Synchronization Sliding Mode Control of Closed-Kinematic Chain Robot Manipulators with Time-Delay Estimation

Control of closed-kinematic chain manipulators (CKCM) with uncertain dynamics is a tremendous challenge due to the synchronization among actual joints and end-effectors, limited workspace, and nonexistent closed-form solutions of forward kinematics. This paper proposes a synchronization control scheme based on the concept of sliding mode control (SMC) developed for CKCMs called nonsingular fast terminal sliding mode control (NFTSMC) in conjunction with the time-delay estimation (TDE) method to address the above issues. First, the cross-coupling error is derived by combining position errors and synchronization errors to achieve the synchronization goal and then used to form a sliding mode surface of the NFTSMC. After that, a control law is developed based on the sliding mode surface to ensure faster asymptotic convergence of the errors of both position and synchronization of the CKCMs in a finite and minimal time. Then, the TDE control scheme with no prior knowledge of manipulator dynamics is employed to estimate the unknown dynamics and disturbances and thereby reject the effects of chattering caused by the NFTSMC. Lyapunov stability theorem is employed to show that the overall system controlled by the proposed control scheme achieves asymptotic convergence of errors and system stability. The performance of the proposed control is assessed by computer simulation on a 2 degrees-of-freedom (DOF) planar CKCM manipulator and simulation results are presented and discussed.