First-Order Continuous Adaptive Sliding Mode Control for Robot Manipulators with Finite-Time Convergence of Trajectories to Real Sliding Mode

In this paper the design, analysis and implementation of improved first-order continuous adaptive sliding mode control (CASMC) based on online estimation of the lumped time-varying uncertainties for tracking control of the robot manipulators is presented. The proposed method allows to address the main drawbacks of conventional sliding mode control: the chattering phenomenon, and the requirement for a priori knowledge of the bounds of the uncertainties, and also the chattering problem associated with adaptive discontinuous sliding mode controllers, while the robustness property of the conventional sliding mode control is preserved. Furthermore, in the previously published version of the controller [1], the estimate of robot inertia matrix is needed to realize the adaptive component of the control law. In this work, the skew-symmetry property (passivity property) of robot dynamic is used to eliminate that requirement. The global stability and robustness of the proposed controller are established in the presence of time-varying uncertainties using Lyapunov's approach and fundamentals of sliding mode theory. The robustness is achieved without knowing the bound of uncertainties. The dynamic model of a two-degrees of freedom (2-DOF) rigid robot is used for simulation study and a 2-DOF flexible-link robot is used as an experimental test-bed to evaluate the performance, and robustness of the controller. Based on the simulations and experimental results, the proposed controller performs remarkably well in terms of the tracking error convergence, estimation of lumped uncertain parameter. And it is robust against un-modeled dynamics and external disturbances.