This study introduces a design of robust finite-time controllers that aims to solve the trajectory tracking of robot manipulators with full-state constraints. The control design is based on the construction of a distributed state constraint non-singular terminal sliding mode (CNTSM). The CNTSM design includes the gain self-adapting tuning method, which can ensure finite-time convergence to the sliding surface aside from the states to its corresponding reference trajectories. The implementation of the time-varying gain ensures the fulfillment of the accurate tracking for the references while the position and velocity constraints are satisfied permanently. A barrier Lyapunov function is proposed to develop the finite-time stability analysis of the designed controllers. The CNTSM realization uses the tracking error as well as its estimated derivative, which is calculated using a variant of adaptive super-twisting algorithm operating as robust differentiator. The proposed CNTSM is numerically evaluated on a two-link RM with uncertain inertia and Coriolis matrices. Simulation and experimental results evidence the efficiency of the CNTSM controller demonstrating a better tracking performance while the full-state constraints are satisfied in counterpart with the classical non-singular terminal sliding mode which is not able to keep such restrictions.

本研究介绍了一种鲁棒有限时间控制器的设计，旨在解决具有全状态约束的机器人操纵器的轨迹跟踪。控制设计基于分布式状态约束非奇异终端滑模（CNTSM）的构造。CNTSM 设计包括增益自适应调整方法，该方法可以确保除了状态到其相应的参考轨迹之外，有限时间收敛到滑动表面。时变增益的实现确保了在永久满足位置和速度约束的同时实现参考的准确跟踪。提出了一个障碍 Lyapunov 函数来开发所设计控制器的有限时间稳定性分析。CNTSM 实现使用跟踪误差及其估计导数，这是使用作为鲁棒微分器操作的自适应超扭曲算法的变体计算的。所提出的 CNTSM 在具有不确定惯性和科里奥利矩阵的两连杆 RM 上进行数值评估。仿真和实验结果证明了 CNTSM 控制器的效率表现出更好的跟踪性能，而全状态约束与不能保持这种限制的经典非奇异终端滑模相匹配。