Robust Regressor-Free Control of Rigid Robots Using Function Approximations

Abstract

This paper develops a novel regressor-free robust controller for rigid robots whose dynamics can be described using the Euler–Lagrange equations of motion. The function approximation technique (FAT) is used to represent the robot’s inertia matrix, the Coriolis matrix, and the gravity vector as finite linear combinations of orthonormal basis functions. The proposed controller establishes a robust FAT control framework that uses a fixed control structure. The control objectives are to track reference trajectories in worst case scenarios where the robot dynamics are too costly to develop or otherwise unavailable. Detailed stability analysis via Lyapunov functions, the passivity property, and continuous switching laws shows uniform ultimate boundedness of the closed-loop dynamics. The simulation results of a three-degree-of-freedom (DOF) robot when the robot parameters are perturbed from their nominal values show good robustness of the proposed controller when compared with some well-established control methods. We also demonstrate success in the real-time experimental implementation of the proposed controller, which validates practicality for real-world robotic applications.