Dong Bo, Zhu Xinye, An Tianjiao, Jiang Hucheng, Ma Bing
Department of Control Science and Engineering, Changchun University of Technology, Changchun, 130012, Jilin, China.
Department of Control Science and Engineering, Changchun University of Technology, Changchun, 130012, Jilin, China.
Neural Netw. 2025 Jan;181:106880. doi: 10.1016/j.neunet.2024.106880. Epub 2024 Nov 6.
In this paper, for addressing the safe control problem of modular robot manipulators (MRMs) system with uncertain disturbances, an approximate optimal control scheme of nonzero-sum (NZS) differential games is proposed based on the control barrier function (CBF). The dynamic model of the manipulator system integrates joint subsystems through the utilization of joint torque feedback (JTF) technique, incorporating interconnected dynamic coupling (IDC) effects. By integrating the cost functions relevant to each player with the CBF, the evolution of system states is ensured to remain within the safe region. Subsequently, the optimal tracking control problem for the MRM system is reformulated as an NZS game involving multiple joint subsystems. Based on the adaptive dynamic programming (ADP) algorithm, a cost function approximator for solving Hamilton-Jacobi (HJ) equation using only critic neural networks (NN) is established, which promotes the feasible derivation of the approximate optimal control strategy. The Lyapunov theory is utilized to demonstrate that the tracking error is uniformly ultimately bounded (UUB). Utilizing the CBF's state constraint mechanism prevents the robot from deviating from the safe region, and the application of the NZS game approach ensures that the subsystems of the MRM reach a Nash equilibrium. The proposed control method effectively addresses the problem of safe and approximate optimal control of MRM system under uncertain disturbances. Finally, the effectiveness and superiority of the proposed method are verified through simulations and experiments.
本文针对具有不确定干扰的模块化机器人操纵器（MRM）系统的安全控制问题，基于控制障碍函数（CBF）提出了一种非零和（NZS）微分博弈的近似最优控制方案。操纵器系统的动态模型通过利用关节转矩反馈（JTF）技术集成关节子系统，纳入了相互连接的动态耦合（IDC）效应。通过将与每个参与者相关的成本函数与CBF相结合，确保系统状态的演变保持在安全区域内。随后，将MRM系统的最优跟踪控制问题重新表述为一个涉及多个关节子系统的NZS博弈。基于自适应动态规划（ADP）算法，建立了仅使用评判神经网络（NN）求解哈密顿-雅可比（HJ）方程的成本函数逼近器，这促进了近似最优控制策略的可行推导。利用李雅普诺夫理论证明跟踪误差是一致最终有界（UUB）的。利用CBF的状态约束机制防止机器人偏离安全区域，NZS博弈方法的应用确保了MRM的子系统达到纳什均衡。所提出的控制方法有效地解决了不确定干扰下MRM系统的安全和近似最优控制问题。最后，通过仿真和实验验证了所提方法的有效性和优越性。
