Robust-Adaptive Controller Design for Robot Manipulators Using the <inline-formula> <tex-math notation="LaTeX">$\mathcal{H}_{\infty}$ </tex-math></inline-formula> Approach

Abstract

This paper proposes a model-free robust-adaptive controller for Euler-Lagrange systems with a quantitative performance analysis in terms of state-errors. The controller has only few parameters, and the procedure of finding the controller parameters is intuitive and easy to implement. The controller acts as an adaptive computed-torque controller and consists of two feedback loops: the inner loop evaluates the robot dynamics to linearize the system and the outer loop is a simple proportional derivative controller. Input-to-state stability is used to derive the control law and tune the controller parameters. Inverse-optimal control using the Hamilton-Jacobi-Isaacs equations is utilized to confirm the optimality of the controller. Robustness of the proposed controller is proved using the H∞ optimality technique. The controller starts with zero system information and adapts itself to the real system dynamics. Finally, the proposed technique is validated on a three-degree-of-freedom and a seven-degree-of-freedom robot manipulator.

Keywords

• Adaptive control
• H∞ optimal control%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H</italic>∞ optimal control
• Hamilton-Jacobi-Isaacs
• input-to-state-stability
• computed torque
• Euler-Lagrange