Cartesian Space Screw Linear Interpolation Trajectory Planning for Redundant Robots

doi:10.3969/j.issn.1004-132X.2025.01.011

Abstract

Abstract: By analyzing the relationship between dual quaternions and rigid body motion, and the relationship between dual quaternions and screw motion, a transformation operator of the end-effector pose was obtained based on dual quaternions with the combination of PoE formula. Based on the Newton-Raphson method, the dual quaternions were applied to solve the numerical solution of the inverse kinematics of redundant robots. Based on the linear interpolation characteristics of dual quaternions, a trajectory planning method was proposed based on screw linear interpolation. Taking two types of redundant robots as examples, the proposed trajectory planning method that achieved smooth motion and controllable velocity in Cartesian space was verified. Dual quaternions have better stability and higher solving speed than homogeneous matrices in solving kinematics numerical solutions.

Key words: dual quaternion, trajectory planning, inverse kinematics, product of exponentials(PoE), redundant robot

摘要： 通过分析对偶四元数与刚体运动、螺旋运动之间的关系并结合指数积公式，得到基于对偶四元数的末端位姿变换算子;根据牛顿拉夫森法，将对偶四元数用于求解冗余机器人的逆运动学数值解;根据对偶四元数的线性插值特点提出一种基于螺旋线性插值的轨迹规划方法。两种冗余机器人验证了提出的轨迹规划方法能实现笛卡儿空间平滑运动和速度可控，且在求解运动学数值解时，使用对偶四元数比齐次矩阵具有更好的稳定性和更高的解算速度。

关键词: 对偶四元数, 轨迹规划, 逆运动学, 指数积, 冗余机器人

CLC Number:

TP242

WANG Zhiqiang1, HAN Jianhai1, 2, 3, LI Xiangpan1, 2, GUO Bingjing1, 2, DU Ganqin4. Cartesian Space Screw Linear Interpolation Trajectory Planning for Redundant Robots[J]. China Mechanical Engineering, 2025, 36(01): 104-112.

王志强1, 韩建海1, 2, 3, 李向攀1, 2, 郭冰菁1, 2, 杜敢琴4. 冗余机器人的笛卡儿空间螺旋线性插值轨迹规划[J]. 中国机械工程, 2025, 36(01): 104-112.

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