Inverse Kinematic Analysis of Redundant Manipulator Under Spinor Theory and Vector Constraints

杨明发; 刘放; 黄文建; 李晨晖; 邓蓉

doi:10.13433/j.cnki.1003-8728.20230330

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Inverse Kinematic Analysis of Redundant Manipulator Under Spinor Theory and Vector Constraints

更新时间：2026-04-23

- Inverse Kinematic Analysis of Redundant Manipulator Under Spinor Theory and Vector Constraints
- Mechanical Science and Technology for Aerospace Engineering Vol. 44, Issue 9, Pages: 1507-1513(2025)
- 作者机构：
  
  1. 西南交通大学轨道交通运维与装备四川省重点实验室,成都,610031
  2. 西南交通大学机械工程学院,成都,610031
- 作者简介：
- 基金信息：
- DOI：10.13433/j.cnki.1003-8728.20230330
  CLC：
- Published：2025
- 稿件说明：
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杨明发, 刘放, 黄文建, et al. Inverse Kinematic Analysis of Redundant Manipulator Under Spinor Theory and Vector Constraints[J]. Mechanical Science and Technology for Aerospace Engineering, 2025, 44(9): 1507-1513.
DOI：

杨明发, 刘放, 黄文建, et al. Inverse Kinematic Analysis of Redundant Manipulator Under Spinor Theory and Vector Constraints[J]. Mechanical Science and Technology for Aerospace Engineering, 2025, 44(9): 1507-1513. DOI： 10.13433/j.cnki.1003-8728.20230330.

摘要

针对一种7自由度冗余机械臂进行逆运动学求解，基于冗余机械臂的偏置肘关节构型和平移自由度特性，提出了一种结合旋量理论和向量约束的逆运动学求解算法。针对机械臂具有肘偏置和平移结构的特点，基于旋量理论建立运动学模型，将第1关节变量作为自变量，进行其他关节变量求解。利用Paden-Kahan子问题建立前3个关节变量的关系式，并建立关节坐标轴之间的空间向量共面的判定方程作为约束条件，联立求解得到前3个关节变量。进一步通过Paden-Kahan子问题和向量关系求解出其他关节变量。通过数值算例验证了该方法的可行性和准确性。

Abstract

Aiming at the inverse kinematics solution of a 7-degree-of-freedom redundant manipulator

an inverse kinematics algorithm combining spinor theory and vector constraint is proposed based on biased elbow joint configuration and translational characteristics of redundant manipulator. Considering the characteristics of the elbow offset and translational structure of the manipulator

a kinematic model is established based on spinor theory

and the first joint variable is used as the independent variable to solve other joint variables. The Paden-Kahan subproblem is used to establish the relationship between the first three joint variables

and the determination equation of the spatial vector coplanar between the joint axes is established as a constraint condition

and the first three joint variables are solved synchronously. Other joint variables are further solved by Paden-Kahan subproblems and vector relations. The feasibility and accuracy of the proposed method are verified by numerical examples.

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