Robust Task-Space Quadratic Programming for Kinematic-Controlled Robots

TL;DR

This paper introduces a robust task-space quadratic programming control method for kinematic-controlled robots, ensuring stability against disturbances and uncertainties, demonstrated through experiments on fixed-base and humanoid robots.

Contribution

It proposes a novel robust QP control formulation with integral feedback, addressing instability issues in high-gain robot control schemes, and provides formal stability proofs.

Findings

Ensures closed-loop robustness against non-modeled dynamics.

Achieves stable, fast motions in fixed-base robots.

Maintains balance in humanoid robots under perturbations.

Abstract

Task-space quadratic programming (QP) is an elegant approach for controlling robots subject to constraints. Yet, in the case of kinematic-controlled (i.e., high-gains position or velocity) robots, closed-loop QP control scheme can be prone to instability depending on how the gains related to the tasks or the constraints are chosen. In this paper, we address such instability shortcomings. First, we highlight the non-robustness of the closed-loop system against non-modeled dynamics, such as those relative to joint-dynamics, flexibilities, external perturbations, etc. Then, we propose a robust QP control formulation based on high-level integral feedback terms in the task-space including the constraints. The proposed method is formally proved to ensure closed-loop robust stability and is intended to be applied to any kinematic-controlled robots under practical assumptions. We assess our approach through experiments on a fixed-base robot performing stable fast motions, and a floating-base humanoid robot robustly reacting to perturbations to keep its balance.