基于自适应动态规划的柔性机械臂跨尺度运动控制研究

Research on Cross-Scale Motion Control of Flexible Robotic Manipulator Based on Adaptive Dynamic Programming

摘要: 本文研究了液压驱动柔性机器人操控臂系统(HDFRMS)的跨尺度运动控制问题，提出了一种基于自适应动态规划(ADP)的控制方法。本文首先推导了一个完整的三阶动力学模型，涵盖三连杆刚柔耦合操控臂、非对称四通阀控制的液压缸和液压执行器。然后，提出了一种新颖的奇异摄动解耦方法，将系统分解为三个时间尺度上的子系统：慢子系统(SSS)、第二快子系统(SFS)和第一快子系统(FFS)，分别描述操控臂的大范围运动、柔性振动和液压伺服控制。通过设计自适应动态规划轨迹跟踪控制(ADP)、鲁棒最优振动控制(ROC)和自适应滑模伺服控制(ASMC)等复合控制器，并利用李雅普诺夫稳定性理论证明了系统的稳定性。仿真结果表明，所提出的控制方法能够在无不确定性和存在不确定性的情况下，实现精确的轨迹跟踪和有效的振动抑制，且在变负载条件下展现出良好的鲁棒性和适应性。

Abstract: This paper investigates the cross-scale motion control problem of a Hydraulic-Driven Flexible Robotic Manipulator System (HDFRMS) and proposes a control methodology based on Adaptive Dynamic Programming (ADP). Initially, a comprehensive third-order dynamic model is derived, encompassing a three-link rigid-flexible coupled manipulator, asymmetric four-way valve-controlled hydraulic cylinders, and hydraulic actuators. Subsequently, a novel decoupling method based on Singular Perturbation Theory (SPT) is introduced to decompose the system into three subsystems operating on distinct timescales: the Slow Subsystem (SSS), the Second Fast Subsystem (SFS), and the First Fast Subsystem (FFS), which respectively characterize the large-scale motion of the manipulator, the flexible vibrations, and the hydraulic servo control. The stability of the system is demonstrated by designing composite controllers, including ADP-based trajectory tracking control, Robust Optimal Vibration Control (ROC), and Adaptive Sliding Mode Servo Control (ASMC), and employing Lyapunov stability theory. Simulation results indicate that the proposed control method can achieve precise trajectory tracking and effective vibration suppression under both deterministic and uncertain conditions while also exhibiting robustness and adaptability under variable payload scenarios.