可伸缩蛇形臂机器人的设计及运动学建模

doi:10.3969/j.issn.1004-132X.2025.12.010

摘要/Abstract

摘要：

提出一种新型蛇形臂机器人，该机器人模块化关节具有主动的可伸缩自由度，增加了整机运动的灵活性和复杂空间适应能力。建立了蛇形臂机器人的运动学模型，分析了驱动空间、关节空间与末端操作空间的映射关系。针对关节具有伸缩自由度的构型特点，提出了两种关节-末端逆运动学算法，即结合传统FABRIK算法与基于雅可比矩阵迭代法的组合算法、杆长迭代更新的改进FABRIK算法。为了验证两种算法的计算精度和效率，进行了数值仿真对比，结果表明两种算法均具有良好的运算精度，改进的FABRIK算法具有更高的运算效率。最后搭建了物理样机并开展了实验验证，证明了所提出蛇形臂机器人具有良好的弯曲性能和伸缩运动性能。

关键词: 蛇形臂机器人, 结构设计, 逆运动学, 改进FABRIK算法, 实验验证

Abstract:

A novel snake-like manipulator was proposed， the modular joints of the manipulator were designed with an active extensible degree of freedom， which increased the overall motion flexibility and adaptability in complex spaces. Kinematics modeling of the snake-like manipulators was carried out. The mappings among actuator space， joint space and end task space were analyzed. Considering the characteristics of the extensible joints， two novel joint-end inverse kinematics algorithms were proposed， i.e. the integrated method by combing the conventional FABRIK algorithm with Jacobian-based iterative algorithm， and the modified FABRIK algorithm with iteratively updated link lengths. Numerical simulations were conducted to verify computational accuracy and efficiency. The results show that both methods have better accuracy， while the modified FABRIK algorithm has higher computational efficiency. Finally， a prototype was constructed， and experiments were carried out to validate motion capabilities of the proposed snake-like manipulators.

Key words: snake-like manipulator, structure design, inverse kinematics, improved FABRIK algorithm, experimental validation

中图分类号:

TH112

王旭浩, 盛卧龙, 吴孟丽, 许贻龙, 赵晓巍, 曹轶然. 可伸缩蛇形臂机器人的设计及运动学建模[J]. 中国机械工程, 2025, 36(12): 2885-2893.

Xuhao WANG, Wolong SHENG, Mengli WU, Yilong XU, Xiaowei ZHAO, Yiran CAO. Design and Kinematics Modeling of Extensible Snake-like Manipulators[J]. China Mechanical Engineering, 2025, 36(12): 2885-2893.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2025.12.010

https://www.cmemo.org.cn/CN/Y2025/V36/I12/2885

图/表 22

图1 可伸缩蛇形臂机器人模型

Fig.1 Model of the extensible snake-like manipulator

图2 可伸缩关节单元模型

Fig.2 Model of the extensible joint unit

图3 关节单元转动自由度模型

Fig.3 Model of revolute DOFs in the joint unit

图4 关节单元伸缩自由度模型

Fig.4 Model of extensible DOF in the joint unit

图5 关节坐标系

Fig.5 Joint coordinate systems

图6 逆运动学组合算法流程图

Fig.6 Flow chart of integrated inverse kinematics algorithm

图7 FABRIK算法迭代过程

Fig.7 Iteration of FABRIK algorithm

图8 向前接近迭代关节极限回避

Fig.8 Joint limit avoidance in forward reaching iteration

图9 改进的FABRIK算法流程图

Fig.9 Flow chart of the modified FABRIK algorithm

图10 杆长补偿方向确定

Fig.10 Link length compensation direction

图11 绳长与关节转角关系

Fig.11 Relation cable length errors

表1 逆运动学算法计算效率

Tab.1 Computational efficiency of inverse kinematics

算法	初始解 q₀	初始解误差		计算时间 t/ms
算法	初始解 q₀	位置误差 dp/mm	姿态误差 dr/（˚）	计算时间 t/ms
基于雅可比矩阵的迭代法	（0，0°，0°，0，0°， 0°，0，0°，0°）^T	147.8670	0.8689	86
组合算法	（9.13 mm，12.91°， 22.86°，9.13 mm， 3.30°，5.58°， 9.13 mm，22.77°， 17.92°）^T	6.1303	0.0361	10.6
改进的 FABRIK算法	—	—	—	1.7

图12 位置误差对比图

Fig.12 Comparison of the position errors

图13 姿态误差对比图

Fig.13 Comparison of the orientation errors

图14 计算时间对比图

Fig.14 Comparison of the operation times

图15 蛇形臂机器人样机

Fig.15 Prototype of the snake-like manipulator

图16 基于动作捕捉系统的测量方案

Fig.16 Measurement scheme based on motion capture system

图17 平面弯曲实验

Fig.17 Plane bending experiment

图18 末端位置及姿态误差

Fig.18 End position and orientation errors

图19 蛇形臂伸长示意图

Fig.19 Extension of the snake-like manipulator

图20 伸缩实验末端位置误差

Fig.20 End position errors under extension experiment

图21 蛇形臂弯曲与伸长运动示意图

Fig.21 Bending and extension of snake-like manipulator

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