FREQUENCY EXTRACTION BASED ON ADAPTIVE FOURIER SERIES - Application to Robotic Yoyo

Tadej Petrič, Andrej Gams, Leon Žlajpah

Abstract

We present a novel method to obtain the basic frequency of an unknown periodic signal with an arbitrary waveform. The method originates from nonlinear dynamical systems for frequency extraction, which are based on adaptive frequency oscillators in a feedback loop. While using several adaptive frequency oscillators in a loop results in extraction of separate frequency components, our method extracts the basic frequency of the input signal without any additional logical operations. The proposed method uses a whole Fourier series representation in the feedback loop. In this way it can extract the frequency and the phase of an unknown periodic signal, in real-time, and without any additional signal processing or preprocessing. The method also determines the Fourier series coefficients and can be used for dynamic Fourier series implementation. It can be used for the control of rhythmic robotic tasks, where only the extraction of the fundamental frequency is crucial. This is demonstrated on a highly nonlinear and dynamic task of playing the robotic yo-yo.

References

  1. Buchli, J. and Ijspeert, A. (2004). A simple, adaptive locomotion toy-system. In Schaal, S., Ijspeert, A., Billard, A., Vijayakumar, S., Hallam, J., and Meyer, J., editors, From Animals to Animats 8. Proceedings of the Eighth International Conference on the Simulation of Adaptive Behavior (SAB'04), pages 153-162. MIT Press.
  2. Buchli, J., Righetti, L., and Ijspeert, A. J. (2008). Frequency Analysis with coupled nonlinear Oscillators. Physica D: Nonlinear Phenomena, 237:1705-1718.
  3. Degallier, S., Righetti, L., Natale, L., Nori, F., Metta, G., and Ijspeert, A. (2008). A modular bio-inspired architecture for movement generation for the infantlike robot iCub. In Proceedings of the 2nd IEEE RAS / EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob).
  4. Gams, A., Ijspeert, A. J., Schaal, S., and Lenarcic, J. (2009). On-line learning and modulation of periodic movements with nonlinear dynamical systems. Auton. Robots, 27(1):3-23.
  5. Gams, A., Z? lajpah, L., and Lenarc?ic?, J. (2007). Imitating human acceleration of a gyroscopic device. Robotica, 25(4):501-509.
  6. Ijspeert, A. J. (2008). Central pattern generators for locomotion control in animals and robots: a review. Neural Networks, 21(4):642-653.
  7. Jin, H.-L., Ye, Q., and Zacksenhouse, M. (2009). Return maps, parameterization, and cycle-wise planning of yo-yo playing. Trans. Rob., 25(2):438-445.
  8. Kasuga, T. and Hashimoto, M. (2005). Human-robot handshaking using neural oscillators. In ICRA, pages 3802-3807.
  9. Matsuoka, K., Ohyama, N., Watanabe, A., and Ooshima, M. (2005). Control of a giant swing robot using a neural oscillator. In ICNC (2), pages 274-282.
  10. Petric?, T., Gams, A., and Z?lajpah, L. (2009). Modeling and control strategy for robotic powerball. In RAAD, page 7.
  11. Righetti, L., Buchli, J., and Ijspeert, A. J. (2006). Dynamic hebbian learning in adaptive frequency oscillators. Physica D, 216(2):269-281.
  12. Righetti, L. and Ijspeert, A. J. (2006). Programmable Central Pattern Generators: an application to biped locomotion control. In Proceedings of the 2006 IEEE International Conference on Robotics and Automation.
  13. Schaal, S. (1999). Is imitation learning the route to humanoid robots? Trends in cognitive sciences, 6:233- 242.
  14. Schaal, S., Mohajerian, P., and Ijspeert, A. (2007). Dynamics systems vs. optimal control-a unifying view. Progress in Brain Research, 165:425-445.
  15. Ude, A., Atkeson, C. G., and Riley, M. (2000). Planning of joint trajectories for humanoid robots using b-spline wavelets. In ICRA, pages 2223-2228.
  16. Z?lajpah, L. (2006). Robotic yo-yo: modelling and control strategies. Robotica, 24(2):211-220.
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Paper Citation


in Harvard Style

Petrič T., Gams A. and Žlajpah L. (2010). FREQUENCY EXTRACTION BASED ON ADAPTIVE FOURIER SERIES - Application to Robotic Yoyo . In Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO, ISBN 978-989-8425-01-0, pages 32-38. DOI: 10.5220/0002933900320038


in Bibtex Style

@conference{icinco10,
author={Tadej Petrič and Andrej Gams and Leon Žlajpah},
title={FREQUENCY EXTRACTION BASED ON ADAPTIVE FOURIER SERIES - Application to Robotic Yoyo},
booktitle={Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},
year={2010},
pages={32-38},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002933900320038},
isbn={978-989-8425-01-0},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,
TI - FREQUENCY EXTRACTION BASED ON ADAPTIVE FOURIER SERIES - Application to Robotic Yoyo
SN - 978-989-8425-01-0
AU - Petrič T.
AU - Gams A.
AU - Žlajpah L.
PY - 2010
SP - 32
EP - 38
DO - 10.5220/0002933900320038