Advances in Applied Clifford Algebras

, Volume 27, Issue 3, pp 2067–2082 | Cite as

Efficient Implementation of Inverse Kinematics on a 6-DOF Industrial Robot using Conformal Geometric Algebra

  • Sondre Sanden Tørdal
  • Geir Hovland
  • Ilya Tyapin


This paper presents an implementation of the inverse kinematics (IK) solution for an industrial robot based on Conformal Geometric Algebra where the correct signs of the joint angles are extracted using the multivector coefficients and applying the forward kinematics. The solution presented is twice as fast as traditional IK algorithms implemented using matrix algebra, and more than 45 times faster than the IK provided by the robot manufacturer. The proposed solution has been successfully demonstrated and benchmarked in a 3-DOF motion compensation experiment. In addition to being efficient the presented solution requires less matrix operations than for the traditional IK.


Inverse kinematics Industrial robotics Conformal geometric algebra Motion compensation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chaoqun, W., Hongtao, W., Qunhua, M.: Inverse kinematics computation in robotics using conformal geometric algebra. IET Conf. Proc. (2009). doi: 10.1049/cp.2009.1527
  2. 2.
    Hildenbrand, D., Simos, T.E., Psihoyios, G., Tsitouras, Ch., Anastassi, Z.: Foundations of Geometric Algebra Computing. Springer (2013). doi: 10.1007/978-3-642-31794-1
  3. 3.
    Hildenbrand, D., Fontijne, D., Wang, Y., Alexa, M., Dorst, L.: Competitive runtime performance for inverse kinematics algorithms using conformal geometric algebra. In: Eurographics Conference of Vienna, 2006Google Scholar
  4. 4.
    Hildenbrand, D., Koch, A.: Gaalop-High Performance Computing Based on Conformal Geometric Algebra. In: Proceedings of the AGACSE Conference Grimma near Leipzig, Germany, August 2008 (2008)Google Scholar
  5. 5.
    Hildenbrand, D., Lange, H., Stock, F., Koch, A.: Efficient inverse kinematics algorithm based on conformal geometric algebra using reconfigurable hardware. Citeseer (2008)Google Scholar
  6. 6.
    Hildenbrand, D., Zamora, J., Bayro-Corrochano, E.: Inverse kinematics computation in computer graphics and robotics using conformal geometric algebra. Adv. Appl. Cliff Algebra 18(3–4), 699–713 (2008)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Lange, H., Stock, F., Koch, A., Hildenbrand, D.: Acceleration and energy efficiency of a geometric algebra computation using reconfigurable computers and GPUs. In: Proceedings of the 17th IEEE Symposium on Field Programmable Custom Computing Machines, 2009. FCCM’09, pp. 255–258. IEEE (2009)Google Scholar
  8. 8.
    Megahed S.M.: Inverse kinematics of spherical wrist robot arms: analysis and simulation. J. Intell. Robot. Syst. 5(3), 211–227 (1992)zbMATHGoogle Scholar
  9. 9.
    Perwass, C.: Geometric Algebra with Applications in Engineering, 1st edn (2009)Google Scholar
  10. 10.
    Pieper, D.L.: The kinematics of manipulators under computer control. Stanford, Calif.: Computer Science Department, Stanford University (1968)Google Scholar
  11. 11.
    Pitt, J., Hildenbrand, D., Stelzer, M., Koch, A.: Inverse kinematics of a humanoid robot based on conformal geometric algebra using optimized code generation. In: Proceedings of the Humanoids 2008-8th IEEE-RAS International Conference on Humanoid Robots, pp. 681–868. IEEE (2008). doi: 10.1109/ICHR.2008.4756025
  12. 12.
    Spong, M.W., Hutchinson, S., Vidyasagar, M.: Robot Modeling and Control, vol. 3. Wiley, New York (2006)Google Scholar

Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.The University of AgderGrimstadNorway

Personalised recommendations