Inverse Displacement Solutions of Serial Robot Based on Conformal Geometric Algebra

doi:10.7652/xjtuxb201701002

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Inverse Displacement Solutions of Serial Robot Based on Conformal Geometric Algebra

更新时间：2025-07-09

- Inverse Displacement Solutions of Serial Robot Based on Conformal Geometric Algebra
- Vol. 51, Issue 1, Pages: 9-12+37(2017)
- 作者机构：
  
  北方工业大学机械与材料工程学院,北京,100144
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb201701002
  CLC： TH112
- Online First：10 January 2017，
  
  Published：2017
- 稿件说明：
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Inverse Displacement Solutions of Serial Robot Based on Conformal Geometric Algebra[J]. 2017, 51(1): 9-12+37.
DOI：

Inverse Displacement Solutions of Serial Robot Based on Conformal Geometric Algebra[J]. 2017, 51(1): 9-12+37. DOI： 10.7652/xjtuxb201701002.

摘要

为获得串联机器人位置逆解的解析解

使用共形几何代数对串联机器人位置逆解进行了研究。利用共形几何代数中基本几何元素的内积和外积运算

获得串联机器人各关节点的位置

然后通过构造经过关节点的直线与直线以及平面与平面的内积

求解出机器人所有关节转角

从而直接获得了串联机器人位置逆解的解析解。该方法求解简捷

几何直观性好

避免了经典机器人运动学理论中欧拉角、矩阵的运算以及复杂的多元高次非线性方程组求解

求解过程和结果可以明显地反映机器人几何结构与机器人运动之间的几何关系。以一种空间6R串联机器人位置逆解为例进行了求解

算例计算表明该方法正确、有效

计算效率提高了近44倍。

Abstract

To obtain all close-form solutions of the inverse displacement problem of a 6R serial robot

a novel method based on conformal geometric algebra(CGA)is presented. The positions of joint points are obtained by the inner product and outer product of the basic geometric entities in CGA. Then all joint rotating angles are computed by the inner product between line and line or plane and plane

and all closed-form solutions are obtained. The presented algorithm is simple and avoids the computations of rational angles

matrices

and complex nonlinear equations. The computation process and results can interpret geometrically the relationship between the geometric structure and the motion of the robot. Finally

a numerical example is solved by the algorithm and the results show that the algorithm is valid and the computational efficiency is improved by nearly 44 times.

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references

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