Skip to main content
SpringerLink
Log in

Can Walking Be Modeled in a Pure Mechanical Fashion

  • Conference paper
  • First Online:
Intelligent Autonomous Systems 15 (IAS 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 867))

Included in the following conference series:

Abstract

The aim of this paper is to investigate the role of some mechanical quantities in the challenging task to make a robot walking or running. Because the upright posture of an humanoid is the main source of instability, the maintenance of the equilibrium during locomotion requires the gait-controller to deal with a number of constraints, such as ZMP, whose dynamical satisfactions prevent the humanoid from an harmful fall. Walking humanoids are open systems heavily interacting with a perturbing environment and the rapid loss of mechanical energy could be an hallmark of instability. In this paper we shall show how certain dimensionless parameters could be useful to design the walking gait of a bipedal robot.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Notes

  1. 1.

    See center of pression.

  2. 2.

    Squatting position.

  3. 3.

    Again referred to the stance leg.

  4. 4.

    As it comes immediately from the definition.

  5. 5.

    The nature not invented the wheel but the walking biped is very similar to a rolling.

References

  1. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions, Applied Mathematics, vol. 55. National Bureau of Standards, Washington, D.C. (1972)

    MATH  Google Scholar 

  2. Akhiezer, N.I.: Elements of the Theory of Elliptic Functions. American Mathematical Society, Providence, Rhode Island (1990)

    Book  Google Scholar 

  3. Alcaraz-Jiménez, J., Herrero-Pérez, D., Martínez-Barberá, H.: Robust feedback control of zmp-based gait for the humanoid robot nao. Int. J. Rob. Res. 32(9–10), 1074–1088 (2013)

    Article  Google Scholar 

  4. Arakawa, T., Fukuda, T.: Natural motion trajectory generation of biped locomotion robot using genetic algorithm through energy optimization. In: IEEE International Conference on Systems, Man and Cybernetics, p. 14951500 (1996)

    Google Scholar 

  5. Cardenas-Maciela, S.L., Castillo, O., Aguilar, L.T.: Generation of walking periodic motions for a biped robot via genetic algorithms. Appl. Soft Comput. 11(8), 5306–5314 (2011)

    Article  Google Scholar 

  6. Cheng, M., Lin, C.: Genetic algorithm for control design of biped locomotion. In: IEEE International Conference on Robotics and Automation, pp. 1315–1320. Nagoya (J), 21–27 May 1995

    Google Scholar 

  7. Fujimoto, Y., Kawamura, A.: Simulation of an autonomous biped walking robot including environmental force interaction. IEEE Robot. Autom. Mag. 5(2), 33–42 (1998)

    Article  Google Scholar 

  8. Furusho, J., Akihito, S., Masamichi, S., Eichi, K.: Realization of bounce gait in a quadruped robot with articular-joint-type legs. In: IEEE International Conference on Robotics and Automation, pp. 697–702. Nagoya (J), 21–27 May 1995

    Google Scholar 

  9. Furusho, J., Masubuchi, M.: Control of a dynamical biped locomotion system for steady walking. Dyn. Syst. Meas. Control 108, 111–118 (1986)

    Article  Google Scholar 

  10. Hirai, K., Hirose, M., Haikawa, Y., Takenaka, T.: The development of the Honda humanoid robot. In: IEEE International Conference on Robotics and Automation (1998)

    Google Scholar 

  11. Huang, Q., Yokoi, K., Kajita, S., Kaneko, K., Arai, H., Koyachi, N., Tanie, K.: Planning walking patterns for a biped robot. IEEE Trans. Robot. Autom. 17(3), 280–289 (2001)

    Article  Google Scholar 

  12. Ijspeert, A.J.: Central pattern generators for locomotion control in animals and robots: a review. Neural Networks 21(4), 642–653 (2008)

    Article  Google Scholar 

  13. Kajita, S., Kanehiro, F., Kaneko, K., Yokoi, K., Hirukawa, H.: The 3D linear inverted pendulum mode: a simple modeling for a biped walking pattern generation. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Maui (Hawaii), USA, pp. 239–246, 29 October–03 November 2001

    Google Scholar 

  14. Kato, I., Tsuiki, H.: The hydraulically powered biped walking machine with a high carrying capacity. In: Fourth Symposium on External Extremities. Dubrovnik (HR) (1972)

    Google Scholar 

  15. Kimura, H., Fukuoka, Y.: Adaptive dynamic walking of the quadruped on irregular terrain - autonomous adaptation using neural system model. In: IEEE International Conference on Robotics and Automation, San Francisco (CA), pp. 436–443, April 2000

    Google Scholar 

  16. Lawden, D.F.: Elliptic Functions and Applications, Applied Mathematical Sciences, vol. 80. Springer-Verlag, New York (1989)

    Book  Google Scholar 

  17. Lee, S.H., Goswami, A.: A momentum-based balance controller for humanoid robots on non-level and non-stationary ground. Auton. Robots 33(4), 116 (2012)

    Article  Google Scholar 

  18. Ogino, M., Toyama, H., Asada, M.: Stabilizing biped walking on rough terrain based on the compliance control. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2007), San Diego (CA), pp. 4047–4052 (2007)

    Google Scholar 

  19. Pettersson, J., Sandholt, H., Wahde, M.: A flexible evolutionary method for the generation and implementation of behaviors in humanoid robots. In: IEEE-RAS International Conference on Humanoid Robots, pp. 279–286 (2001)

    Google Scholar 

  20. Raibert, M.: Legged Robots that Balance. The MIT Press, Cambridge (1986)

    Book  Google Scholar 

  21. Reinhardt, W.P., Walker, P.L.: Jacobian Elliptic Functions, Digital Library of Mathematical Functions, vol. 22. NISTDigital Library of Mathematical Functions (2015). http://dlmf.nist.gov/22

  22. Siegwart, R., Nourbakhsh, I.R.: Introduction to Autonomous Mobile Robots. The MIT Press, Cambridge (2004)

    Google Scholar 

  23. Vukobratović, M., Juricic, D.: Contribution to the synthesis of biped gait. IEEE Biomed. Eng. 16(1), 1–6 (1969)

    Article  Google Scholar 

  24. Walker, M., Orin, D.: Efficient dynamic computer simulation of robotic mechanisms. Dyn. Syst. Meas. Control 104, 205–211 (1982)

    Article  Google Scholar 

  25. Wieber, P.B.: Trajectory free linear model predictive control for stable walking in the presence of strong perturbations. In: 6th IEEE-RAS International Conference on Humanoid Robots, p. 137142 (2006)

    Google Scholar 

  26. Yi, S.J., Zhang, B.T., Hong, D., Lee, D.D.: Practical bipedal walking control on uneven terrain using surface learning and push recovery. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, San Francisco (CA), pp. 3963–3968 (2011)

    Google Scholar 

  27. Yu, J., Tan, M., Chen, J., Zhang, J.: A survey on CPG-inspired control models and system implementation. IEEE Trans. Neural Netw. Learn. Syst. 25(3), 441–56 (2014)

    Article  Google Scholar 

Download references

Acknowledgement

This work was partially supported by a collaboration with the Intelligent Autonomous Systems Laboratory (IAS-Lab) of the University of Padua through a Grant of Consorzio Ethics, Abano Terme, Italy, for a three-years project (2014–2016) on a Study on experimenting Exoskeletons in Medical Institutions: we thank Enrico Pagello and Roberto Bortoletto et al. of IAS Lab for their valuable suggestions and discussions.

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Udine University, Udine, Italy

    Antonio D’Angelo

Authors
  1. Antonio D’Angelo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antonio D’Angelo .

Editor information

Editors and Affiliations

  1. Baden-Wuerttemberg Cooperative State University, Karlsruhe, Germany

    Marcus Strand

  2. Humanoids and Intelligence Systems Lab, KIT - Karlsruher Institut für Technologie, Karlsruhe, Germany

    Rüdiger Dillmann

  3. University of Padua , Padua, Italy

    Emanuele Menegatti

  4. University of Padua, Padua, Italy

    Stefano Ghidoni

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

D’Angelo, A. (2019). Can Walking Be Modeled in a Pure Mechanical Fashion. In: Strand, M., Dillmann, R., Menegatti, E., Ghidoni, S. (eds) Intelligent Autonomous Systems 15. IAS 2018. Advances in Intelligent Systems and Computing, vol 867. Springer, Cham. https://doi.org/10.1007/978-3-030-01370-7_23

Download citation

Publish with us

Policies and ethics

Search

Navigation