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Towards a theoretical foundation for morphological computation with compliant bodies

Abstract

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.

References

  1. Atiya AF, Parlos AG (2000) New results on recurrent network training: unifying the algorithms and accelerating convergence. IEEE Trans Neural Networks 11(3): 697–709

    Article  CAS  Google Scholar 

  2. 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 1188–1192

    Google Scholar 

  3. Boyd S (1985) Volterra series: engineering fundamentals. PhD thesis, UC Berkeley

  4. Boyd S, Chua L (1985) Fading memory and the problem of approximating nonlinear operators with volterra series. IEEE Trans Circuits Syst 32(11): 1150–1161

    Article  Google Scholar 

  5. Collins S, Ruina A, Tedrake R, Wisse M (2005) Efficient bipedal robots based on passive-dynamic walkers. Science 307: 1082–1085

    PubMed  Article  CAS  Google Scholar 

  6. Ferris DP, Louie M, Farley CT (1998) Running in the real world: adjusting leg stiffness for different surfaces. Proc Biol Sci 265(1400): 989–994

    PubMed  Article  CAS  Google Scholar 

  7. Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9:1735–1780. ISSN 0899-7667

    Google Scholar 

  8. Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Networks 2(5): 359–366

    Article  Google Scholar 

  9. Iida F, Pfeifer R (2006) Sensing through body dynamics. Robot Auton Syst 54(8): 631–640

    Article  Google Scholar 

  10. Khalil HK (2002) Nonlinear Systems, 3rd edn, Prentice Hall, Upper Saddle River

  11. 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.

  12. Maass W, Sontag ED (2000) Neural systems as nonlinear filters.. Neural Comput 12(8): 1743–1772

    PubMed  Article  CAS  Google Scholar 

  13. Maass W, Natschlaeger T, Markram H (2002) Real-time computing without stable states: A new framework for neural computation based on perturbations. Neural Comput 14(11): 2531–2560

    PubMed  Article  Google Scholar 

  14. McGeer T (1990) Passive dynamic walking. Int J Robot Res 9(2):62–82 ISSN 0278-3649

    Google Scholar 

  15. Palm WJ III (1999) Modeling, analysis, and control of dynamic systems, 2nd edn. Wiley, New York. ISBN 0-471-07370-9

  16. Paul C (2006) Morphological computation: a basis for the analysis of morphology and control requirements. Robot Auton Syst 54(8): 619–630

    Article  Google Scholar 

  17. Paul C, Valero-Cuevas FJ, Lipson H (2006) Design and control of tensegrity robots for locomotion. IEEE Trans Robot 22(5):944–957. ISSN 1552-3098. doi:10.1109/TRO.2006.878980

    Google Scholar 

  18. Pfeifer R, Bongard JC (2007) How the body shapes the way we think. MIT Press, Cambridge. ISBN 0262162393

  19. Pfeifer R, Lungarella M, Iida F (2007) Self-organization, embodiment, and biologically inspired robotics. Science 318: 1088–1093

    PubMed  Article  CAS  Google Scholar 

  20. 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 756–765

  21. Slotine J-J E, Li J-J W (1991) Applied nonlinear control, 1st edn. Prentice Hall, Englewood Cliffs

    Google Scholar 

  22. 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, 2005

  23. Vapnik VN (1998) Statistical learning theory. Wiley, New York

    Google Scholar 

  24. Wiskott L, Sejnowski TJ (2002) Slow feature analysis: unsupervised learning of invariances. Neural Comput 14(4):715–770. ISSN 0899-7667

    Google Scholar 

  25. 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)

  26. 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

  27. Ziegler M, Iida F, Pfeifer R (2006) “Cheap” underwater locomotion: roles of morphological properties and behavioural diversity. In: CLAWAR

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Acknowledgments

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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Correspondence to Helmut Hauser.

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Hauser, H., Ijspeert, A.J., Füchslin, R.M. et al. Towards a theoretical foundation for morphological computation with compliant bodies. Biol Cybern 105, 355–370 (2011). https://doi.org/10.1007/s00422-012-0471-0

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Keywords

  • Morphological computation
  • Embodiment
  • Analog computation
  • Volterra series
  • Nonlinear mass-spring systems