Robust Task-Space Quadratic Programming for Kinematic-Controlled Robots

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-gain position or velocity) robots, the 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 article, we address such instability shortcomings. First, we highlight the nonrobustness of the closed-loop system against nonmodeled 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.