust and reliable controllers are still a challenge for the control community dealing with humanoid robotics. Momentum-based strategies have proven their effectiveness for controlling humanoids balancing, but the stability analysis of these controllers is still missing. The contribution of this paper is twofold. First, we numerically show that the application of state-of-the-art momentum-based control strategies may lead to unstable zero dynamics. Secondly, we propose simple modifications to the control architecture that avoid instabilities at the zero-dynamics level. Asymptotic stability of the closed loop system is shown by means of a Lyapunov analysis on the linearized system's joint space. The theoretical results are validated with both simulations and experiments on the iCub humanoid robot.