Skip to main content
Log in

A dynamic gait stabilization algorithm for quadrupedal locomotion through contact time modulation

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, we propose a stabilization method for dynamic gaits of quadrupedal walking robots covering a wide range of speeds and various types of gait. Our stabilization method is based on adjusting the contact time between the four legs and ground. By modulating the contact time, the impact applied to the body can be controlled and stabilized. The stability provided by the proposed algorithm was proved in the sense of Lyapunov. The proposed algorithm also demonstrated robust performance under large external disturbances, and the performance was compared with other algorithms through simulations. Simulation results of bounding gaits under different ground conditions were compared, and the various types of stable gait implemented by the proposed algorithm are also presented.

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

Access this article

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

Similar content being viewed by others

References

  1. Alexander, R.M.: Principles of Animal Locomotion. Princeton University Press, Princeton (2003)

    Book  Google Scholar 

  2. Alexander, R.M., Jayes, A.: A dynamic similarity hypothesis for the gaits of quadrupedal mammals. J. Zool. 201(1), 135–152 (1983)

    Article  Google Scholar 

  3. Arakawa, T., Fukuda, T.: Natural motion generation of biped locomotion robot using hierarchical trajectory generation method consisting of ga, ep layers. In: Proceedings of International Conference on Robotics and Automation, vol. 1, pp. 211–216. IEEE (1997)

  4. Ba, D.X., Yeom, H., Kim, J., Bae, J.: Gain-adaptive robust backstepping position control of a bldc motor system. IEEE/ASME Trans. Mechatron. 23(5), 2470–2481 (2018)

    Article  Google Scholar 

  5. Barasuol, V., Buchli, J., Semini, C., Frigerio, M., De Pieri, E.R., Caldwell, D.G.: A reactive controller framework for quadrupedal locomotion on challenging terrain. In: 2013 IEEE International Conference on Robotics and Automation, pp. 2554–2561. IEEE (2013)

  6. Bertram, J.E.: Understanding Mammalian Locomotion: Concepts and Applications. Wiley, Hoboken (2016)

    Book  Google Scholar 

  7. Buono, P.L., Golubitsky, M.: Models of central pattern generators for quadruped locomotion i. Primary gaits. J. Math. Biol. 42(4), 291–326 (2001)

    Article  MathSciNet  Google Scholar 

  8. Camurri, M., Ramezani, M., Nobili, S., Fallon, M.: Pronto: a multi-sensor state estimator for legged robots in real world scenarios. Front. Robot. AI 7, 68 (2020)

    Article  Google Scholar 

  9. Chen, W.H., Ballance, D.J., Gawthrop, P.J., O’Reilly, J.: A nonlinear disturbance observer for robotic manipulators. IEEE Trans. Ind. Electron. 47(4), 932–938 (2000)

    Article  Google Scholar 

  10. Havoutis, I., Ortiz, J., Bazeille, S., Barasuol, V., Semini, C., Caldwell, D.G.: Onboard perception-based trotting and crawling with the hydraulic quadruped robot (hyq). In: 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 6052–6057. IEEE (2013)

  11. Hwangbo, J., Lee, J., Dosovitskiy, A., Bellicoso, D., Tsounis, V., Koltun, V., Hutter, M.: Learning agile and dynamic motor skills for legged robots. Sci. Robot. 4(26) (2019)

  12. Ito, S., Asano, H., Kawasaki, H.: A balance control in biped double support phase based on center of pressure of ground reaction forces. IFAC Proc. Vol. 36(17), 189–194 (2003)

    Article  Google Scholar 

  13. Kimura, H., Fukuoka, Y., Cohen, A.H.: Adaptive dynamic walking of a quadruped robot on natural ground based on biological concepts. Int. J. Robot. Res. 26(5), 475–490 (2007)

    Article  Google Scholar 

  14. Koolen, T., De Boer, T., Rebula, J., Goswami, A., Pratt, J.: Capturability-based analysis and control of legged locomotion, part 1: theory and application to three simple gait models. Int. J. Robot. Res. 31(9), 1094–1113 (2012)

    Article  Google Scholar 

  15. Lee, Y.H., Tran, D.T., Hyun, J.H., Phan, L.T., Koo, I.M., Yang, S.U., Choi, H.R.: A gait transition algorithm based on hybrid walking gait for a quadruped walking robot. Intell. Serv. Robot. 8(4), 185–200 (2015)

    Article  Google Scholar 

  16. Maes, L.D., Herbin, M., Hackert, R., Bels, V.L., Abourachid, A.: Steady locomotion in dogs: temporal and associated spatial coordination patterns and the effect of speed. J. Exp. Biol. 211(1), 138–149 (2008)

    Article  Google Scholar 

  17. MATLAB: version 9.7.0.1319299 (R2019b). The MathWorks Inc., Natick, Massachusetts (2019)

  18. McGhee, R.B., Frank, A.A.: On the stability properties of quadruped creeping gaits. Math. Biosci. 3, 331–351 (1968)

    Article  Google Scholar 

  19. Park, H.W., Chuah, M.Y., Kim, S.: Quadruped bounding control with variable duty cycle via vertical impulse scaling. In: 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3245–3252. IEEE (2014)

  20. Park, H.W., Kim, S.: Quadrupedal galloping control for a wide range of speed via vertical impulse scaling. Bioinspir. Biomim. 10(2), 025003 (2015)

    Article  Google Scholar 

  21. Pfeiffer, F., Zielińska, T.: Walking: Biological and Technological Aspects. Springer, Berlin (2004)

    Book  Google Scholar 

  22. Raibert, M.: Legged Robots that Balance. Artificial Intelligence Series. MIT Press, Cambridge (1986)

    MATH  Google Scholar 

  23. Rutishauser, S., Sprowitz, A., Righetti, L., Ijspeert, A.J.: Passive compliant quadruped robot using central pattern generators for locomotion control. In: 2008 2nd IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics, pp. 710–715. IEEE (2008)

  24. Schmidt-Nielsen, K.: Locomotion: energy cost of swimming, flying, and running. Science 177(4045), 222–228 (1972)

    Article  Google Scholar 

  25. Seok, S., Wang, A., Chuah, M.Y., Otten, D., Lang, J., Kim, S.: Design principles for highly efficient quadrupeds and implementation on the mit cheetah robot. In: 2013 IEEE International Conference on Robotics and Automation, pp. 3307–3312. IEEE (2013)

  26. Shang, W., Wu, Z., Liu, Q., Duan, L., Wang, C.: Foot placement estimator for quadruped push recovery. In: 2019 IEEE 9th Annual International Conference on CYBER Technology in Automation, Control, and Intelligent Systems (CYBER), pp. 1530–1534. IEEE (2019)

  27. Shih, C.L., Li, Y., Churng, S., Lee, T.T., Gruver, W.A.: Trajectory synthesis and physical admissibility for a biped robot during the single-support phase. In: Proceedings., IEEE International Conference on Robotics and Automation, pp. 1646–1652. IEEE (1990)

  28. Sun, S.S.: A theoretical study of gaits for legged locomotion systems. Ph.D. thesis, The Ohio State University (1974)

  29. Tucker, V.A.: The energetic cost of moving about: walking and running are extremely inefficient forms of locomotion. much greater efficiency is achieved by birds, fish-and bicyclists. Am. Sci. 63(4), 413–419 (1975)

    Google Scholar 

  30. Vukobratović, M., Borovac, B.: Zero-moment point-thirty five years of its life. Int. J. Hum. Robot. 1(01), 157–173 (2004)

    Article  Google Scholar 

  31. Walter, R.M., Carrier, D.R.: Ground forces applied by galloping dogs. J. Exp. Biol. 210(2), 208–216 (2007)

    Article  Google Scholar 

  32. Walter, R.M., Carrier, D.R.: Rapid acceleration in dogs: ground forces and body posture dynamics. J. Exp. Biol. 212(12), 1930–1939 (2009)

    Article  Google Scholar 

  33. Yi, K.Y.: Locomotion of a biped robot with compliant ankle joints. In: Proceedings of International Conference on Robotics and Automation, vol. 1, pp. 199–204. IEEE (1997)

  34. Zhang, S., Liu, M., Yin, Y., Rong, X., Li, Y., Hua, Z.: Static gait planning method for quadruped robot walking on unknown rough terrain. IEEE Access 7, 177651–177660 (2019)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the 2021 Research Fund (1.210052.01) of UNIST (Ulsan National Institute of Science and Technology), and the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIT) (No. NRF-2019R1A2C2084677).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Joonbum Bae.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary material 1 (mp4 78173 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yeom, H., Bae, J. A dynamic gait stabilization algorithm for quadrupedal locomotion through contact time modulation. Nonlinear Dyn 104, 2275–2289 (2021). https://doi.org/10.1007/s11071-021-06376-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-06376-5

Keywords

Navigation