Inverse kinematic solution for generic 3R positional robots using Conformal Geometric Algebra
arXiv:2609.00311v1 Announce Type: new 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.
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[Submitted on 31 Aug 2026]
Title:Inverse kinematic solution for generic 3R positional robots using Conformal Geometric Algebra
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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.
Subjects:
Robotics (cs.RO)
Cite as: 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)
Journal reference: In: Holderbaum, W., Selig, J.M. (eds) Advances in the Mathematics of Robotics. IMA 2025. Springer Proceedings in Advanced Robotics, vol 39. Springer, Cham
Related DOI:
https://doi.org/10.1007/978-3-032-10510-3_8
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From: Durgesh Haribhau Salunkhe [view email] [v1] Mon, 31 Aug 2026 20:01:15 UTC (10,934 KB)
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