Robust-Adaptive Controller Design for Robot Manipulators Using the $\mathcal{H}_{\infty}$ Approach

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 $\mathcal {H}_{\infty }$ 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.