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Dynamic Stability of the Hybrid Ball-bouncing Task

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Informatics in Control, Automation and Robotics (ICINCO 2017)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 495))

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Abstract

The authors previously proposed a method to test different hypotheses concerning the human motor control strategies in a computationally efficient way. Its efficiency was demonstrated by modeling the human visual servoing of the 1D bouncing ball benchmark, which involves rhythmic interactions with the environment. Three candidate human-inspired control laws were discriminated based on their capacity to stabilize the task, as analyzed by means of Poincaré maps. It was shown that the linear approximation, derived on these equilibrium points, of the human-like controller could be viewed as a state-feedback. Thus, the human-like controller was compared to the Linear Quadratic controller around the equilibrium point. The present study extends the analyzes made in this previous study by taking into account the influence of the arm and neural dynamics on the behavior adaptation to perturbations and task constraints. Particularly, the influence of these dynamics on the task stability is studied. Obtained results contribute to a better understanding of the human motor control strategies and will help to replicate these performances in robotics thanks to a more robust and less model-dependent robotic control architecture.

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References

  1. Avrin, G., Makarov, M., Rodriguez-Ayerbe, P., Siegler, I.A.: Dynamic stability of repeated agent-environment interactions during the hybrid ball-bouncing task. In: Proceedings of International Conference Informatics in Control, Automation and Robotics, pp. 486–496 (2017)

    Google Scholar 

  2. Yu, J., Tan, M., Chen, J., Zhang, J.: A survey on CPG-inspired control models and syst. implementation. IEEE Trans. Neural Netw. Learn. Syst. 25, 441–456 (2014)

    Google Scholar 

  3. Kulchenko, P., Todorov, E.: First-exit model predictive control of fast discontinuous dynamics: application to ball bouncing. In: IEEE International Conference on Robotics and Automation (ICRA), 2011, pp. 2144–2151 (2011)

    Google Scholar 

  4. Sternad, D., Duarte, M., Katsumata, H., Schaal, S.: Bouncing a ball: tuning into dynamic stability. J. Exp. Psychol. Hum. Percept. Perform. 27, 1163 (2001)

    Google Scholar 

  5. Williamson, M.: Designing rhythmic motions using neural oscillators. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). vol. 1, pp. 494–500 (1999)

    Google Scholar 

  6. Avrin, G., Makarov, M., Rodriguez-Ayerbe, P., Siegler, I.A.: Particle swarm optimization of Matsuoka’s oscillator parameters in human-like control of rhythmic movements. In: Proceedings of IEEE American Control Conference (2016)

    Google Scholar 

  7. de Rugy, A., Wei, K., Müller, H., Sternad, D.: Actively tracking passive stability in a ball bouncing task. Brain Res. 982, 64–78 (2003)

    Article  Google Scholar 

  8. Buehler, M., Koditschek, D.E., Kindlmann, P.: A simple juggling robot: Theory and experimentation. In: Experimental Robotics I, pp. 35–73. Springer, Berlin (1990)

    Google Scholar 

  9. Dijkstra, T., Katsumata, H., de Rugy, A., Sternad, D.: The dialogue between data and model: passive stability and relaxation behav. in a ball-bouncing task. Nonlinear Stud. 11, 319–344 (2004)

    Google Scholar 

  10. Holmes, P.J.: The dynamics of repeated impacts with a sinusoidally vibrating table. J. Sound Vib. 84, 173–189 (1982)

    Article  MathSciNet  Google Scholar 

  11. Vincent, T.L.: Controlling a ball to bounce at a fixed height. In: Proceedings of the American Control Conference, vol. 1, pp. 842–846. IEEE (1995)

    Google Scholar 

  12. Choudhary, S.K.: Lqr based optimal control of chaotic dynamical systems. Int. J. Model. Simul. 35, 104–112 (2016)

    Article  Google Scholar 

  13. Vincent, T.L., Mees, A.I.: Controlling a bouncing ball. Int. J. Bifurc. Chaos 10, 579–592 (2000)

    MathSciNet  MATH  Google Scholar 

  14. Siegler, I.A., Bazile, C., Warren, W.: Mixed control for perception and action: timing and error correction in rhythmic ball-bouncing. Exp. Brain Res. 226, 603–615 (2013)

    Article  Google Scholar 

  15. Avrin, G., Siegler, I.A., Makarov, M., Rodriguez-Ayerbe, P.: Model of rhythmic ball bouncing using a visually controlled neural oscillator. J. Neurophysiol. (in press)

    Google Scholar 

  16. Ronsse, R., Sepulchre, R.: Feedback control of impact dynamics: the bouncing ball revisited. In: Proceedings of the 45th IEEE Conference on Decision and Control, pp. 4807–4812. IEEE (2006)

    Google Scholar 

  17. Schaal, S., Sternad, D., Atkeson, C.G.: One-handed juggling: a dynamical approach to a rhythmic movement task. J. Mot. Behav. 28, 165–183 (1996)

    Article  Google Scholar 

  18. Tufillaro, N., Mello, T., Choi, Y., Albano, A.: Period doubling boundaries of a bouncing ball. J. de Physique 47, 1477–1482 (1986)

    Google Scholar 

  19. Morice, A., Siegler, I.A., Bardy, B., Warren, W.: Action-perception patterns in virtual ball bouncing: combating syst. latency and tracking functional validity. Exp. Brain Res. 181, 249–265 (2007)

    Google Scholar 

  20. Siegler, I.A., Bardy, B.G., Warren, W.H.: Passive vs. active control of rhythmic ball bouncing: the role of visual information. J. Exp. Psychol. Hum. Percept. Perform. 36, 729–50 (2010)

    Google Scholar 

  21. Stuart, A., Humphries, A.R.: Dynamical Systems and Numerical Analysis, vol. 2. Cambridge University Press, New York (1998)

    Google Scholar 

  22. Kwakernaak, H., Sivan, R.: Linear Optimal Control Systems. vol. 1. Wiley-interscience, New York (1972)

    Google Scholar 

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Correspondence to Guillaume Avrin .

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Avrin, G., Makarov, M., Rodriguez-Ayerbe, P., Siegler, I.A. (2020). Dynamic Stability of the Hybrid Ball-bouncing Task. In: Gusikhin, O., Madani, K. (eds) Informatics in Control, Automation and Robotics . ICINCO 2017. Lecture Notes in Electrical Engineering, vol 495. Springer, Cham. https://doi.org/10.1007/978-3-030-11292-9_36

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