Cruz-Ortiz David, Chairez Isaac, Poznyak Alexander
Department of Bioengineering, UPIBI-Instituto Politécnico Nacional, Av. Acueducto 550, 07340, Mexico City, Mexico.
Department of Bioprocesses, UPIBI-Instituto Politécnico Nacional, Av. Acueducto 550, 07340, Mexico City, Mexico; Tecnologico de Monterrey, School of Engineering and Sciences, Campus Guadalajara, Mexico.
ISA Trans. 2022 Aug;127:273-282. doi: 10.1016/j.isatra.2021.08.023. Epub 2021 Aug 25.
This study aims to propose an adaptive state-dependent gain finite-time convergent controller (using the fundamentals of the sliding mode theory) that solves the trajectory tracking for a class of state constraint master-slave robotic system (M-SRS) formed by two manipulators with the same number of articulations. The control design considers the effect of state constraints by implementing a state dependent adaptive gain. A Lyapunov-stability analysis leads to design the gain variation laws yielding proving the finite-time convergence of the sliding surface as well as the asymptotic convergence of the tracking error. The state constraints of the slave system motivate the characterization of the convergence-time as a function of the bounded uncertainties affecting the M-SRS dynamics. The forward-complete setting of the M-SRS justified the application of a robust and exact differentiator which estimated the articulation velocities for the slave robot. The estimated velocities are used as part of the realization of the output feedback controller. Numerical simulations demonstrate that the proposed control scheme provides a smaller quadratic norm of the tracking error compared with the obtained with other controllers (proportional-derivative and conventional sliding modes). The proposed control approach satisfies the state constraints while the sliding manifold converges to the origin in finite-time as justified by the theoretical stability analysis.
本研究旨在提出一种自适应状态依赖增益有限时间收敛控制器（利用滑模理论的基本原理），该控制器用于解决一类由具有相同关节数的两个机械手组成的状态约束主从机器人系统（M-SRS）的轨迹跟踪问题。控制设计通过实现状态依赖自适应增益来考虑状态约束的影响。李雅普诺夫稳定性分析导致设计增益变化规律，从而证明滑模面的有限时间收敛以及跟踪误差的渐近收敛。从系统的状态约束促使将收敛时间表征为影响M-SRS动力学的有界不确定性的函数。M-SRS的前向完备设置证明了应用鲁棒且精确的微分器来估计从机器人的关节速度是合理的。估计的速度用作输出反馈控制器实现的一部分。数值模拟表明，与其他控制器（比例微分和传统滑模）相比，所提出的控制方案提供了更小的跟踪误差二次范数。理论稳定性分析证明，所提出的控制方法满足状态约束，同时滑模流形在有限时间内收敛到原点。
