Skip to main content

Advertisement

SpringerLink
Log in

Modeling, control and simulation of upward jump of a biped

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

This paper explores the vertical upward jumping of a planar biped. The jumping process is decomposed into the crouching phase, the thrust in the knees, the flight phase, the touchdown, and the straightening up movement of the biped. A mathematical model for this kind of jump of the biped is developed. Torques are applied in the hip and knee joints. The degree of underactuation of the mechanism is equal to one in the support phase and to three in the flight phase. The control algorithm is designed to ensure the jump of the biped. This algorithm is such that the center of mass of the mechanism is always placed on the same vertical line. The biped touches the ground in the same place where it starts from. The synthesis of the jumping process is supported by simulations which give consistent results with human data from existing biomechanical literature. Furthermore, the stick diagram of the jump derived from these simulation results seems natural for the human jumping. The problem of energy recovery is considered for the jumping of the biped by using springs in the hip and knee joints. The springs have an influence to minimize the mechanical energy consumed by the drives in the hip and knee joints. The springs in the knees help to increase the lifting of the bipedal mechanism.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Notes

  1. Here, symbol “t” denotes transposition.

References

  1. Ali, B.E.: Contribution à la commande du centre de masse d’un robot bipède. Thèse de doctorat, Institut National Polytechnique de Grenoble (1999)

  2. Anderson, F.C., Pandy, M.G.: A dynamic optimization solution for vertical jumping in three dimensions. Comput. Methods Biomech. Biomed. Eng. 2, 201–231 (2009)

    Article  Google Scholar 

  3. Aoustin, Y., Chevallereau, C., Formal’skii, A.M.: Numerical and experimental study of the virtual quadruped—semiquad. Multibody Syst. Dyn. 16, 1–20 (2006)

    Article  MATH  Google Scholar 

  4. Appell, P.: Dynamique des Systèmes—Mécanique Analytique. Gauthiers-Villars, Paris (1931)

    Google Scholar 

  5. Boone, G.N., Hodgins, J.K.: Slipping and tripping reflexes for bipedal running robots. J. Auton. Syst. 4(3), 51–66 (1997)

    Google Scholar 

  6. Chetaev, N.G.: Theoretical Mechanics. Springer, Berlin (1989)

    MATH  Google Scholar 

  7. Chevallereau, C., Abba, G., Aoustin, Y., Plestan, F., Westervelt, E., Canuddas-de Wit, C., Grizzle, J.: Rabbit: a testbed for advanced control theory. IEEE Control Syst. Mag. 23(5), 57–79 (2003)

    Article  Google Scholar 

  8. Chevallereau, C., Aoustin, Y.: Optimal reference trajectories for walking and running of a biped. Robotica 19(5), 557–569 (2001)

    Article  Google Scholar 

  9. Chevallereau, C., Bessonnet, G., Abba, G., Aoustin, Y.: Bipedal Robots: Modeling, Design and Building Walking Robots. ISTE Wiley, New York (2009)

    Google Scholar 

  10. Collins, S.H., Wisse, M., Ruina, A.: A three dimensional passive-dynamic walking robot with two legs and knees. Int. J. Robot. Res. 20(7), 607–615 (2001)

    Article  Google Scholar 

  11. Demura, K., Tachi, N., Maekawa, T., Ueno, K.-C.T.: Design of a humanoid for running. In: RoboCup 2001: Robot Soccer World Cup V. Lecture Notes in Control and Information Sciences, vol. 2377, pp. 283–315 (2006)

    Google Scholar 

  12. Engell-Norregard, M., Niebe, S., Erleben, K.: A Joint-constraint Model for Human Joints Using Signed Distance-fields. Multibody System Dynamics (2011). doi:10.1007/s11044-011-9296-1

  13. Farrel, K.D., Chevallereau, C., Westervelt, E.R.: Energetic effects of adding springs at the passive ankles of a walking biped robot. In: Proc. of the IEEE Conf. on Robotics and Automation, Roma, Italy, pp. 3591–3596 (2007)

    Google Scholar 

  14. Formal’skii, A.: Locomotion of Anthropomorphic Mechanisms. Nauka, Moscow (1982) (in Russian)

    Google Scholar 

  15. Goswami, D., Vadakkepat, P.: Planar bipedal jumping gaits with stable landing. IEEE Trans. Robot. 25(5), 1030–1046 (2009)

    Article  Google Scholar 

  16. Grishin, A., Formal’skii, A., Lensky, A., Zhitomirsky, S.: Dynamic walking of a vehicle with two telescopic legs controlled by two drives. Int. J. Robot. Res. 13(2), 137–147 (1994)

    Article  Google Scholar 

  17. Hurst, J.W., Chestnutt, J.J., Rizzi, A.A.: Design and philosophy of the bimasc, a highly dynamic biped. In: Proc. of the IEEE Conf. on Robotics and Automation, Roma, Italy, pp. 1863–1868 (2007)

    Google Scholar 

  18. Itiki, C., Kalaba, R., Udwadia, F.: Inequality constraints in the process of jumping. Appl. Math. Comput. 78, 163–173 (1996)

    Article  MATH  Google Scholar 

  19. Jackson, M., Benkhemis, I., Begon, M., Sardain, P., Vallée, C., Lacouture, P.: Identifying the criterion spontaneously minimized during the take-off phase of a sub-maximal long jump through optimal synthesis. Multibody Syst. Dyn. (2011). doi:10.1007/s11044-011-9278-3

    Google Scholar 

  20. Kajita, S., Nagasaki, T., Kaneko, K., Yokio, K., Tanie, K.: A hop towards running humanoid biped. In: Proc. of the IEEE Conf. on Robotics and Automation, pp. 629–635 (2004)

    Google Scholar 

  21. Ker, R., Bennett, M.B., Bibby, S.R., Kerster, R.C., Alexander, R.M.: The spring in the arc of the human foot. Nature 325, 147–149 (1987)

    Article  Google Scholar 

  22. Khang, G., Zajac, F.E.: Paraplegic standing controlled by functional neuromuscular stimulation, part 1: computer model and control-system design. IEEE Trans. Biomed. Eng. 36(9), 873–884 (1989)

    Article  Google Scholar 

  23. Linthorne, N.P.: Analysis of standing vertical jumps using a force platform. Am. J. Phys. 69(11), 1198–1204 (2001)

    Article  Google Scholar 

  24. McGeer, T.: Passive dynamic walking. Int. J. Robot. Res. 9(2), 62–82 (1990)

    Article  Google Scholar 

  25. Meghdari, A., Aryanpour, M.: Dynamic modeling and analysis of the human jumping process. J. Intell. Robot. Syst. 37, 97–115 (2003)

    Article  Google Scholar 

  26. Nagasaka, K., Kuroki, Y., Suzuki, S., Itoh, Y., Yamaguchi, J.: Integrated motion control for walking, jumping and running on small bipedal entertainment robot. In: Proc. of the IEEE Int. Conf. on Robotics and Automation, pp. 3189–3194 (2004)

    Google Scholar 

  27. Pandy, M.G., Zajac, F.E.: Optimal muscular coordination strategies for jumping. J. Biomech. 24(1), 1–10 (1991)

    Article  Google Scholar 

  28. Pratt, G., Williamson, M.: Series elastic actuators. In: Proc. IEEE Conf. on Intelligent Robots and Systems, vol. 1, pp. 399–406 (1995)

    Google Scholar 

  29. Pratt, J.E., Krupp, B.T.: Series elastic actuators for legged robots. In: Proc. of SPIE, vol. 5422, pp. 135–144 (2004)

    Google Scholar 

  30. Raibert, M.H., Brown, J.H.B., Chepponis, M.: Experiments in balance with a 3d one-legged hopping machine. Int. J. Robot. Res. 3(2), 75–92 (1984)

    Article  Google Scholar 

  31. Rogozhin, D.D.: Impulsive control for anthropomorphic mechanism in the running with instantaneous support phase. Theory Pract. Phys. Train. 5, 27–38 (1989) (in Russian)

    Google Scholar 

  32. Sabourin, C., Bruneau, O., Buche, G.: Control strategy for the robust dynamic walk of a biped robot. Int. J. Robot. Res. 25(9), 843–860 (2006)

    Article  Google Scholar 

  33. Sakka, S., Yokoi, K.: Humanoid vertical jumping based on force feedback and inertial forces optimization. In: Proc. of the IEEE Int. Conf. on Robotics and Automation, Barcelona, 2005, pp. 3752–3757 (2005)

    Google Scholar 

  34. Schaub, T., Scheint, M., Sobotka, M., Seiberl, W., Buss, M.: Effects of compliant ankles on bipedal locomotion. In: Proc. of the IEEE Int. Conf. on Robotics and Automation, pp. 2761–2766 (2009)

    Google Scholar 

  35. Song, S., Waldron, K.: Machines That Walk: The Adaptive Suspension Vehicle. MIT Press, Cambridge (1988)

    Google Scholar 

  36. van der Linde, R.Q., Wisse, M., Schwab, A.L.: A 3D passive dynamic biped with yaw and roll compensation. Robotica 19, 275–284 (2001)

    Google Scholar 

  37. Vanderborght, B.: Dynamic stabilization of the biped Lucy powered by actuators with controllable stiffness. PhD thesis, Vrije University Brussels (2007)

  38. Yamaguchi, J., Nishino, D., Takanishi, A.: Realization of dynamic biped walking varying joint stiffness using antagonistic driven joints. In: Proc. of the IEEE Conf. on Robotics and Automation, pp. 2022–2029 (1998)

    Google Scholar 

  39. Yamaguchi, J., Takanishi, A.: Development of a biped walking robot having antagonistic driven joints using nonlinear spring mechanism. In: Proc. of the IEEE Conf. on Robotics and Automation, pp. 185–192 (1997)

    Google Scholar 

  40. Zajac, F.E., Wicke, R.W., Levine, W.S.: Dependence of jumping performance on muscle properties when humans use only calf muscles for propulsion. Comput. Methods Biomech. Biomed. Eng. 17(7), 513–523 (1984)

    Google Scholar 

Download references

Acknowledgements

This work was supported by Russian Foundation for Basic Research, Grant 07-01-92167 and CNRS via a Project of International Collaboration Scientific, PICS 3866.

Author information

Authors and Affiliations

  1. LUNAM, Institut de Recherche en Communications et Cybernétique de Nantes, UMR 6597, CNRS, École Centrale de Nantes, Université de Nantes, rue de la Noë, BP 92101, 44321, Nantes, France

    Y. Aoustin

  2. Institute of Mechanics, Lomonosov Moscow State University, Michurinskii Prospect, Moscow, 119192, Russia

    A. M. Formalskii

Authors
  1. Y. Aoustin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. M. Formalskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Y. Aoustin.

Appendix: Expressions for matrices D(α), C(α) and E

Appendix: Expressions for matrices D(α), C(α) and E

1.1 Symmetrical Matrix D(α):

1.2 Matrix C(α):

1.3 Diagonal constant matrix E:

$$ \left [ \begin{array}{c@{\quad }c@{\quad }c@{\quad }c@{\quad }c} -(m_{1}s_{1}+m_{2}l_{1}+m_{3}l_{1}) & 0 & 0 & 0 & 0 \\ 0 & -(m_{2}s_{2}+m_{3}l_{2}) & 0 &0 & 0\\ 0 & 0 & -m_{3}s_{3} & 0 & 0\\ 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & m_{1}+m_{2}+m_{3} \\ \end{array} \right ] $$

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aoustin, Y., Formalskii, A.M. Modeling, control and simulation of upward jump of a biped. Multibody Syst Dyn 29, 425–445 (2013). https://doi.org/10.1007/s11044-012-9319-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-012-9319-6

Keywords

Search

Navigation