Prescribed-time prescribed-performance backstepping sliding mode control of robotic manipulator with input-output constraints

To resolve the issues related to low control accuracy and poor disturbance rejection in robotic manipulators, which are caused by input-output constraints and unknown external disturbances, a novel prescribed-time prescribed-performance backstepping sliding mode (PPBSM) control method is designed. To overcome the dependency of conventional prescribed-performance control (PPC) on the initial values of constrained variables, an asymmetric finite-time performance function (AFTPF) is designed. Furthermore, to avoid the complexity of traditional logarithmic transformations, an asymmetric time-varying tangent-type barrier Lyapunov function (TTBLF) is constructed to handle the asymmetric output constraints directly, significantly simplifying the controller design process. By integrating the backstepping sliding mode control strategy with prescribed-time control (PTC), a globally prescribed-time convergent controller is proposed to make certain that the trajectory tracking error strictly converges to zero within a prescribed time frame. To counteract the undesirable effects of actuator saturation, a novel prescribed-time saturation compensator (PTSC) is designed, guaranteeing that the auxiliary variable converges to zero within a prescribed time interval, thereby preventing long-term impacts on tracking performance. Meanwhile, a prescribed-time disturbance observer (PTDO) is introduced to achieve accurate disturbance estimation within a predetermined time, thereby enhancing system robustness. The stability of the proposed method is analyzed using Lyapunov stability theory, and its efficiency and superiority are verified through numerical simulations.