Robust Task-Space Quadratic Programming for Kinematic-Controlled Robots

• Published in: IEEE transactions on robotics Vol. 39; no. 5; pp. 1 - 18
• Main Authors: Djeha, Mohamed, Gergondet, Pierre, Kheddar, Abderrahmane
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Closed loops; Computer Science; Feedback control; High gain; Humanoid; Kinematic-controlled robots; Kinematics; Perturbation; Quadratic programming; quadratic programming (QP) control; Robot control; Robot sensing systems; Robotics; Robots; Robust control; Robust stability; robust task-space control; set robust stability; Stability analysis; Task analysis; Task space; Torque; Kinematic-controlled robots; Set robust stability; Robust task-space control; Quadratic Programming control
• ISSN: 1552-3098; 1941-0468
• DOI: 10.1109/TRO.2023.3286069

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.