Biological Cybernetics

, Volume 97, Issue 1, pp 47–61 | Cite as

Animal navigation: the difficulty of moving in a straight line

  • Allen CheungEmail author
  • Shaowu Zhang
  • Christian Stricker
  • Mandyam V. Srinivasan
Original Paper


In principle, there are two strategies for navigating a straight course. One is to use an external directional reference and continually reorienting with reference to it, while the other is to infer body rotations from internal sensory information only. We show here that, while the first strategy will enable an animal or mobile agent to move arbitrarily far away from its starting point, the second strategy will not do so, even after an infinite number of steps. Thus, an external directional reference—some form of compass—is indispensable for ensuring progress away from home. This limitation must place significant constraints on the evolution of biological navigation systems. Some specific examples are discussed. An important corollary arising from the analysis of compassless navigation is that the maximum expected displacement represents a robust measure of the straightness of a path.


Random Walk Step Length Mobile Agent Path Integration Angular Error 
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. Batschelet E (1981) Circular statistics in biology. Academic, LondonGoogle Scholar
  2. Benhamou S, Sauvé J-P, Bovet P (1990) Spatial memory in large scale movements: efficiency and limitation of the egocentric coding process. J Theor Biol 145:1–12CrossRefGoogle Scholar
  3. Bovet P, Benhamou S (1988) Spatial analysis of animals’ movements using a correlated random walk model. J Theor Biol 131:419–433CrossRefGoogle Scholar
  4. Byers J (2001) Correlated random walk equations of animal dispersal resolved by simulation. Ecology 82(6):1680–1690CrossRefGoogle Scholar
  5. Capaldi EA, Smith AD, Osborne JL, Fahrbach SE, Farris SM, Reynolds DR, Edwards AS, Martin A, Robinson GE, Poppy GM, Riley JR (2000) Ontogeny of orientation flight in the honeybee revealed by harmonic radar. Nature 403(6769):537–540PubMedCrossRefGoogle Scholar
  6. Chittka L, Williams NM, Rasmussen H, Thomson JD (1999) Navigation without vision: Bumblebee orientation in complete darkness. Proc R Soc Lond B 266:45–50CrossRefGoogle Scholar
  7. Collett TS, Rees JA (1997) View-based navigation in hymenoptera: multiple strategies of landmark guidance in the approach to a feeder. J Comp Physiol A 181:47–58CrossRefGoogle Scholar
  8. Dacke M, Nilsson D-E, Scholtz C, Byrne M, Warrant EJ (2003) Animal behaviour: Insect orientation to polarized moonlight. Nature 424:33PubMedCrossRefGoogle Scholar
  9. Etienne AS, Maurer R, Berlie J, Reverdin B, Rowe T, Georgakopoulos J, Séguinot V (1998) Navigation through vector addition. Nature 396:161–164PubMedCrossRefGoogle Scholar
  10. Etienne AS, Maurer R, Séguinot V (1996) Path integration in mammals and its interaction with visual landmarks. J Exp Biol 199:201-209PubMedGoogle Scholar
  11. Gallistel CR (1990) The Organisation of Learning. MIT Press, CambridgeGoogle Scholar
  12. Görner P, Claas B (1985) Homing behavior and orientation in the funnel-web spider, Agelena labyrinthica. In: Barth FG (ed) Neurobiology of arachnids. Springer, Berlin, pp 275–297Google Scholar
  13. Hartmann G, Wehner R (1995) The ant’s path integration system: a neural architecture. Biol Cybern 73:483–497Google Scholar
  14. Ingemar JC (1991) Blanche—an experiment in guidance and navigation of an autonomous robot vehicle. IEEE Trans Robot Autom 7:193–204CrossRefGoogle Scholar
  15. Kareiva PM, Shigesada N (1983) Analyzing insect movement as a correlated random walk. Oecologia 56:234–238CrossRefGoogle Scholar
  16. McCulloch CE, Cain ML (1989) Analyzing discrete movement data as a correlated random walk. Ecology 70(2):383–388CrossRefGoogle Scholar
  17. Mantegna RN, Stanley HE (1994) Stochastic process with ultraslow convergence to a Gaussian: the truncated Lévy flight. Phys Rev Lett 73:2946–2949PubMedCrossRefGoogle Scholar
  18. Mardia KV (1972) Statistics of directional data. Academic, LondonGoogle Scholar
  19. Mittelstaedt H, Mittelstaedt ML (1982) Homing by path integration. In: Papi F, Wallraff HG (eds) Avian navigation. Springer, Berlin, pp 290–297Google Scholar
  20. Nahapetian B (1991) Limit theorems and some applications in statistical physics. Teubner, Leipzig, pp 22–23Google Scholar
  21. Nossal R, Weiss G (1974) A descriptive theory of cell migration on surfaces. J Theor Biol 47:103–113PubMedCrossRefGoogle Scholar
  22. Rosenblatt M (1956) Remarks on some nonparametric estimates of a density function. Ann Math Stat 27:832–835Google Scholar
  23. Seyfarth EA, Hergenröder R, Ebbes H, Barth FG (1982) Idiothetic orientation of a wandering spider: compensation of detours and estimates of goal distance. Behav Ecol Sociobiol 11:139–148CrossRefGoogle Scholar
  24. Shlesinger MF (1995) Comment on “Stochastic process with ultraslow convergence to a Gaussian: the truncated Lévy flight”. Phys Rev Lett 74:4959PubMedCrossRefGoogle Scholar
  25. Thrun S (1997) To know or not to know: on the utility of models in mobile robots. AI Mag 18:47–54Google Scholar
  26. Viswanathan GM, Buldyrev SV, Havlin S, da Luz MGE, Raposo EP, Stanley HE (1999) Optimizing the success of random searches. Nature 401:911–914PubMedCrossRefGoogle Scholar
  27. Wehner R (1987) Spatial organization of foraging behavior in individually searching desert ants, Cataglyphis (Sahara Desert) and Ocymyrmex (Namib Desert). Behav Soc Insects (Experientia Supplementum) 54:15–42Google Scholar
  28. Wehner R (1992) Arthropods. In: Papi F (ed) Animal homing. Chapman and Hall, London, pp 45–144Google Scholar
  29. Wehner R (1994) The polarization-vision project: championing organismic biology. Fortschritte der Zoologie 39:103–143Google Scholar
  30. Wiltschko W, Wiltschko R (2005) Magnetic orientation and magnetoreception in birds and other animals. J Comp Physiol A 191(8):675–693CrossRefGoogle Scholar
  31. Wittmann T, Schwegler H (1995) Path integration—a network model. Biol Cybern 73:569–575CrossRefGoogle Scholar
  32. Wolf H and Wehner R (2005) Desert ants compensate for navigation uncertainty. J Exp Biol 208:4223–4230PubMedCrossRefGoogle Scholar
  33. Zollikofer CPE (1994) Stepping patterns in ants. II. Influence of body morphology. J Exp Biol 192:107–118PubMedGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Allen Cheung
    • 1
    Email author
  • Shaowu Zhang
    • 1
  • Christian Stricker
    • 2
  • Mandyam V. Srinivasan
    • 1
  1. 1.Centre of Excellence in Vision Science, Research School of Biological SciencesAustralian National UniversityCanberraAustralia
  2. 2.John Curtin School of Medical ResearchAustralian National UniversityCanberraAustralia

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