3-P(RR-RRR)SR运动冗余并联机器人动力学系统分解建模与控制

doi:10.3901/JME.2025.17.066

摘要/Abstract

摘要： 相较于常规并联机构，运动学冗余并联机器人具备更多的自由度与刚体数目，因此其动力学建模更加复杂与困难。针对3-P(RR-RRR)SR运动学冗余并联运动整体动力学模型复杂且计算量大的缺陷，提出了一种动力学系统分解建模策略。首先求解了驱动关节速度与球铰速度的支链雅可比矩阵，然后推导了支链内各构件的速度，并通过拉格朗日法建立了支链子系统动力学模型。接着推导动平台与冗余连杆的速度，求解了其与广义速度之间的雅可比矩阵，并运用虚功原理建立了动平台子系统动力学模型。之后由球铰处虚拟力，通过力雅可比映射到关节空间的方法将一个动平台子系统与三个支链子系统相关联，形成整体的动力学模型，并利用ADAMS验证模型正确性。最后基于该子系统动力学模型设计了一种计算力矩控制器，将其应用于实物样机轨迹跟踪控制并与PD控制进行对比，通过对误差数据的分析证明了该控制器有效提高了轨迹跟踪的精度与响应速度。研究结果可为该机构动力学特性的深入分析和控制策略的研究提供了参考。

关键词: 运动学冗余, 并联机构, 子系统动力学建模, 拉格朗日法, 虚功原理, 计算力矩控制

Abstract: Compared to conventional parallel mechanisms, kinematic redundant parallel mechanisms have more degrees of freedom and rigid body counts, making their dynamic modeling more complex and challenging. Addressing the complexity and computational intensity of the overall dynamic model for the 3-P(RR-RRR)SR kinematic redundant parallel robot, a subsystem dynamic modeling strategy is proposed. Firstly, the branch Jacobian matrix for the driven joint velocity and spherical joint velocity is solved. Then, the velocities of various components within the branch are derived, and a branch subsystem dynamics model is established using Lagrange’s method. Subsequently, the velocities of the moving platform and redundant connecting rod are derived, and the Jacobian matrix between them and the generalized velocities is solved. The virtual work principle is then applied to establish a dynamic model for the moving platform subsystem. After that, a method of mapping virtual forces at the spherical joints to the joint space through the force Jacobian is used to correlate one moving platform subsystem with three branch subsystems, forming an overall dynamic model. The correctness of the model is verified using ADAMS. Finally, based on this subsystem dynamics model, a computed torque controller is designed and applied to the trajectory tracking control of a physical prototype. Compared with PD control, analysis of error data demonstrates that this controller effectively improves the accuracy and response speed of trajectory tracking. The research results provide a reference for in-depth analysis of the dynamic characteristics of the mechanism and the study of control strategies.

Key words: kinematic redundancy, parallel mechanism, subsystem dynamics modeling, Lagrangian method, virtual work principle, computed torque control

中图分类号:

TD156

张海峰, 何其臻, 陈巧红, 叶伟. 3-P(RR-RRR)SR运动冗余并联机器人动力学系统分解建模与控制[J]. 机械工程学报, 2025, 61(17): 66-79.

ZHANG Haifeng, HE Qizhen, CHEN Qiaohong, YE Wei. 3-P(RR-RRR)SR Kinematic Redundant Parallel Robot Dynamics Decomposition Modeling and Control[J]. Journal of Mechanical Engineering, 2025, 61(17): 66-79.

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