Extremum Seeking-Based Adaptive Sliding Mode Control with Sliding Perturbation Observer for Robot Manipulators

This paper proposed an adaptive robust sliding mode control (SMC) with a nonlinear sliding perturbation observer (SPO) for robot manipulators. SPO estimates the perturbation (nonlinearities, uncertainties, and disturbances) with minimal system information and enhances the controller performance. The estimation is mainly dependent on the selection of SMCSPO gain, and if not tuned well, it might result in increased error dynamics of the system. Therefore, minimizing the error dynamics by improving the estimation is the primary goal of this research. In this regard, the current study accomplishes adaptation of controller gain in real-time by using an optimization technique called extremum seeking (ES). The quality adaptation is controlled with the help of a cost function. Based on the Lyapunov-based stability analysis of SMCSPO, the cost function consisting of the estimation error of the observer and error dynamics is proposed. The unique cost function now guarantees the tracking performance within the defined error tolerance. The effectiveness of the proposed algorithm is illustrated and validated in simulation and experiments. It is shown that the adaptation based on ES with the proposed cost function converges to the optimal control gain enabling the reduced estimation error and error dynamics with enhanced tracking performance.