Trajectory-Tracking Control for Manipulators Based on Fuzzy Equivalence and a Terminal Sliding Mode

To suppress the chattering of manipulators under heavy-load operations, a control method called fuzzy equivalence & terminal sliding mode (FETSM) was applied to the trajectory tracking of motion curves for manipulators. Based on the switching term of the equivalent sliding mode (ESM), a fuzzy parameter matrix processed by the simple fuzzy rules was introduced, and the fuzzy switching term was obtained. By summing the fuzzy switching term and the equivalent term of the equivalence and a terminal sliding mode (ETSM), the control law of the FETSM for manipulators was obtained. On this basis, the stability of the system was analysed and the finite arrival time of it was deduced. On the premise of ensuring the stability of the system, the fuzzy rules and membership functions were designed for the fuzzy constants in the fuzzy switching term. Simulation tests show that the proposed FETSM can ensure sufficient trajectory-tracking precision, error convergence speed, and robustness. Compared with the ETSM, the proposed FETSM can reduce the chattering time by 94.75 % on average; compared with the proportion-integral-differential (PID) control method, the maximum chattering amplitude by the FETSM can be reduced by at least 99.21 %. Thus, the proposed FETSM is suitable for those manipulators under heavy-load operations.