Biological Cybernetics

, Volume 96, Issue 3, pp 323–340 | Cite as

Hexapod Walking: an expansion to Walknet dealing with leg amputations and force oscillations

  • Malte Schilling
  • Holk Cruse
  • Paolo Arena
Original Paper


The control of the legs of a walking hexapod is a complex problem as the legs have three joints each, resulting in a total of 18 degrees of freedom. We addressed this problem using a decentralized architecture termed Walknet, which consists of peripheral pattern generators being coordinated through influences acting mainly between neighbouring legs. Both, the coordinating influences and the local control modules (each acting only on one leg), are biologically inspired. This investigation shows that it is possible to adapt this approach to account for additional biological data by (1) changing the structure of the selector net in a biological plausible way (including force as an analog variable), (2) introducing a biologically motivated coordination influence for coactivation between legs and (3) adding a hypothetical influence between hind and front legs. This network of controllers has been tested using a dynamic simulation. It is able to describe (a) the behaviour of animals walking with one or two legs being amputated and (b) force oscillations that occur in a specific experimental situation, the standing legs of a walking animal.


Stick Insect Stable Gait Tripod Gait Posterior Extreme Position Simulated Animal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Bässler U (1977) Sense organs in the femur of the stick insect and their relevance to the control of position of the femur-tibia-joint. J Comp Physiol A 121:99–113CrossRefGoogle Scholar
  2. Batschelet E (1965) Statistical methods for the analysis of problems in animal orientation and certain biological rhythms. A.I.B.S. monographGoogle Scholar
  3. Beckers U (2002) Die Kontrolle sechsbeinigen Laufens: Erweiterung des Simulationssystems Walknet zur quantitativen Beschreibung verschiedener biologischer Experimente. Master’s thesis, Department of Biological Cybernetics, University of BielefeldGoogle Scholar
  4. Bläsing B, Cruse H (2004) Stick insect locomotion in a complex environment: climbing over large gaps.J Exp Biol 207: 1273–1286CrossRefGoogle Scholar
  5. Brooks RA (1991) Intelligence without reason. In: Myopoulos J, Reiter R (eds) Proceedings of the 12th international Joint conference on artificial Intelligence (IJCAI-91), p 569–595, Sydney, Australia, Morgan Kaufmann publishers Inc.: San Mateo, CA, USA. ISBN 1-55860-160-0.Google Scholar
  6. Clarac F, Chasserat C (1979) Experimental modification of interlimb coordination during locomotion of a crustacea. Neurosci Lett 12:271–276PubMedCrossRefGoogle Scholar
  7. Cruse H (2002) The functional sense of central oscillations in walking. Biol Cybernet 86:271–280CrossRefGoogle Scholar
  8. Cruse H (1976a) On the function of the legs in the free walking stick insect Carausius morosus. J Comp Physiol 112:235–262CrossRefGoogle Scholar
  9. Cruse H (1976b) The control of the body position in the stick insect (Carausius morosus), when walking over uneven surfaces. Biol Cybernet 24:25–33CrossRefGoogle Scholar
  10. Cruse H (1985a) Which parameters control the leg movement of a walking insect? II. The start of the swing phase. J Exp Biol 116:357–362Google Scholar
  11. Cruse H (1985b) Which parameters control the leg movement of a walking insect? I. Velocity control during the stance phase. J Exp Biol 116:343–355Google Scholar
  12. Cruse H, Saxler G (1980a) The coordination of force oscillations and of leg movement in a walking insect (carausius morosus). Biol Cybernet 36:165–171CrossRefGoogle Scholar
  13. Cruse H, Saxler G (1980b) Oscillations of force in the standing legs of a walking insect (Carausius morosus). Biol Cybernet 36:159–163CrossRefGoogle Scholar
  14. Cruse H, Clarac F, Chasserat C (1983) The control of walking movements in the leg of the rock lobster. Biol Cybernet 47: 87–94CrossRefGoogle Scholar
  15. Cruse H, Riemenschneider D, Stammer W (1989) Control of body position of a stick insect standing on uneven surfaces. Biol Cybernet 61:71–77CrossRefGoogle Scholar
  16. Cruse H, Schmitz J, Braun U, Schweins A (1993) Control of body height in a stick insect walking on a tread-wheel. J Exp Biol 181(1):141–155Google Scholar
  17. Cruse H, Kindermann T, Schumm M, Dean J, Schmitz J (1998) Walknet - a biologically inspired network to control six-legged walking. Neural Netw. 11(7-8):1435–1447 ISSN 0893-6080. Scholar
  18. Delcomyn F (1991a) Perturbation of the motor system in freely walking cockroaches. II. The timing of motor activity in leg muscles after amputation of a middle leg. J Exp Biol 156: 503–517 ISSN 0022-0949 (Print)Google Scholar
  19. Delcomyn F (1991b) Perturbation of the motor system in freely walking cockroaches. I. Rear leg amputation and the timing of motor activity in leg muscles. J Exp Biol 156:483–502 ISSN 0022-0949 (Print)Google Scholar
  20. Diederich B, Schumm M, Cruse H (2002) Stick insects walking along inclined surfaces. Integr Comp Biol 42(1):165–173CrossRefGoogle Scholar
  21. Dürr V, Schmitz J, Cruse H (2004) Behaviour-based modelling of hexapod locomotion: Linking biology and technical application. Arthropod Struct Dev 33(3):237–250CrossRefPubMedGoogle Scholar
  22. Graham D (1977) The effect of amputation and leg restraint on the free walking coordination of the stick insect Carausius morosus. J Comp Physiol A 116(1): 91–116CrossRefGoogle Scholar
  23. Duysens J, Clarac F, Cruse H (2000) Load-regulating mechanisms in gait and posture: comparative aspects. Physiol Rev 80:83–133PubMedGoogle Scholar
  24. Kindermann T (2002) Behavior and adaptability of a six-legged walking system with highly distributed control. Adapt Behav 9(1):16–41CrossRefGoogle Scholar
  25. Klein J (2003) breve: a 3D environment for the simulation of decentralized systems and artificial life. In: ICAL 2003: Proceedings of the eighth international conference on Artificial life, pp 329–334, Cambridge, MIT ISBN 0-262-69281-3Google Scholar
  26. Pearson KG (1972) Central programming and reflex control of walking in the cockroach. J Exp Biol 56:173–193Google Scholar
  27. Schmitz J (1993) Load compensatory reactions in the proximal leg joints of stick insects during standing and walking. J Exp Biol 183:15–33Google Scholar
  28. Schmitz J, Haßfeld G (1989) The treading-on-tarsus reflex in stick insects: phase-dependence and modifications of the motor output during walking. J Exp Biol 143:373–388Google Scholar
  29. Schmitz J, von Kamp A, Kindermann T, Cruse H (1998) Adaptations to increased load in a control system governing movements of biological and artificial walking machines. In: Blickhan R, Nachtigall W (eds) BIONA reports 13: Motion SystemsGoogle Scholar
  30. Wendler G (1964) Laufen und Stehen der Stabheuschrecke Carausius morosus: Sinnesborstenfelder in den Beingelenken als Glieder von Regelkreisen. Z vergl Physiol 48:198–250CrossRefGoogle Scholar
  31. Wendler G (1966) The coordination of walking movements in arthropods. Symp Soc Exp Biol 20:229–259PubMedGoogle Scholar
  32. Wendler G (1968) Ein Analogmodell der Beinbewegungen eines laufenden Insekts. In Kybernetik 1968, Beihefte zu “elektronischen Anlagen”, Bd. 18, 68–74. Oldenbourg, München, Wien, 1968Google Scholar
  33. Zill S, Schmitz J, Büschges A (2004) Load sensing and control of posture and locomotion. Arthrop Struct Dev 33:273–286CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Biological Cybernetics and Theoretical BiologyUniversity of BielefeldBielefeldGermany
  2. 2.Dipartimento di Ingegneria Elettrica Elettronica e dei SistemiUniversita degli Studi di CataniaCataniaItaly

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