绳驱连续型机器人准静态建模与路径跟踪研究

张轲; 张树翠; 赵佳源; 张欣刚; 姚文莉; 王贵飞

doi:10.21656/1000-0887.460093

绳驱连续型机器人准静态建模与路径跟踪研究

doi: 10.21656/1000-0887.460093

张轲^{1, 2,},
张树翠^1, ,,
赵佳源¹,
张欣刚¹,
姚文莉¹,
王贵飞¹

1.
青岛理工大学理学院，山东青岛 266525
2.
中通客车股份有限公司，山东聊城 252000

基金项目:

国家自然科学基金 12202224

国家自然科学基金 12272197

山东省自然科学基金 ZR2022MA066

山东省自然科学基金 ZR2025MS76

山东省自然科学基金 ZR2025MS13

详细信息

作者简介:
张轲(1998—)，男，硕士生(E-mail: zhangke6011@163.com)

通讯作者:
张树翠(1986—)，女，副教授，硕士生导师(通信作者. E-mail: zhangshucui@qut.edu.cn)

中图分类号: O313.7
计量
- 文章访问数: 39
- HTML全文浏览量: 10
- PDF下载量: 8
- 被引次数: 0
出版历程
- 收稿日期: 2025-05-09
- 修回日期: 2025-10-11
- 刊出日期: 2026-07-01

Study on Quasi-Static Modeling and Path Tracking of Cable-Driven Continuum Robots

1.
School of Science, Qingdao University of Technology, Qingdao, Shandong 266525, P.R. China
2.
Zhongtong Bus Holding Co., Ltd., Liaocheng, Shandong 252000, P.R. China

摘要

摘要: 绳-孔滑动摩擦造成的驱动迟滞效应是制约绳驱连续型机器人多功能、多领域应用的关键难题之一. 在轨迹跟踪过程中，驱动绳索经历密集的收、放绳切换，滑动摩擦力在过线孔内频繁换向，导致柔性臂的当前构型因驱动历史的不同而产生明显差异. 本文基于多柔体系统动力学理论开展绳驱连续型机器人的准静态建模，构建了刚、柔运动解耦的节点力平衡方程，详细推导了节点力、绳索驱动力的切线刚度矩阵，提高节点力平衡方程的收敛速度. 将轨迹跟踪问题解释为多体系统的伺服约束问题，采用非线性最小二乘求解器嵌套Newton-Raphson迭代算法，开展有、无末端负载两种条件下的路径跟踪仿真，得到了连续型机器人的构型演化规律.
- 绳驱连续型机器人 /
- 准静态建模 /
- 迟滞 /
- 滑动摩擦 /
- 路径跟踪
Abstract: The actuation hysteresis effect caused by cable-hole sliding friction is one of the critical challenges limiting the multi-functional and multi-domain applications of cable-driven continuum robots. During trajectory tracking, the driving cables undergo frequent switching between winding and unwinding, leading to repeated reversals of sliding friction within the guiding holes. As a result, the current configuration of the flexible arm varies significantly depending on the actuation history. A quasi-static model for the cable-driven continuum robot was developed based on the dynamics theory of flexible multibody systems. A nodal force equilibrium equation with decoupled rigid and flexible motions was established, and the tangent stiffness matrices for both nodal forces and cable driving forces were rigorously derived to enhance the convergence rate of the equilibrium equation. The trajectory tracking problem was formulated as a servo constraint problem in multibody systems. A nonlinear least-squares solver incorporating the Newton-Raphson iterative algorithm was employed to conduct path tracking simulations under both loaded and unloaded end-effector conditions. The configuration evolution law of the continuum robot was thereby obtained.
- cable-driven continuum robot /
- quasi-static modeling /
- hysteresis /
- sliding friction /
- path tracking

HTML全文

图 1 连续型机器人空间构型

Figure 1. The spatial configuration of a continuum robot

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图 2 全局和局部坐标系

Figure 2. Global and local coordinate systems

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图 3 绳索逐段启滑示意图

Figure 3. Schematic diagram of segment-by-segment cable sliding

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图 4 绳索张力与stick-slip状态更新流程图

Figure 4. The flowchart of cable tension and stick-slip state update

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图 5 绳驱连续型机器人实验平台

Figure 5. The experimental platform for the CDCR system

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图 6 摩擦因数测定装置

Figure 6. The friction coefficient measuring device

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图 7 绳驱连续型机器人系统静载实验

Figure 7. The static load experiment for the CDCR system

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图 8 收、放绳实验

Figure 8. The cable reeling and unreeling experiment

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图 9 摩擦因数对工作空间的影响

Figure 9. Influences of the friction coefficient on the workspace

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图 10 变曲率情况分析

Figure 10. Analysis of variable curvature scenarios

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图 11 空间十字形路径跟踪

Figure 11. The spatial cross-shaped path tracking

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表 1 绳驱连续型机器人系统仿真参数

Table 1. Simulation parameters of continuous robot system driven by cable

parameter	value	parameter	value
backbone length/m	0.45	disk number	10
backbone diameter/mm	8.5	disk diameter/cm	3
elastic modulus/MPa	7.1×10⁴	hole-to-center distance/cm	1.2
Poisson’s ratio	0.4	disk quality/g	1.2

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表 2 误差分析

Table 2. Error analysis

load/N	Euclidean distance/mm
load/N	node 2	node 3	node 4	node 5	node 6	node 7	node 8	node 9	node 10
0	1.59	0.68	1.49	3.15	5.33	5.12	5.39	6.35	4.21
2	0.26	0.57	1.25	2.86	3.36	4.49	4.56	5.88	6.54
3	0.14	0.20	0.41	0.55	1.41	1.42	3.26	4.53	6.94
4	0.13	0.05	0.07	0.91	5.42	2.81	5.72	7.77	5.26
5	0.14	0.82	0.76	1.15	2.64	3.53	3.76	4.88	4.14
6	0.45	1.20	1.79	2.23	2.99	3.40	5.38	7.65	10.30
7	0.80	0.06	0.84	0.33	1.73	2.82	5.35	9.58	13.09

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表 3 收敛性分析

Table 3. Convergence analysis

№.	maximum absolute error
№.	initial	step ①	step ②	step ③	step ④	step ⑤	step ⑥	step ⑦
1	1.22×10^-2	2.34×10^-3	4.43×10^-3	8.16×10^-5	1.40×10^-5	5.73×10^-8	0	0
2	1.52×10^-2	8.60×10^-4	1.50×10^-4	6.16×10^-6	1.10×10^-7	0	0	0
3	1.12×10^-2	4.11×10^-3	7.10×10^-4	1.85×10^-3	1.92×10^-4	1.11×10^-5	1.30×10^-6	1.07×10^-7
4	1.49×10^-2	1.04×10^-3	1.68×10^-3	1.02×10^-5	2.08×10^-7	0	0	0

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