Inverse kinematic solution for generic 3R positional robots using Conformal Geometric Algebra

Abstract: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.

Robotics (cs.RO)

arXiv:2609.00311 [cs.RO]

(or arXiv:2609.00311v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2609.00311 arXiv-issued DOI via DataCite (pending registration)

In: Holderbaum, W., Selig, J.M. (eds) Advances in the Mathematics of Robotics. IMA 2025. Springer Proceedings in Advanced Robotics, vol 39. Springer, Cham

https://doi.org/10.1007/978-3-032-10510-3_8 DOI(s) linking to related resources