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“Inverse Kinematics for Industrial Robots using Conformal Geometric Algebra”

Authors: Adam L. Kleppe and Olav Egeland,
Affiliation: NTNU
Reference: 2016, Vol 37, No 1, pp. 63-75.

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Keywords: Conformal Geometric Algebra, Inverse Kinematics, Agilus sixx R900, UR5

Abstract: This paper shows how the recently developed formulation of conformal geometric algebra can be used for analytic inverse kinematics of two six-link industrial manipulators with revolute joints. The paper demonstrates that the solution of the inverse kinematics in this framework relies on the intersection of geometric objects like lines, circles, planes and spheres, which provides the developer with valuable geometric intuition about the problem. It is believed that this will be very useful for new robot geometries and other mechanisms like cranes and topside drilling equipment. The paper extends previous results on inverse kinematics using conformal geometric algebra by providing consistent solutions for the joint angles for the different configurations depending on shoulder left or right, elbow up or down, and wrist flipped or not. Moreover, it is shown how to relate the solution to the Denavit-Hartenberg parameters of the robot. The solutions have been successfully implemented and tested extensively over the whole workspace of the manipulators.

PDF PDF (1005 Kb)        DOI: 10.4173/mic.2016.1.6





References:
[1] Dorst, L., Fontijne, D., and Mann, S. (2009). Dorst, L, , Fontijne, D., and Mann, S. Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry. Morgan Kaufmann Publishers Inc. San Francisco, CA, USA. http://www.geometricalgebra.net/, .
[2] Hildenbrand, D. (2013). Hildenbrand, D, Foundations of Geometric Algebra Computing, volume8 of Geometry and Computing. Springer Berlin Heidelberg, Berlin, Heidelberg. doi:10.1007/978-3-642-31794-1
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BibTeX:
@article{MIC-2016-1-6,
  title={{Inverse Kinematics for Industrial Robots using Conformal Geometric Algebra}},
  author={Kleppe, Adam L. and Egeland, Olav},
  journal={Modeling, Identification and Control},
  volume={37},
  number={1},
  pages={63--75},
  year={2016},
  doi={10.4173/mic.2016.1.6},
  publisher={Norwegian Society of Automatic Control}
};

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