共形幾何代数を用いた汎用3R位置決めロボットの逆運動学解法
Inverse kinematic solution for generic 3R positional robots using Conformal Geometric Algebra
共形幾何代数を用いて、汎用3Rロボットの逆運動学問題を2つの円の交点として再定式化し、theta_2に関する単変数多項式を直接導出する新しい解法を提案した。
著者: Abhilash Nayak, Durgesh Haribhau Salunkhe
分類: cs.RO
原文アブストラクト
The inverse kinematics of generic 3R robots has been investigated through multiple approaches, mainly algebraic methods involving the solution of certain equation sets. Previous geometric interpretations of the solution, characterized as the intersection of a pair of conics have been confined to the joint-space domain. In this article, we study the Inverse Kinematic Model (IKM) of 3R robots, using the advantages of Conformal Geometric Algebra (CGA) to provide further insights on its kinematic properties. Our approach directly yields a univariate polynomial in terms of theta_2 without the need to eliminate theta_1 and theta_3 by reframing the problem as the intersection of two circles, which are fundamental elements within this algebraic framework.