Natural Computing

, Volume 6, Issue 3, pp 311–337 | Cite as

Reflex-oscillations in evolved single leg neurocontrollers for walking machines

  • Arndt von Twickel
  • Frank Pasemann


As a prerequisite for developing neural control for walking machines that are able to autonomously navigate through rough terrain, artificial structure evolution is used to generate various single leg controllers. The structure and dynamical properties of the evolved (recurrent) neural networks are then analysed to identify elementary mechanisms of sensor-driven walking behaviour. Based on the biological understanding that legged locomotion implies a highly decentralised and modular control, neuromodules for single, morphological distinct legs of a hexapod walking machine were developed by using a physical simulation. Each of the legs has three degrees of freedom (DOF). The presented results demonstrate how extremely small reflex-oscillators, which inherently rely on the sensorimotor loop and e.g. hysteresis effects, generate effective locomotion. Varying the fitness function by randomly changing the environmental conditions during evolution, neural control mechanisms are identified which allow for robust and adaptive locomotion. Relations to biological findings are discussed.


artificial evolution modular locomotion control neural control neurodynamics reflex-oscillators walking machines 



Anterior extreme position


Central pattern generator




Degrees of freedom










Posterior extreme position




Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The authors would like to thank Martin Hülse, Steffen Wischmann and Keyan Zahedi for providing the evolution environment ISEE, Manfred Hild, Niko Kladt and Hans-Georg Heinzel for carefully reading and commenting on an earlier draft of this paper and an anonymous reviewer for valuable comments.


  1. Bässler U, Büschges A (1998) Pattern generation for stick insect walking movements – multisensory control of a locomotor program. Brain Research Reviews 27:65–88CrossRefGoogle Scholar
  2. Beer R, Gallagher J (1992) Evolving dynamical neural networks for adaptive behavior. Adaptive Behavior 1:91–122CrossRefGoogle Scholar
  3. Brooks RA (1989) A Robot that Walks: Emergent Behaviors from a Carefully Evolved Network. Technical Report AI MEMO 1091, MITGoogle Scholar
  4. Brooks RA (1991) Intelligence without representation. Artificial Intelligence 47:139–159CrossRefGoogle Scholar
  5. Buddenbrock Wv (1921) Der Rhythmus der Schreitbewegungen der Stabheuschrecke Dyxippus. Biologisches Zentralblatt 41:41–48Google Scholar
  6. Büschges A (2005) Sensory control and organization of neural networks mediating coordination of multisegmental organs for locomotion. Journal of Neurophysiology 93:1127–1135CrossRefGoogle Scholar
  7. Büschges A, Schmitz J, Bässler U (1995) Rhythmic patterns in the thoracic nerve cord of the stick insect induced by pilocarpine. Journal of Experimental Biology 198:435–456Google Scholar
  8. Chiel H, Beer R (1997) The brain has a body: adaptive behavior emerges from interactions of nervous system, body and environment. Trends in Neurosciences 20:553–557CrossRefGoogle Scholar
  9. Cruse H (1990) What mechanisms coordinate leg movement in walking arthropods? Trends in Neurosciences 13:15–21CrossRefGoogle Scholar
  10. Cruse H (2002) The functional sense of central oscillations in walking. Biological Cybernetics 86:271–280zbMATHCrossRefGoogle Scholar
  11. Cruse H, Bartling C (1995) Movement of joint angles in the legs of a walking insect, Carausius morosus. Journal of Insect Physiology 41(9):761–771CrossRefGoogle Scholar
  12. Dean J (1998) Animats and what they can tell us. Trends in Cognitive Science 2(2):60–67CrossRefGoogle Scholar
  13. Dean J, Kindermann T, Schmitz J, Schumm M, Cruse H (1999) Control of walking in the stick insect: from behavior and physiology to modeling. Autonomous Robots 7:271–288CrossRefGoogle Scholar
  14. Delcomyn F (1999) walking robots and the central and peripheral control of locomotion in insects. Autonomous Robots 7:259–270CrossRefGoogle Scholar
  15. Dickinson MH, Farley CT, Full RJ, Koehl MAR, Kram R, Lehmann S (2000) How animals move: an integrative view. Science 288:100–106CrossRefGoogle Scholar
  16. Dumont JPC, Robertson RM (1986) Neuronal circuits: an evolutionary perspective. Science 233:849–853CrossRefGoogle Scholar
  17. Ekeberg O, Blümel M, Büsschges A (2004) Dynamic simulation of insect walking. Arthropod Structure & Development 33:287–300CrossRefGoogle Scholar
  18. Ferrell C (1995) A comparison of three insect inspired locomotion controllers. Robotics and Autonomous Systems 16:135–159CrossRefGoogle Scholar
  19. Full RJ (1997) Invertebrate locomotor systems. In: Dantzler W (ed) The Handbook of Comparative Physiology, pp. 853–930. Oxford University PressGoogle Scholar
  20. Grillner S, Ekeberg O, Manira AE, Lansner A, Parker D, Tegner J, Wallen P (1998) Intrinsic function of a neuronal network – a vertebrate central pattern generator. Brain Research Reviews 26(2–3):184–197CrossRefGoogle Scholar
  21. Hatsopoulos NG, Burrows M, Laurent G (1995) Hysteresis reduction in proprioception using presynaptic shunting inhibition. Journal of Neurophysiology 73(3):1031–1042Google Scholar
  22. Heinzel H-G, Weimann JM, Marder E (1993) The behavioral repertoire of the gastric mill in the crab, cancer pagurus: an in situ endoscopic and electrophysiological examination. The Journal of Neuroscience 13(4):1793–1803Google Scholar
  23. Hülse M, Wischmann S, Pasemann F (2004) Structure and function of evolved neuro-controllers for autonomous robots. Connection Science 16(4):294–266CrossRefGoogle Scholar
  24. Jacob D, Polani D and Nehaniv CL (2005) Legs that can walk: embodiment-based modular reinforcement learning applied. In: IEEE Computational Intelligence in Robotics & Automata (IEEE CIRA 2005). pp 365–372Google Scholar
  25. Jindrich DL, Full RJ (2002) Dynamic stabilization of rapid hexapedal locomotion. Journal of Experimental Biology 205:2803–2823Google Scholar
  26. Kononenko NI, Dudek FE (2006) Persistent calcium current in rat suprachiasmatic nucleus neurons. Neuroscience 138:377–388CrossRefGoogle Scholar
  27. Kostyukov AI (1998) Muscle hysteresis and movement control: a theoretical study. Neuroscience 83(1):303–320CrossRefGoogle Scholar
  28. Lee RH, Heckman CJ (1998) Bistability in spinal motoneurons in vivo: systematic variations in persistent inward currents. Journal of Neurophysiology 80:583–593Google Scholar
  29. Linder CR (2005) Embodiment in two dimensions. In: Proceedings of the 7th International Conference on Climbing and Walking Robots 2004Google Scholar
  30. Nolfi S, Floreano D (2000) Evolutionary robotics: the biology, intelligence, and technology of self-organizing machines. MIT Press, Cambridge, MAGoogle Scholar
  31. Orlovsky G, Deliagina T and Grillner S (1999) Neuronal Control of Locomotion. Oxford University PressGoogle Scholar
  32. Pasemann F (1993) Dynamics of a single model neuron. International Journal of Bifurcation and Chaos 2:271–278CrossRefGoogle Scholar
  33. Pasemann F (2002) Complex dynamics and the structure of small neural networks. Network: Computation in neural systems 13:195–216zbMATHGoogle Scholar
  34. Pasemann F, Hild M and Zahedi K (2003) SO(2)-networks as neural oscillators. In: Mira J and Alvarez J (eds) Computational Methods in Neural Modeling, pp. 144–151. Springer, BerlinGoogle Scholar
  35. Pearson KG, Franklin R (1984) Characteristics of leg movements and patterns of coordination in locusts walking on rough terrain. International Journal of Robotics Research 3(2):101–112CrossRefGoogle Scholar
  36. Prochazka A, Gillard D, Bennett DJ (1997) Implications of positive feedback in the control of movement. The Journal of Neurophysiology 77(6):3237–3251Google Scholar
  37. Psujek S, Ames J, Beer R (2006) Connection and coordination: the interplay between architecture and dynamics in evolved model pattern generators. Neural Computation 18:729–747zbMATHCrossRefGoogle Scholar
  38. Quinn RD, Nelson GM, Bachmann RJ, Kingsley DA, Offi JT, Allen TJ, Ritzmann RE (2003) Parallel complementary strategies for implementing biological principles into mobile robots. International Journal of Robotics Research 22(3):169–186CrossRefGoogle Scholar
  39. Schmitz J, Dean J, Kindermann T, Schumm M, Cruse H (2001) A biologically inspired controller for hexapod walking: simple solutions by exploiting physical properties. The Biological Bulletin 200:195–200CrossRefGoogle Scholar
  40. Selverston AI, Panchin YV, Arshavsky YI, Orlovsky GN (1999) Neurons, Networks, and Motor Behavior, Chapt. Shared Features of Invertebrate Central Pattern Generators. MIT Press, Cambridge, MA, pp. 105–117Google Scholar
  41. Toth TI, Hughes SW, Crunelli V (1998) Analysis and biophysical interpretation of bistable behaviour in thalamocortical neurons. Neuroscience 87(2):519–523CrossRefGoogle Scholar
  42. Wendler G (1966) The co-ordination of walking movements in arthropods. Symposia of the Society for Experimental Biology 20:229–249Google Scholar
  43. Zill SN and Jepson-Innes K (1988) Evolutionary adaptation of a reflex system: sensory hysteresis counters muscle ‘catch’ tension. Journal of Comparative Physiology A 164:43–48CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Fraunhofer Institute AISSankt AugustinGermany

Personalised recommendations