Advertisement

Autonomous Robots

, Volume 28, Issue 3, pp 247–269 | Cite as

CPG-based control of a turtle-like underwater vehicle

  • Keehong Seo
  • Soon-Jo Chung
  • Jean-Jacques E. Slotine
Article

Abstract

This paper presents biologically inspired control strategies for an autonomous underwater vehicle (AUV) propelled by flapping fins that resemble the paddle-like forelimbs of a sea turtle. Our proposed framework exploits limit cycle oscillators and diffusive couplings, thereby constructing coupled nonlinear oscillators, similar to the central pattern generators (CPGs) in animal spinal cords. This paper first presents rigorous stability analyses and experimental results of CPG-based control methods with and without actuator feedback to the CPG. In these methods, the CPG module generates synchronized oscillation patterns, which are sent to position-servoed flapping fin actuators as a reference input. In order to overcome the limitation of the open-loop CPG that the synchronization is occurring only between the reference signals, this paper introduces a new single-layered CPG method, where the CPG and the physical layers are combined as a single layer, to ensure the synchronization of the physical actuators in the presence of external disturbances. The key idea is to replace nonlinear oscillators in the conventional CPG models with physical actuators that oscillate due to nonlinear state feedback of the actuator states. Using contraction theory, a relatively new nonlinear stability tool, we show that coupled nonlinear oscillators globally synchronize to a specific pattern that can be stereotyped by an outer-loop controller. Results of experimentation with a turtle-like AUV show the feasibility of the proposed control laws.

Keywords

Biomimetic underwater vehicle Central pattern generator Synchronization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material

Below is the link to the electronic supplementary material. (WMV 15.1 MB)

Below is the link to the electronic supplementary material. (WMV 7.37 MB)

References

  1. Arena, P., Fortuna, L., & Frasca, M. (2002). Multi-template approach to realize central pattern generators for artificial locomotion control. International Journal of Circuit Theory and Applications, 30(4), 441–458. zbMATHCrossRefGoogle Scholar
  2. Bandyopadhyay, P., Singh, S., Thivierge, D., Annaswamy, A., Leinhos, H., Fredette, A., & Beal, D. (2008). Synchronization of animal-inspired multiple high-lift fins in an underwater vehicle using olivo–cerebellar dynamics. IEEE Journal of Oceanic, Engineering, 33(4), 563–578. CrossRefGoogle Scholar
  3. Beal, D. N., & Bandyopadhyay, P. R. (2007). A harmonic model of hydrodynamic forces produced by a flapping fin. Experiments in Fluids, 43(5), 675–682. CrossRefGoogle Scholar
  4. Buchli, J., Righetti, L., & Ijspeert, A. J. (2006). Engineering entrainment and adaptation in limit cycle systems. Biological Cybernetics, 95, 645–664. zbMATHCrossRefMathSciNetGoogle Scholar
  5. Chen, Z., & Iwasaki, T. (2008). Circulant synthesis of central pattern generators with application to control of rectifier systems. IEEE Transactions on Automatic Control, 53(1), 273–286. CrossRefMathSciNetGoogle Scholar
  6. Chung, S.-J., & Slotine, J.-J. E. (2009). Cooperative robot control and concurrent synchronization of Lagrangian systems. IEEE Transactions on Robotics, 25(3), 686–700. Google Scholar
  7. Collins, J. J., & Stewart, I. N. (1993). Coupled nonlinear oscillators and the symmetry of animal gaits. Journal of Nonlinear Science, 3, 349–392. zbMATHCrossRefMathSciNetGoogle Scholar
  8. Crespi, A., & Ijspeert, A. (2006). Amphibot II: an amphibious snake robot that crawls and swims using a central pattern generator. In Proceedings of the 9th international conference on climbing and walking robots (CLAWAR 2006) (pp. 19–27). Brussels, Belgium. Google Scholar
  9. Ekeberg, Ö. (1993). A combined neuronal and mechanical model of fish swimming. Biological Cybernetics, 69, 363–374. zbMATHGoogle Scholar
  10. Grillner, S., Deliagina, T., Ekeberg, Ö., El Manira, A., Hill, R., Lansner, A., Orlovski, G., & Wallen, P. (1995). Neural networks that co-ordinate locomotion and body orientation in the lamprey. Trends in Neurosciences, 18, 270–279. CrossRefGoogle Scholar
  11. Grillner, S., Ekeberg, Ö., El Manira, A., Lansner, A., Parker, D., Tegnér, J., & Wallén, P. (1998). Intrinsic function of a neuronal network—a vertebrate central pattern generator. Brain Research Reviews, 26, 184–197. CrossRefGoogle Scholar
  12. Hirose, S. (1993). Biologically inspired robots: snake-like locomotors and manipulators. Oxford: Oxford University Press. Google Scholar
  13. Ijspeert, A., Crespi, A., Ryczko, D., & Cabelguen, J.-M. (2007). From swimming to walking with a salamander robot driven by a spinal cord model. Science, 315(5817), 1416–1420. CrossRefGoogle Scholar
  14. Iwasaki, T., & Zheng, M. (2006). Sensory feedback mechanism underlying entertainment of central pattern generator to mechanical resonance. Biological Cybernetics, 94(4), 245–261. zbMATHCrossRefMathSciNetGoogle Scholar
  15. Khalil, H. K. (2002). Nonlinear Systems (3rd edn.). New York: Prentice-Hall. zbMATHGoogle Scholar
  16. Krouchev, N., Kalaska, J. F., & Drew, T. (2006). Sequential activation of muscle synergies during locomotion in the intact cat as revealed by cluster analysis and direct decomposition. Journal of Neurophysiology, 96, 1991–2010. CrossRefGoogle Scholar
  17. Lewis, M. A., Tenore, F., & Etienne-Cummings, R. (2005). CPG design using inhibitory networks. In Proceedings of the 2005 IEEE international conference on robotics and automation (pp. 3682–3687). Barcelona, Spain. Google Scholar
  18. Licht, S., Polidoro, V., Flores, M., Hover, F., & Triantafyllou, M. (2004). Design and projected performance of a flapping foil AUV. IEEE Journal of Oceanic Engineering, 29(3), 786–794. CrossRefGoogle Scholar
  19. Morimoto, J., Endo, G., Nakanishi, J., Hyon, S.-H., Cheng, G., Bentivegna, D., & Atkeson, C. G. (2006). Modulation of simple sinusoidal patterns by a coupled oscillator model for biped walking. In Proceedings of the 2006 IEEE international conference on robotics and automation (pp. 1579–1584). Google Scholar
  20. Olfati-Saber, R., & Murray, R. M. (2004). Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 49(9), 1520–1533. CrossRefMathSciNetGoogle Scholar
  21. Pham, Q.-C., & Slotine, J.-J. E. (2007). Stable concurrent synchronization in dynamic system networks. Neural Networks, 20(1), 62–77. zbMATHCrossRefGoogle Scholar
  22. Pikovsky, A., Rosenblum, M., & Kurths, J. (2001). Synchronization: a universal concept in nonlinear sciences. Cambridge: Cambridge University Press. zbMATHGoogle Scholar
  23. Rybak, I. A., Shevtsova, N. A., Lafreniere-Roula, M., & McCrea, D. A. (2006). Modelling spinal circuitry involved in locomotor pattern generation: insights from deletions during fictive locomotion. Journal of Physiology, 577(2), 617–639. CrossRefGoogle Scholar
  24. Seo, K., Chung, S.-J., & Slotine, J.-J. (2008). CPG-based control of a turtle-like underwater vehicle. In Proceedings of robotics: science and systems IV. Zurich, Switzerland. Google Scholar
  25. Seo, K., & Slotine, J.-J. E. (2007). Models for global synchronization in CPG-based locomotion. In Proceedings of 2007 IEEE international conference on robotics and automation (pp. 281–286). Rome, Italy. Google Scholar
  26. Stent, G. S., Kristan, W. B. Jr., Friesen, W. O., Ort, C. A., Poon, M., & Calabrese, R. L. (1978). Neuronal generation of the leech swimming movement. Science, New Series, 200(4348), 1348–1357. Google Scholar
  27. Strogatz, S. (2000). From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D, 143, 1–20. zbMATHCrossRefMathSciNetGoogle Scholar
  28. Strogatz, S. (2001). Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering (studies in nonlinearity). Cambridge: Perseus Books Group. Google Scholar
  29. Taga, G. (1998). A model of the neuro-musculo-skeletal system for anticipatory adjustment of human locomotion during obstacle avoidance. Biological Cybernetics, 78(1), 9–17. zbMATHCrossRefGoogle Scholar
  30. Taga, G., Yamaguchi, Y., & Shimizu, H. (1991). Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment. Biological Cybernetics, 65(3), 147–159. zbMATHCrossRefGoogle Scholar
  31. Triantafyllou, M., & Triantafyllou, G. (1995). An efficient swimming machine. Scientific American, 272(3), 64–70. CrossRefGoogle Scholar
  32. Tuwankotta, J. M. (2000). Studies on Rayleigh equation. INTEGRAL, 5(1). Google Scholar
  33. Vogelstein, R. J., Tenore, F., Etienne-Cummings, R., Lewis, M. A., & Cohen, A. H. (2006). Dynamic control of the central pattern generator for locomotion. Biological Cybernetics, 95(6), 555–566. zbMATHCrossRefGoogle Scholar
  34. Wang, W., & Slotine, J.-J. E. (2005). On partial contraction analysis for coupled nonlinear oscillators. Biological Cybernetics, 92(1), 38–53. zbMATHCrossRefMathSciNetGoogle Scholar
  35. Wang, M., & Yu, J. (2008). Intelligent robotics and applications, Part I. In LNAI : Vol. 5314. Parameter design for a central pattern generator based locomotion controller (pp. 352–361). Berlin: Springer. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Keehong Seo
    • 1
  • Soon-Jo Chung
    • 1
  • Jean-Jacques E. Slotine
    • 1
  1. 1.Nonlinear Systems Lab.Massachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations