对称并联运动机构的无模型交叉耦合控制

doi:10.3969/j.issn.1004-132X.2025.08.005

摘要/Abstract

摘要：

并联机构驱动关节间的动力学耦合效应是影响其轨迹跟踪性能的关键难题，现有并联平台的多电机协同控制方法常常不考虑机构关节间的相互耦合关系及其关节协同关系，影响了机构末端的运动精度。针对上述问题，提出一种提高机构任务空间跟踪精度的无模型交叉耦合控制方法。通过引入表示相邻电机运动关系的电机协同误差，采用时延估计（TDE）技术间接地进行机构动力学闭环控制，解决动力学模型不确性问题；同时采用Lyapunov定理分析证明所提方法的稳定性，并在对称并联运动机构上进行所提方法的实验验证。结果表明，相比现有的时延控制（TDC）方法，所提方法可以通过并联机构的高效位置跟踪和稳定操作有效减小其末端运动跟踪误差。

关键词: 对称并联运动机构, 无模型控制器, 协同控制, 时延估计, 轨迹跟踪

Abstract:

The dynamic coupling effectiveness between the driving joints of parallel mechanisms was a key challenge affecting their trajectory tracking performance. Existing multi-motor cooperative control methods for parallel platforms often ignored the inter-joint coupling relationships and their coordination， which affected the motion accuracy of the end-effector. To address this issue， a model-free cross-coupling control method was proposed to improve the tracking accuracy of the mechanisms in the task space. By introducing the motor cooperative erros that represented the relationship between the motions of neighboring motors，the method employed the TDE technique to indirectly perform the closed-loop control of the mechanism dynamics， solving the uncertainty problems of the dynamics model. Additionally， the stability of the proposed method was analyzed and proven using the Lyapunov theorem， and experimental validations were performed on a symmetric parallel kinematic mechanism. The results show that， compared to the existing TDC method， the proposed method may effectively reduce the end-effector’s motion tracking errors through efficient position tracking and stable operations of the parallel mechanisms.

Key words: symmetric parallel kinematic mechanism, model-free controller, cooperative control, time delay estimation（TDE）, trajectory tracking

中图分类号:

TH112

周志伟, 高健, 张揽宇. 对称并联运动机构的无模型交叉耦合控制[J]. 中国机械工程, 2025, 36(8): 1691-1699.

Zhiwei ZHOU, Jian GAO, Lanyu ZHANG. A Model-free Cross-coupling Control Method for Parallel Kinematic Mechanisms with Symmetric Structure[J]. China Mechanical Engineering, 2025, 36(8): 1691-1699.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2025.08.005

https://www.cmemo.org.cn/CN/Y2025/V36/I8/1691

图/表 12

图1 对称并联运动机构的结构

Fig. 1 Structural of a symmetric parallel motion mechanism

图2 对称并联运动机构的运动学模型

Fig. 2 Kinematic model of a symmetric parallel motion mechanism

图3 所提无模型交叉耦合控制方法的控制框图

Fig. 3 Control diagram of the proposed model-free cross-coupling control method

图4 对称并联运动机构的实验系统

Fig.4 Experimental system of a symmetric parallel motion mechanism

图5 X轴、Z轴和B轴的期望轨迹

Fig.5 Desired trajectories for the X， Z and B axis

图6 所提方法和TDC在关节空间的跟踪误差

Fig.6 Tracking error in joint space with the proposed method and TDC

图7 所提方法和TDC在关节空间的协同误差

Fig.7 Cooperative error in joint space with the proposed method and TDC

图8 所提方法和TDC在任务空间的跟踪误差

Fig.8 Tracking error in task space with the proposed method and TDC

表1 所提方法和TDC在关节空间的跟踪误差、协同误差比较

Tab. 1 Comparison of tracking error and cooperative error in joint space between the proposed method and TDC

		RMSE			IAE
		q₁	q₂	q₃	q₁	q₂	q₃
跟踪误差/μm	TDC	7.49	4.91	2.41	28.21	39.25	13.35
	所提方法	6.42	3.69	1.61	24.61	29.85	9.94
	减幅/%	14.3	24.8	33.2	12.8	23.9	25.5
协同误差/μm	TDC	9.31	5.65	8.07	62.54	45.55	37.82
	所提方法	7.57	4.21	6.13	49.16	34.54	28.46
	减幅/%	18.7	25.5	23.9	21.4	24.2	24.7

表2 所提方法和TDC在任务空间的跟踪误差比较

Tab.2 Comparison of tracking error in task space between the proposed method and TDC

控制方案	RMSE			IAE
控制方案	X/μm	Z/μm	B/μrad	X/μm	Z/μm	B/mrad
TDC	4.91	6.98	89.61	39.25	32.75	0.61
所提方法	3.69	4.51	72.88	29.85	20.95	0.47
减幅/%	24.8	35.4	18.7	23.9	36.1	21.3

图9 并联机构各电机的伺服指令

Fig.9 Servo commands for each motor of the parallel mechanism

图10 并联机构X和Z轴的跟踪误差

Fig.10 Tracking errors of X and Z axis of the parallel mechanism

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