Towards a theoretical foundation for morphological computation with compliant bodies
The control of compliant robots is, due to their often nonlinear and complex dynamics, inherently difficult. The vision of morphological computation proposes to view these aspects not only as problems, but rather also as parts of the solution. Non-rigid body parts are not seen anymore as imperfect realizations of rigid body parts, but rather as potential computational resources. The applicability of this vision has already been demonstrated for a variety of complex robot control problems. Nevertheless, a theoretical basis for understanding the capabilities and limitations of morphological computation has been missing so far. We present a model for morphological computation with compliant bodies, where a precise mathematical characterization of the potential computational contribution of a complex physical body is feasible. The theory suggests that complexity and nonlinearity, typically unwanted properties of robots, are desired features in order to provide computational power. We demonstrate that simple generic models of physical bodies, based on mass-spring systems, can be used to implement complex nonlinear operators. By adding a simple readout (which is static and linear) to the morphology such devices are able to emulate complex mappings of input to output streams in continuous time. Hence, by outsourcing parts of the computation to the physical body, the difficult problem of learning to control a complex body, could be reduced to a simple and perspicuous learning task, which can not get stuck in local minima of an error function.
KeywordsMorphological computation Embodiment Analog computation Volterra series Nonlinear mass-spring systems
Written under partial support by the European Union projects # FP7-216593 (SECO), # 216886 (PASCAL2), # 248311 (AMARSi), and by the Austrian Science Fund FWF, project # P17229- N04. We also want to thank the anonymous reviewers for their very helpful suggestions and comments.
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- Bartlett PL, Maass W (2003) Vapnik-Chervonenkis dimension of neural nets. In: Arbib MA (eds) The handbook of brain theory and neural networks, 2nd edn. MIT Press, Cambridge, pp 1188–1192Google Scholar
- Boyd S (1985) Volterra series: engineering fundamentals. PhD thesis, UC BerkeleyGoogle Scholar
- Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9:1735–1780. ISSN 0899-7667Google Scholar
- Khalil HK (2002) Nonlinear Systems, 3rd edn, Prentice Hall, Upper Saddle RiverGoogle Scholar
- Legenstein R, Chase SA, Schwartz AB, Maass W (2010) Functional network reorganization in motor cortex can be explained by reward-modulated Hebbian learning. In: Proceedings of NIPS 2009: advances in neural information processing systems, vol 22. MIT Press, pp 1105–1113.Google Scholar
- McGeer T (1990) Passive dynamic walking. Int J Robot Res 9(2):62–82 ISSN 0278-3649Google Scholar
- Palm WJ III (1999) Modeling, analysis, and control of dynamic systems, 2nd edn. Wiley, New York. ISBN 0-471-07370-9Google Scholar
- Pfeifer R, Bongard JC (2007) How the body shapes the way we think. MIT Press, Cambridge. ISBN 0262162393Google Scholar
- Shim Y, Husbands P (2007) Feathered flyer: integrating morphological computation and sensory reflexes into a physically simulated flapping-wing robot for robust flight manoeuvre. In: Almeida e Costa F et al (eds) ECAL. Springer, Berlin, pp 756–765Google Scholar
- Slotine J-J E, Li J-J W (1991) Applied nonlinear control, 1st edn. Prentice Hall, Englewood CliffsGoogle Scholar
- Tedrake R, Zhang TW, Seung HS (2005) Learning to walk in 20 minutes. In: Proceedings of the fourteenth yale workshop on adaptive and learning systems. Yale University, New Haven, CT, 2005Google Scholar
- Vapnik VN (1998) Statistical learning theory. Wiley, New YorkGoogle Scholar
- Wiskott L, Sejnowski TJ (2002) Slow feature analysis: unsupervised learning of invariances. Neural Comput 14(4):715–770. ISSN 0899-7667Google Scholar
- Wisse M, Van Frankenhuyzen J (2003) Design and construction of MIKE; a 2D autonomous biped based on passive dynamic walking. In: Proceedings of international symposium of adaptive motion and animals and machines (AMAM03)Google Scholar
- Wood RJ (2007) Design, fabrication, and analysis of a 3DOF, 3cm flapping-wing MAV. IEEE/RSJ international conference on intelligent robots and systems, 2007. IROS 2007, 29 Oct–Nov 2 2007, pp 1576–1581. doi: 10.1109/IROS.2007.4399495
- Ziegler M, Iida F, Pfeifer R (2006) “Cheap” underwater locomotion: roles of morphological properties and behavioural diversity. In: CLAWARGoogle Scholar