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

Envisioned applications for humanoid robots require the presence of balancing and walking controllers. Whilepromising results have been achieved recently, robust and reliable controllers are still a challenge for the control community. State-of-the-art balancing controllers are based on the control of the robot momentum, but the stability analysis of these controllers is still missing. The contribution of this paper is twofold. We first 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. The theoretical results are validated with both simulations and experiments on the iCub humanoid robot.