Adaptive incremental sliding mode control for a robot manipulator

An adaptive incremental sliding mode control (AISMC) scheme for a robot manipulator is presented in this paper. Firstly, an incremental backstepping (IBS) controller is designed using time-delay estimation (TDE) to reduce dependence on the mathematical model. After substituting IBS controller into the nonlinear system, a linear system w.r.t. tracking errors is obtained while TDE error is the disturbance. Then, the AISMC scheme, including a nominal controller and an SMC, is developed for the resulted linear system to improve control performance. According to the equivalent control method, the SMC in the AISMC scheme is to handle TDE error. To receive optimal control performance at the sliding manifold, an LQR controller is selected as the nominal controller. The SMC is designed based on positive semi-definite barrier function (PSDBF) since it prevents switching gains from being over/under-estimated, and two practical problems are addressed in this paper: A new PSDBF is designed and conservative (large) setting bounds affecting tracking precision and/or system stability are avoided; An improved PSDBF based SMC is developed where the PSDBF and an adaptive parameter are used simultaneously to regulate switching gains, and the system is still stable when sliding variable occasionally exceeds the predefined vicinity. Moreover, finite-time convergence property of the sliding variable is strictly analyzed. Finally, real-time experiments are conducted to verify the effectiveness of the proposed control method.