Skip to main content

Contact Dynamics

  • Reference work entry
  • First Online:
Humanoid Robotics: A Reference

Abstract

This chapter describes the contact dynamics. It is essential for humanoid robot motion since it largely influences the whole behavior of the robot in the following manner. The actuation forces are propagated in the body structure and act to the external world via the contact points. Then, the reaction force accelerates the robot itself. The contact points are not permanently connected to the world but can make relative movements to it, due to which the overall system dynamics discontinuously varies. It is necessary to understand the contact dynamics in order to describe and predict correctly how the contact points move with respect to the contact forces.

The contact forces are resulted from nanoscopic molecular interactions. For humanoid robots, however, those interactions are typically approximated in microscopic or macroscopic scales by various models, some of which are presented in this chapter. They are useful not only for understanding the robot behavior but also for some practical purposes. While a rather detailed model is acceptable in simulation and analysis, a macroscopic model based on the relationship between momentum and impulse is preferred for planning and control. Which model is to be chosen depends on properties of the objects to contact, available computation time, spatiotemporal scale of the phenomenon to study, and so forth.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 899.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 1,099.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Y. Fujimoto, A. Kawamura, Simulation of an autonomous biped walking robot including environmental force interaction. IEEE Robot. Autom. Mag. 5(2), 33–41 (1998)

    Article  Google Scholar 

  2. H. Hertz, Über die Berührung fester elastischer Körper und über die Harte, Gesammelte Werke, vol. 1 (J. A. Barth, Leipzig, 1895), pp. 174–196

    Google Scholar 

  3. K.H. Hunt, F.R.E. Crossley, Coefficient of restitution interpreted as damping in Vibroimpact. Trans ASME J. Appl. Mech. 42(2), 440–445 (1975)

    Article  Google Scholar 

  4. N. Diolaiti, C. Melchiorri, S. Stramigioli, Contact impedance estimation for robotic systems. IEEE Trans. Robot. 21(5), 925–935 (2005)

    Article  Google Scholar 

  5. G. Amontons, De la resistance causée dans les Machines, tant par les frottemens des parties qui les composent, que par roideur des cordes qu’on y employe, & la maniere de calculer l’un & l’autre, Mémoires de l’Académie royale des sciences, in Histoire de l’Académie royale des sciences, (De l’imprimerie royale, Paris, 1966), pp. 206–222

    Google Scholar 

  6. C.A. de Coulomb, Théorie des machines simples, en ayant égard au frottement de leurs parties, et a la roideur des cordages, in Mémoires des Savants Étrangers de l’Académie des Sciences, vol. 10 (Bachelier, Paris, 1809), pp. 163–332

    Google Scholar 

  7. P.R. Dahl, A solid friction model, technical report of aerospace corporation, TOR-0158(3107-18)-1, 1968

    Google Scholar 

  8. P.R. Dahl, Solid friction damping of mechanical vibrations. AIAA J. 14(2), 1675–1682 (1976)

    Article  Google Scholar 

  9. R. Stribeck, Kugellager fur beliebige Belastungen. Zeitschrift des Vereines deutscher Ingenieure 45(3), 73–79 & 45(4), 118–125 (1901)

    Google Scholar 

  10. R. Stribeck, Die wesentlischen Eigenschaften der Gleit- und Rollenlager. Zeitschrift des Vereines deutscher Ingenieure 46(37), 1341–1348 & 46(38), 1432–1438 & 46(39), 1463–1470 (1902)

    Google Scholar 

  11. C. Canudas de Wit, H. Olsson, K.J. ∘ Aström, P. Lischinsky, A new model for control of systems with friction. IEEE Trans. Autom. Control 40(3), 419–425 (1995)

    Google Scholar 

  12. B. Mirtich, J. Canny, Impulse-based dynamic simulation, Technical report, CSD-94-815, 1994

    Google Scholar 

  13. F. Génot, B. Brogliato, New results on Painlevé paradoxes. Eur. J. Mech. A. Solids 18(4), 653–677 (1999)

    Article  MathSciNet  Google Scholar 

  14. D.E. Stewart, J.C. Trinkle, An implicit timestepping scheme for rigid body dynamics with inelastic collisions and Coulomb friction. Int. J. Numer. Methods Eng. 39(15), 2673–2691 (1996)

    Article  MathSciNet  Google Scholar 

  15. M. Anitescu, F.A. Potra, Formulating dynamic multi-rigid-body contact problems with friction as solvable linear complementarity problems. Nonlinear Dyn. 14(3), 231–247 (1997)

    Google Scholar 

  16. D.E. Stewart, Rigid-body dynamics with friction and impact. SIAM Rev. 42(1), 3–39 (2000)

    Article  MathSciNet  Google Scholar 

  17. P. Lötstedt, Numerical simulation of time-dependent contact and friction problems in rigid body mechanics. SIAM J. Sci. Stat. Comput. 5(2), 370–393 (1984)

    Article  MathSciNet  Google Scholar 

  18. C.E. Lemke, Bimatrix equilibrium points and mathematical programming. Manag. Sci. 11, 681–689 (1965)

    Article  MathSciNet  Google Scholar 

  19. C.E. Lemke, J.T. Howson, Equilibrium points of bi-matrix games. SIAM J. 12, 413–423 (1964)

    Google Scholar 

  20. G.H. Golub, P.C. Hansen, D.P. OĹeary, Tikhonov regularization and total least squares. SIAM J. Mat. Anal. Appl. 21(1), 185–194 (1999)

    Article  MathSciNet  Google Scholar 

  21. J. Baumgarte, Stabilization of constraints and integrals of motion in dynamical systems. Comput. Methods Appl. Mech. Eng. 1, 1–16 (1972)

    Article  MathSciNet  Google Scholar 

  22. T. Sugihara, Y. Nakamura, Balanced micro/macro contact model for forward dynamics of rigid multibody, in Proceedings of the 2006 IEEE International Conference on Robotics & Automation, 2006, pp. 1880–1885

    Google Scholar 

  23. E. Todorov, A convex, smooth and invertible contact model for trajectory optimization, in Proceedings of 2011 IEEE International Conference on Robotics & Automation, 2011, pp. 1071–1076

    Google Scholar 

  24. N. Wakisaka, T. Sugihara, Fast and reasonable contact force computation in forward dynamics based on momentum-level penetration compensation, in Proceedings of 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2014, pp. 2434–2439

    Google Scholar 

  25. Y. Nakamura, K. Yamane, Dynamics computation of structure-varying kinematic chains and its application to human figures. IEEE Trans. Robot. Autom. 16(2), 124–134 (2000)

    Article  Google Scholar 

  26. A. Herzog, S. Schaal, L. Righetti, Structured contact force optimization for kino-dynamic motion generation, 2016. arXiv preprint, arXiv:1605.08571

    Google Scholar 

  27. D.E. Orin, A. Goswami, S.-H. Lee, Centroidal dynamics of a humanoid robot. Auton. Robot. 35, 161–176 (2013)

    Article  Google Scholar 

  28. H. Hirukawa, S. Hattori, S. Kajita, K. Harada, K. Kaneko, F. Kanehiro, M. Morisawa, S. Nakaoka, A pattern generator of humanoid robots walking on a rough terrain, in Proceedings of the 2007 IEEE International Conference on Robotics & Automation, 2007, pp. 2181–2187

    Google Scholar 

  29. J.Y.S. Luh, M.W. Walker, R.P.C. Paul, On-line computational scheme for mechanical manipulators. Trans. ASME J. Dyn. Syst. Meas. Control 102, 69–76 (1980)

    Article  MathSciNet  Google Scholar 

  30. H. Hirukawa, S. Hattori, K. Harada, S. Kajita, K. Kaneko, F. Kanehiro, K. Fujiwara, M. Morisawa, A universal stability criterion of the foot contact of legged robots – adios ZMP, in Proceedings of the 2006 IEEE International Conference on Robotics & Automation, 2006, pp. 1976–1938

    Google Scholar 

  31. J.-P. Aubin, A. Cellina, Differential Inclusions, Set-Valued Maps And Viability Theory. Grundlehren der mathematischen wissenschaften, vol. 264 (Springer, Berlin/Heidelberg, 1984)

    Google Scholar 

  32. M. Posa, M. Tobenkin, R. Tedrake, Stability analysis and control of rigid-body systems with impacts and friction. IEEE Trans. Autom. Control 61(6), 1423–1437 (2016)

    Article  MathSciNet  Google Scholar 

  33. R. Kikuuwe, B. Brogliato, A new representation of systems with frictional unilateral constraints and its Baumgarte-like relaxation. Multibody Syst. Dyn. 39(3), 267–290 (2017)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tomomichi Sugihara .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature B.V.

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Sugihara, T. (2019). Contact Dynamics. In: Goswami, A., Vadakkepat, P. (eds) Humanoid Robotics: A Reference. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6046-2_5

Download citation

Publish with us

Policies and ethics