Adaptive faster fixed-time trajectory tracking control for manipulator

This work proposes an adaptive nonsingular fixed-time controller to boost trajectory tracking precision and velocity for the manipulator system with lumped disturbance. First, while the system state is in the sliding phase, a fixed-time sliding mode (SM) surface is designed to improve tracking speed and accuracy. Secondly, an enhanced reaching law is designed by combining inverse trigonometric functions, which can reduce chattering while increasing the convergence velocity of the SM variables. Then, the adaptive law is developed to handle the upper bound of the unknown disturbance to overcome the difficulty of establishing the upper bound of the uncertain disturbance. It is demonstrated by the Lyapunov function theorem that the SM variables and tracking errors can reach a region near the zero point at a fixed time. As a result, by comparing the fixed-time controller presented in this work to other controllers, it is clear that the proposed fixed-time controller is better than other controllers.