Biological Cybernetics

, Volume 106, Issue 10, pp 595–613 | Cite as

The role of feedback in morphological computation with compliant bodies

  • Helmut HauserEmail author
  • Auke J. Ijspeert
  • Rudolf M. Füchslin
  • Rolf Pfeifer
  • Wolfgang Maass
Open Access
Original Paper


The generation of robust periodic movements of complex nonlinear robotic systems is inherently difficult, especially, if parts of the robots are compliant. It has previously been proposed that complex nonlinear features of a robot, similarly as in biological organisms, might possibly facilitate its control. This bold hypothesis, commonly referred to as morphological computation, has recently received some theoretical support by Hauser et al. (Biol Cybern 105:355–370, doi: 10.1007/s00422-012-0471-0, 2012). We show in this article that this theoretical support can be extended to cover not only the case of fading memory responses to external signals, but also the essential case of autonomous generation of adaptive periodic patterns, as, e.g., needed for locomotion. The theory predicts that feedback into the morphological computing system is necessary and sufficient for such tasks, for which a fading memory is insufficient. We demonstrate the viability of this theoretical analysis through computer simulations of complex nonlinear mass–spring systems that are trained to generate a large diversity of periodic movements by adapting the weights of a simple linear feedback device. Hence, the results of this article substantially enlarge the theoretically tractable application domain of morphological computation in robotics, and also provide new paradigms for understanding control principles of biological organisms.


Morphological computation Nonlinear system Limit cycles compliant robots 



Written under partial support by the European Union projects project # FP7-231267 (ORGANIC), # 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, Stefan Häusler for fruitful discussions, and Rodney Douglas for his advice regarding biological data.

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Supplementary material

422_2012_516_MOESM1_ESM.pdf (228 kb)
ESM 1 (PDF 228 kb)


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Copyright information

© The Author(s) 2012

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Helmut Hauser
    • 1
    Email author
  • Auke J. Ijspeert
    • 3
  • Rudolf M. Füchslin
    • 1
    • 2
  • Rolf Pfeifer
    • 1
  • Wolfgang Maass
    • 4
  1. 1.Artificial Intelligence Laboratory, Department of InformaticsUniversity of ZurichZurichSwitzerland
  2. 2.ZHAW Zurich University of Applied Sciences, Center for Applied Mathematics and Physics ZAMPWinterthurSwitzerland
  3. 3.École Polytechnique Fédérale de Lausanne, Biorobotics Laboratory BIOROBLausanneSwitzerland
  4. 4.Graz University of Technology, Institute for Theoretical Computer ScienceGrazAustria

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