The Detect-Condition Algorithm for Robotic Inverse Kinematics and Common Root Analysis

Authors

https://doi.org/10.48314/anowa.v2i1.68

Abstract

CThis paper presents the Detect-Condition algorithm, a novel method based on Grobner systems for identifying conditions on the parameters of polynomial systems to determine their common roots. The power of this algrithm is demonstrated through a central application: automating the inverse kinematics (IK) for a planar 3R robotic manipulator. We translate the IK problem, finding the joint angles for a desired end-effector pose, into a system of parametric polynomials. The algorithm then partitions the parameter space (link lengths and target pose) to derive the exact algebraic conditions for solutions to exist. Specifically, it symbolically computes the robot’s workspace boundary and provides closed-form expressions for the joint angles. Implemented in Mapleand validated with a numerical example, this approach offers a complete, symbolic, and automated solution. The results provide significant advantages over iterative numerical methods, including guaranteed precision and deep insight into kinematic constraints, establishing the algorithm as a powerful tool for robotic design and analysis.

Keywords:

Detect-Condition algorithm, Inverse Kinematics, Parametric polynomials, Grobner systems, 3R Robot, Workspace analysis

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Published

2026-03-22

Issue

Vol. 2 No. 1 (2026): Annals of Optimization With Applications (ANOWA)

Section

Articles

How to Cite

Dehghani Darmian, M. . (2026). The Detect-Condition Algorithm for Robotic Inverse Kinematics and Common Root Analysis. Annals of Optimization With Applications, 2(1), 75-90. https://doi.org/10.48314/anowa.v2i1.68

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