Nonlinear dynamical systems are an interesting approach for the generation of trajectories for robots with many degrees of freedom (e.g. legged locomotion). There are many interesting properties of nonlinear dynamical systems which can be exploited, e.g. attractor properties (fixed point, limit cycles) and robustness against perturbations, synchronization effects with signals from the body and the environment, filtering and fusing of noisy sensory signals, production of robust, high-dimensional oscillatory signals for gaits etc. Designing a nonlinear dynamical system to satisfy a given specification and goal is however not an easy task, and, hitherto no methodology exists to approach this problem in a unified way. The goal of this project is to design adaptive mechanism for tuning and shaping the nonlinear dynamical systems to exhibit specific properties.
Nonlinear dynamical systems used in locomotion control are basically models of complex systems. Namely models of the neural structures connected with the biomechanical systems. We therefore propose to discuss such systems in the light of complex dynamical systems. When looking at the basic concepts of pattern formation and non-equilibrium thermodynamics it gets clear that it is natural to discuss natural locomotion control (e.g. CPGs) with pattern formation formalism. The resulting models are low dimensional, nonlinear dynamical systems. However, there is a difference between physical (e.g. Bénard Cells) and "super-physical" (e.g. biological swarming behavior) pattern formation. Motivated by this difference we recently proposed to use plastic dynamical systems and multi-scale feedback loops for adaptive controllers for robots. Ref. [1] presents a simple example. We are currently working on a generalized description of multiscale feedback loop systems.
The hope is that with such formalism we can encompass different learning, adaptive and evolutionary systems and shed a light on their common properties and their differences.
People involved: Jonas Buchli, Ludovic Righetti, Sarah Dégallier
The potential illustration of a plastic dynamical system.
An attractor is formed in a one-shot learning system. The system is based on the principles of plasticity and multi-scale properties.
L. Righetti, J. Buchli, and A.J. Ijspeert. Dynamic hebbian learning in adaptive frequency oscillators. Physica D, 216(2):269-281, 2006.
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[2]
J. Buchli, L. Righetti, and A.J. Ijspeert. A dynamical systems approach to learning: a frequency-adaptive hopper robot. In Proceedings of the VIIIth European Conference on Artificial Life ECAL 2005, Lecture Notes in Artificial Intelligence, pages 210-220. Springer Verlag, 2005.
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[3]
L. Righetti, J. Buchli, and A.J. Ijspeert. From dynamic hebbian learning for oscillators to adaptive central pattern generators. In Proceedings of 3rd International Symposium on Adaptive Motion in Animals and Machines - AMAM 2005. Verlag ISLE, Ilmenau, 2005. Full paper on CD.
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[4]
L. Righetti, J. Buchli, and A.J. Ijspeert. From dynamic hebbian learning for oscillators to adaptive central pattern generators. In Proceedings of 3rd International Symposium on Adaptive Motion in Animals and Machines - AMAM 2005, page 45. Verlag ISLE, Ilmenau, 2005. Abstract.
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[5]
J. Buchli, L. Righetti, and A.J. Ijspeert. Adaptive dynamical systems for movement control. In Proceedings of 3rd International Symposium on Adaptive Motion in Animals and Machines - AMAM 2005, page 7. Verlag ISLE, Ilmenau, 2005. Abstract.
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[6]
J. Buchli and A.J. Ijspeert. A simple, adaptive locomotion toy-system. In S. Schaal, A.J. Ijspeert, A. Billard, S. Vijayakumar, J. Hallam, and J.A. Meyer, 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, 2004.
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[7]
J. Buchli and A.J. Ijspeert. Distributed central pattern generator model for robotics application based on phase sensitivity analysis. In A.J. Ijspeert, M. Murata, and N. Wakamiya, editors, Biologically Inspired Approaches to Advanced Information Technology: First International Workshop, BioADIT 2004, volume 3141 of Lecture Notes in Computer Science, pages 333-349. Springer Verlag Berlin Heidelberg, 2004.
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