Exponentially convergence for the regressor-free adaptive fuzzy impedance control of robots by gradient descent algorithm

Having the capability to estimate parametric and non-parametric uncertainties, this paper investigates a regressor-free adaptive model-reference scheme for impedance control of robotic systems interacting with an environment. Using the gradient descent algorithm for designing a fuzzy estimator makes the tune of controller’s parameters possible in different physical situations and uncertainties. Thanks to the voltage control strategy and fuzzy systems, there is no need for designers to have the knowledge of robots and actuators’ dynamics. In addition, the force feedback is not employed in the structure of control law. Using the Lyapunov-like stability analysis, not only the exponential convergence of error signal and its time derivative to zero are guaranteed in the decentralised form but also the boundedness of all signals is ensured. To confirm the efficiency of proposed control algorithm, several simulations as well as a comparison with a positioned-based impedance controller and a regressor-based adaptive impedance controller are conducted on a two-link planar robot manipulator considering a tunable desired trajectory and different stiffness of environment. Additionally, the proposed adaptive impedance controller is applied to a six degree of freedom revolute-joint manipulator to provide better evaluation.