Abstract
On-line determination of the basic frequency of an unknown periodic signal with an arbitrary waveform is crucial in imitating and performing rhythmic tasks with robots. We present a novel method to determine the basic frequency of a periodic signal on-line. The method is based on adaptive frequency oscillators in a feedback loop. While so far several adaptive frequency oscillators in a loop had to be used and the basic frequency determined using logical algorithms that choose from the determined frequency components, our method extracts the basic frequency of the input signal without any additional logical operations. The proposed novel method uses a single oscillator combined with a whole Fourier series representation in a feedback loop. Such formulation allows extracting 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. The method can be used for the control of rhythmic robotic tasks, where successful performing of a task crucially depends on the extraction of the fundamental frequency. We demonstrate the properties and usefulness of the method in simulation and on a highly nonlinear and dynamic task of playing the robotic yo-yo.
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References
Buchli, J., Ijspeert, A.J.: A simple, adaptive locomotion toy-system. In: Schaal, S., Ijspeert, A.J., Billard, A., Vijayakumar, S., Hallam, J., Meyer, J.A. (eds.) From Animals to Animats 8. Proceedings of the Eighth International Conference on the Simulation of Adaptive Behavior (SAB 2004), pp. 153–162. MIT Press, Cambridge (2004)
Buchli, J., Righetti, L., Ijspeert, A.J.: Frequency Analysis with coupled nonlinear Oscillators. Physica D: Nonlinear Phenomena 237, 1705–1718 (2008)
Degallier, S., Righetti, L., Natale, L., Nori, F., Metta, G., Ijspeert, A.: A modular bio-inspired architecture for movement generation for the infant-like robot iCub. In: Proceedings of the 2nd IEEE RAS / EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob) (2008)
Gams, A., Petric, T., Zlajpah, L.: Controlling yo-yo and gyroscopic device with nonlinear dynamic systems. In: 18th International Workshop on Robotics in Alpe-Adria-Danube Region, Brasov, Romania, RAAD 2009, May 25-27, p. 6 (2009)
Gams, A., Ijspeert, A.J., Schaal, S., Lenarcic, J.: On-line learning and modulation of periodic movements with nonlinear dynamical systems. Auton. Robots 27(1), 3–23 (2009)
Gams, A., Žlajpah, L., Lenarčič, J.: Imitating human acceleration of a gyroscopic device. Robotica 25(4), 501–509 (2007)
Ijspeert, A.J.: Central pattern generators for locomotion control in animals and robots: A review. Neural Networks 21(4), 642–653 (2008)
Jin, H.-L., Ye, Q., Zacksenhouse, M.: Return maps, parameterization, and cycle-wise planning of yo-yo playing. Trans. Rob. 25(2), 438–445 (2009)
Kasuga, T., Hashimoto, M.: Human-robot handshaking using neural oscillators. In: ICRA, pp. 3802–3807 (2005)
Matsuoka, K., Ohyama, N., Watanabe, A., Ooshima, M.: Control of a giant swing robot using a neural oscillator. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005. LNCS, vol. 3611, pp. 274–282. Springer, Heidelberg (2005)
Petrič, T., Gams, A., Žlajpah, L.: Modeling and control strategy for robotic powerball. In: RAAD, p. 7 (2009)
Righetti, L., Ijspeert, A.J.: Programmable Central Pattern Generators: an application to biped locomotion control. In: Proceedings of the 2006 IEEE International Conference on Robotics and Automation (2006)
Righetti, L., Buchli, J., Ijspeert, A.J.: Dynamic hebbian learning in adaptive frequency oscillators. Physica D 216(2), 269–281 (2006)
Schaal, S.: Is imitation learning the route to humanoid robots? Trends in cognitive sciences 6, 233–242 (1999)
Schaal, S., Mohajerian, P., Ijspeert, A.: Dynamics systems vs. optimal control — a unifying view, vol.(165), pp. 425–445 (2007)
Ude, A., Atkeson, C.G., Riley, M.: Planning of joint trajectories for humanoid robots using b-spline wavelets. In: ICRA, pp. 2223–2228 (2000)
Žlajpah, L.: Robotic yo-yo: modelling and control strategies. Robotica 24(2), 211–220 (2006)
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Petrič, T., Gams, A., Žlajpah, L. (2011). Extracting the Frequency of Robotic Tasks with an Adaptive Fourier Series: Application to Yo-Yo. In: Cetto, J.A., Ferrier, JL., Filipe, J. (eds) Informatics in Control, Automation and Robotics. Lecture Notes in Electrical Engineering, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19539-6_12
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DOI: https://doi.org/10.1007/978-3-642-19539-6_12
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