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.

翻译：任务空间二次规划（QP）是一种优雅的约束机器人控制方法。然而，对于运动学控制（即高增益位置或速度）机器人，闭环QP控制方案的稳定性可能取决于任务或约束相关增益的选择。本文针对此类不稳定问题展开研究。首先，我们揭示了闭环系统对未建模动态（如关节动力学、柔顺性、外部扰动等）的非鲁棒性。随后，提出一种基于任务空间（含约束）高层积分反馈项的鲁棒QP控制公式。理论上严格证明了该方法可确保闭环鲁棒稳定性，并适用于实际假设下的任意运动学控制机器人。通过固定基座机器人的稳定快速运动实验及浮动基座仿人机器人在扰动下保持平衡的鲁棒反应实验，验证了所提方法的有效性。