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Can Walking Be Modeled in a Pure Mechanical Fashion

  • Antonio D’AngeloEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 867)

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.

Notes

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.

References

  1. 1.
    Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions, Applied Mathematics, vol. 55. National Bureau of Standards, Washington, D.C. (1972)zbMATHGoogle Scholar
  2. 2.
    Akhiezer, N.I.: Elements of the Theory of Elliptic Functions. American Mathematical Society, Providence, Rhode Island (1990)CrossRefGoogle Scholar
  3. 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)CrossRefGoogle Scholar
  4. 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. 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)CrossRefGoogle Scholar
  6. 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 1995Google Scholar
  7. 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)CrossRefGoogle Scholar
  8. 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 1995Google Scholar
  9. 9.
    Furusho, J., Masubuchi, M.: Control of a dynamical biped locomotion system for steady walking. Dyn. Syst. Meas. Control 108, 111–118 (1986)CrossRefGoogle Scholar
  10. 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. 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)CrossRefGoogle Scholar
  12. 12.
    Ijspeert, A.J.: Central pattern generators for locomotion control in animals and robots: a review. Neural Networks 21(4), 642–653 (2008)CrossRefGoogle Scholar
  13. 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 2001Google Scholar
  14. 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. 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 2000Google Scholar
  16. 16.
    Lawden, D.F.: Elliptic Functions and Applications, Applied Mathematical Sciences, vol. 80. Springer-Verlag, New York (1989)CrossRefGoogle Scholar
  17. 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)CrossRefGoogle Scholar
  18. 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. 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. 20.
    Raibert, M.: Legged Robots that Balance. The MIT Press, Cambridge (1986)CrossRefGoogle Scholar
  21. 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. 22.
    Siegwart, R., Nourbakhsh, I.R.: Introduction to Autonomous Mobile Robots. The MIT Press, Cambridge (2004)Google Scholar
  23. 23.
    Vukobratović, M., Juricic, D.: Contribution to the synthesis of biped gait. IEEE Biomed. Eng. 16(1), 1–6 (1969)CrossRefGoogle Scholar
  24. 24.
    Walker, M., Orin, D.: Efficient dynamic computer simulation of robotic mechanisms. Dyn. Syst. Meas. Control 104, 205–211 (1982)CrossRefGoogle Scholar
  25. 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. 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. 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)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUdine UniversityUdineItaly

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