Linearization-Based Forward Kinematic Algorithm for Tensegrity Structures with Compressible Struts

Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 187)


This paper presents a new local linearization method for elastic forces in tensegrity structures, which can be used to solve forward kinematic problems. Forward kinematic problems are often solved as a part of inverse kinematic algorithms and trajectory planning in robotics, and it is often desirable to be able to perform those algorithms online. The proposed method allows us to solve forward kinematics as a quadratic program, which makes it fast and reliable and allows us to take advantage of the existing convex programming software. The paper demonstrates the work of the proposed method using a three-link tensegrity structure.


Tensegrity Soft robotics Forward kinematics Numeric optimization Convex programming Local linearization 



The research is supported by the grant of the Russian Science Foundation (project No:19-79-10246).


  1. 1.
    Guest, S.D.: The stiffness of tensegrity structures. IMA J. Appl. Math. 76(1), 57–66 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Motro, R.: Tensegrity systems: the state of the art. Int. J. Space Struct. 7(2), 75–83 (1992)CrossRefGoogle Scholar
  3. 3.
    Sadao, S.: Fuller on tensegrity. Int. J. Space Struct. 11(1–2), 37–42 (1996)CrossRefGoogle Scholar
  4. 4.
    Snelson, K.: Snelson on the tensegrity invention. Int. J. Space Struct. 11(1–2), 43–48 (1996)CrossRefGoogle Scholar
  5. 5.
    Caluwaerts, K., et al.: Design and control of compliant tensegrity robots through simulation and hardware validation. J. R. Soc. Interface 11(98), 20140520 (2014)CrossRefGoogle Scholar
  6. 6.
    Paul, C., Valero-Cuevas, F.J., Lipson, H.: Design and control of tensegrity robots for locomotion. IEEE Trans. Rob. 22(5), 944–957 (2006)CrossRefGoogle Scholar
  7. 7.
    Smaili, A., Motro, R.: Foldable/unfoldable curved tensegrity systems by finite mechanism activation. J. Int. Assoc. Shell Spat. Struct. 48(3), 153–160 (2007)Google Scholar
  8. 8.
    Bouderbala, M., Motro, R.: Folding tensegrity systems. In: IUTAM-IASS Symposium on Deployable Structures: Theory and Applications, pp. 27–36 (2000)Google Scholar
  9. 9.
    Paul, C., Roberts, J.W., Lipson, H. Cuevas, F.V.: July. Gait production in a tensegrity based robot. In: ICAR’05. Proceedings of 12th International Conference on Advanced Robotics, 2005, pp. 216–222. IEEE (2005)Google Scholar
  10. 10.
    Kim, K. et al.: Rapid prototyping design and control of tensegrity soft robot for locomotion. In: 2014 IEEE International Conference on Robotics and Biomimetics (ROBIO 2014), pp. 7–14. IEEE (2014)Google Scholar
  11. 11.
    Rieffel, J., Trimmer, B., Lipson, H.: Mechanism as mind-what tensegrities and caterpillars can teach us about soft robotics. In: ALIFE, pp. 506–512 (2008)Google Scholar
  12. 12.
    Friesen, J., Pogue, A., Bewley, T., de Oliveira, M., Skelton, R. and Sunspiral, V.: DuCTT: A tensegrity robot for exploring duct systems. In: 2014 IEEE International Conference on Robotics and Automation (ICRA), pp. 4222–4228. IEEE (2014)Google Scholar
  13. 13.
    Tietz, B.R, Carnahan, R.W, Bachmann, R.J, Quinn, R.D, SunSpiral V. Tetraspine: Robust terrain handling on a tensegrity robot using central pattern generators. In: 2013 IEEE/ASME International Conference on Advanced Intelligent Mechatronics pp. 261–267. IEEEGoogle Scholar
  14. 14.
    Hustig-Schultz, D., SunSpiral, V. Teodorescu, M.: Morphological design for controlled tensegrity quadruped locomotion. In: 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 4714–4719 (2016)Google Scholar
  15. 15.
    Bruce, J., Caluwaerts, K., Iscen, A., Sabelhaus, A.P., SunSpiral, V.: Design and evolution of a modular tensegrity robot platform. In: 2014 IEEE International Conference on Robotics and Automation (ICRA), pp. 3483–3489. IEEE (2014)Google Scholar
  16. 16.
    Caluwaerts, K., Bruce, J., Friesen, J.M., SunSpiral, V.: State estimation for tensegrity robots. In: 2016 IEEE International Conference on Robotics and Automation (ICRA), pp. 1860–1865. IEEE (2016)Google Scholar
  17. 17.
    Mirletz, B.T., Quinn, R.D., SunSpiral, V.: Cpgs for adaptive control of spine-like tensegrity structures. In: Proceedings of 2015 International Conference on Robotics and Automation (ICRA2015) Workshop on Central Pattern Generators for Locomotion Control: Pros, Cons and Alternatives (2015)Google Scholar
  18. 18.
    Savin, S., Balakhnov, O., Klimchik, A.: Energy-based local forward and inverse kinematics methods for tensegrity robots (2020). (in Publication)Google Scholar
  19. 19.
    Aldrich, J.B., Skelton, R.E., Kreutz-Delgado, K.: Control synthesis for a class of light and agile robotic tensegrity structures. In: Proceedings of the 2003 American Control Conference 6, pp. 5245–5251. IEEE (2003)Google Scholar
  20. 20.
    Diamond, S., Boyd, S.: CVXPY: A Python-embedded modeling language for convex optimization. J. Mach. Learn. Res. 17(1), 2909–2913 (2016)MathSciNetzbMATHGoogle Scholar
  21. 21.
    Boyd, S., Vandenberghe, L.: Convex optimization. Cambridge University Press (2004)Google Scholar
  22. 22.
    Grant, M., Boyd, S., Ye, Y.P: Disciplined convex programming. Glob. Opt. 155–210 (2006)Google Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021

Authors and Affiliations

  1. 1.Innopolis UniversityInnopolisRussia

Personalised recommendations