Improved Barrier Function With Adjustable Parameter-Based Tracking Control for Robot Under Position Constraints

An improved time-variant asymmetric integral barrier function with adjustable parameters is constructed for the first time in this study. The presented barrier function, which is constructed by designing an integral upper limit function, can be used in the constraint issues of nonlinear systems. With the aid of the adjustable parameters in the barrier function, the control performance of the system can be improved by only changing the adjustment parameters when fixing the control parameters of the controller. Then, the tracking controller is developed by using the presented barrier function with adjustable parameters to solve the position constraint of the robot with n-degrees. Additionally, a disturbance observer is designed to enhance the robustness of the system. We prove that under the presented controller, the robotic system’s error signals can trend to zero asymptotically and the position constraint boundary is not broken at all time with the help of the proposed Theorem 1 and Lyapunov analysis. In the end, the effectiveness of the presented improved barrier function with adjustable parameters in handling state constraints is clarified by completing multiple simulation cases.