Kinematic Modeling of a Novel Rigid⁃Flexible Hybrid Continuum Robots

doi:10.3969/j.issn.1004-132X.2025.11.025

China Mechanical Engineering ›› 2025, Vol. 36 ›› Issue (11): 2678-2684.DOI: 10.3969/j.issn.1004-132X.2025.11.025

Kinematic Modeling of a Novel Rigid⁃Flexible Hybrid Continuum Robots

Jiaxiang DONG¹(), Quanquan LIU²^,³(), Xiping HU², Xuezhi ZHAO¹

^1.School of Mechanical and Automotive Engineering，South China University of Technology，Guangzhou，510641
^2.Artificial Intelligence Research Institute & Guangdong-Hong Kong-Macao Joint Laboratory，Shenzhen MSU-BIT University，Shenzhen，Guangdong，518172
^3.Department of Neurology，The First Affiliated Hospital of Shenzhen University，Shenzhen，Guangdong，518035

Received:2024-10-23 Online:2025-11-25 Published:2025-12-09
Contact: Quanquan LIU

新型刚柔混联连续体机器人运动建模

董佳祥¹(), 刘铨权²^,³(), 胡希平², 赵学智¹

^1.华南理工大学机械与汽车工程学院, 广州, 510641
^2.深圳北理莫斯科大学人工智能研究院&粤港澳联合实验室, 深圳, 518172
^3.深圳大学第一附属医院神经内科, 深圳, 518035

通讯作者: 刘铨权
作者简介:董佳祥，男，1997年生，博士研究生。研究方向为微创手术机器人创新设计与精准控制。E-mail： 202110183011@mail.scut.edu.cn
刘铨权^*（通信作者），男，1984年生，副教授。研究方向为智能机器人与系统集成、医疗机器人机构综合与控制。E-mail： quanquanliu@smbu.edu.cn。
基金资助:
国家自然科学基金(61963007);广东省基础与应用基础研究基金(2023A1515012427);广东省基础与应用基础研究基金(2023A1515140026);深圳市科技计划(JCYJ20210324122200002);广东省医学科学技术研究基金(A2021169);广东省医学科学技术研究基金(B2023109);深圳市大鹏新区医疗健康集团医疗卫生科研项目(DPJTKY202306)

Abstract

Abstract:

A study of the kinemetic modeling was carried out for a novel rigid-flexible hybrid continuum robot driven by tension-torsion synergistic actuation. A kinetostatic model was developed based on the piecewise constant curvature（PCC） framework， which comprehensively considered various loads. To solve the highly nonlinear inverse kinematics， a BP neural network model optimized by the Newton-Raphson based optimizer（NRBO）， denoted as NRBO-BP model， was constructed. Experimental results show that the average bending angle errors at the end of the single/dual-segment flexible robots are as 4.2° and 7.1°， respectively. The maximum position error in trajectory tracking based on NRBO-BP model is as 2.5 mm， which verifies the accuracy and effectiveness of the proposed methods.

Key words: flexible shaft, continuum robot, kinetostatic model, neural network, inverse kinematics

摘要：

针对一种新型软轴拉扭协同驱动的刚柔混联连续体机器人，开展了其运动建模研究。建立了基于分段恒曲率（PCC）并综合考虑多种载荷的运动静力学模型。为求解其高度非线性的逆运动学，构建了一种由牛顿-拉夫逊优化算法（NRBO）优化的反向传播（BP）神经网络模型（NRBO-BP模型）。实验结果表明，单/双段柔性体机器人末端弯曲角度平均误差分别为4.2°和7.1°；基于NRBO-BP模型的轨迹跟踪最大位置误差为2.5 mm，验证了所提方法的准确性与有效性。

关键词: 软轴, 连续体机器人, 运动静力学模型, 神经网络, 逆运动学

CLC Number:

TP242

Jiaxiang DONG, Quanquan LIU, Xiping HU, Xuezhi ZHAO. Kinematic Modeling of a Novel Rigid⁃Flexible Hybrid Continuum Robots[J]. China Mechanical Engineering, 2025, 36(11): 2678-2684.

董佳祥, 刘铨权, 胡希平, 赵学智. 新型刚柔混联连续体机器人运动建模[J]. 中国机械工程, 2025, 36(11): 2678-2684.

Figures/Tables 13

Fig.1 Rigid⁃flexible hybrid continuum robot mechanism

Fig.2 Definition of the manipulator's coordinate system

Fig.3 Definition of the rigid joint coordinate system

Tab.1 Modified D⁃H parameters of the rigid joint

i	$α i - 1 / (°)$	$d i / m m$	$θ i / (°)$
11	0	$m 2$	-90
12	-90	0	$θ R 1$
13	90	$m 1$	$θ R 2$
14	0	$m 0$	0

Tab.1 Modified D⁃H parameters of the rigid joint

i	$α i - 1 / (°)$	$d i / m m$	$θ i / (°)$
11	0	$m 2$	-90
12	-90	0	$θ R 1$
13	90	$m 1$	$θ R 2$
14	0	$m 0$	0

Fig.4 Definition of the coordinate system for the continuum robot

Fig.5 Distribution of the manipulator end⁃effector position dataset

Fig.6 Principle of end⁃effector position prediction for flexible shaft actuation based on BP neural network

Fig.7 Diagram of the manipulator's static analysis

Fig.8 Robot prototype and experimental validation system

Fig.9 Real-time force data under the configuration of F4=30 N， F5=F6=2 N

Fig.10 In-plane bending angle of the continuum robot continuum robot prototype

Fig.11 Comparison of target， simulated， and experimental trajectories

Fig.12 Errors in the x， y， and z directions among simulated， experimental， and target trajectories

References 10

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Kinematic Modeling of a Novel Rigid⁃Flexible Hybrid Continuum Robots

新型刚柔混联连续体机器人运动建模

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