, Volume 52, Issue 3, pp 587–601 | Cite as

Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler

  • Paolo Gidoni
  • Antonio DeSimoneEmail author
Advances in Biomechanics: from foundations to applications


We formulate and solve the locomotion problem for a bio-inspired crawler consisting of two active elastic segments (i.e., capable of changing their rest lengths), resting on three supports providing directional frictional interactions. The problem consists in finding the motion produced by a given, slow actuation history. By focusing on the tensions in the elastic segments, we show that the evolution laws for the system are entirely analogous to the flow rules of elasto-plasticity. In particular, sliding of the supports and hence motion cannot occur when the tensions are in the interior of certain convex regions (stasis domains), while support sliding (and hence motion) can only take place when the tensions are on the boundary of such regions (slip surfaces). We solve the locomotion problem explicitly in a few interesting examples. In particular, we show that, for a suitable range of the friction parameters, specific choices of the actuation strategy can lead to net displacements also in the direction of higher friction.


Soft bio-mimetic robots Crawling motility Directional surfaces Rate-independent systems 



This work has been supported by the ERC Advanced Grant 340685-MicroMotility.


  1. 1.
    Arroyo M, Heltai L, Milan D, DeSimone A (2012) Reverse engineering the euglenoid movement. Proc Nat Acad Sci USA 109:17874–17879. doi: 10.1073/pnas.1213977109 ADSCrossRefGoogle Scholar
  2. 2.
    Bolotnik N, Pivovarov M, Zeidis I, Zimmermann K (2015) On the motion of lumped-mass and distributed-mass self-propelling systems in a linear resistive environment. Z Angew Math Mech. doi: 10.1002/zamm.201500091
  3. 3.
    Borisenko IN, Figurina TYu, Chernousko FL (2014) The quasi-static motion of a three body system on a plane. J Appl Math Mech 78:220–227. doi: 10.1016/j.jappmathmech.2014.09.003 MathSciNetCrossRefGoogle Scholar
  4. 4.
    DeSimone A, Tatone A (2012) Crawling motility through the analysis of model locomotors: two case studies. Eur Phys J E 35:85. doi: 10.1140/epje/i2012-12085-x CrossRefGoogle Scholar
  5. 5.
    DeSimone A, Guarnieri F, Noselli G, Tatone A (2013) Crawlers in viscous environments: linear vs non-linear rheology. Int J Non-Linear Mech 56:142–147. doi: 10.1016/j.ijnonlinmec.2013.02.007 CrossRefGoogle Scholar
  6. 6.
    DeSimone A, Gidoni P, Noselli G (2015) Liquid crystal elastomer strips as soft crawlers. J Mech Phys Solids 85:254–272. doi: 10.1016/j.jmps.2015.07.017 ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Gidoni P, Noselli G, DeSimone A (2014) Crawling on directional surfaces. Int J Non-Linear Mech 61:65–73. doi: 10.1016/j.ijnonlinmec.2014.01.012 CrossRefGoogle Scholar
  8. 8.
    Hirose S (1993) Biologically inspired robots: snake-like locomotors and manipulators. Oxford University Press, OxfordGoogle Scholar
  9. 9.
    Ikuta K, Hasegawa T, Daifu S (2003) Hyper redundant miniature manipulator Hyper Finger for remote minimally invasive surgery in deep area. In: Proceeding of IEEE International Conference on Robotics and Automation, Vol. 1, Taipei, pp 1098–1102Google Scholar
  10. 10.
    Magnasco MO (1993) Forced thermal ratchets. Phys Rev Lett 71:1477–1481. doi: 10.1103/PhysRevLett.71.1477 ADSCrossRefGoogle Scholar
  11. 11.
    Menciassi A, Dario P (2003) Bio-inspired solutions for locomotion in the gastrointestinal tract: background and perspectives. Phil Trans R Soc Lond A 361:2287–2298. doi: 10.1098/rsta.2003.1255 ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Menciassi A, Accoto D, Gorini S, Dario P (2006) Development of a biomimetic miniature robotic crawler. Auton Robot 21:155–163. doi: 10.1007/s10514-006-7846-9 CrossRefGoogle Scholar
  13. 13.
    Mielke A, Theil F (2004) On rate-independent hysteresis models. NoDEA Nonlinear Differ Equ Appl 11(2):151–189. doi: 10.1007/s00030-003-1052-7 MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Mielke A (2005) Evolution of rate-independent systems. In: Dafermos C, Feireisl E (eds) Handbook of Differential Equations, evolutionary equations. Elsevier, AmsterdamGoogle Scholar
  15. 15.
    Mielke A, Roubíček T (2015) Rate-independent systems. Theory and application. Springer, BerlinCrossRefzbMATHGoogle Scholar
  16. 16.
    Montino A, DeSimone A (2015) Three-sphere low-Reynolds-number swimmer with a passive elastic arm. Eur Phys J E 38:42. doi: 10.1140/epje/i2015-15042-3 CrossRefGoogle Scholar
  17. 17.
    Noselli G, DeSimone A, Tatone A (2013) Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost. Mech Res Commun 58:73–81. doi: 10.1016/j.mechrescom.2013.10.023 CrossRefGoogle Scholar
  18. 18.
    Noselli G, DeSimone A (2014) A robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model. Proc Roy Soc Lond A 470:20140333. doi: 10.1098/rspa.2014.0333 ADSCrossRefGoogle Scholar
  19. 19.
    Recho P, Truskinovsky L (2016) Maximum velocity of self-propulsion for an active segment. Math Mech Solids 21:263–278. doi: 10.1177/1081286515588675 MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Sheshka R, Recho P, Truskinovsky L (2015) Pseudo energy wells in active systems. Preprint arXiv:1509.02753v1
  21. 21.
    Steigenberger J, Behn C (2012) Worm-like locomotion systems. An intermediate theoretical approach. Oldenbourg Wissenschaftsverlag, BerlinCrossRefzbMATHGoogle Scholar
  22. 22.
    Zimmermann K, Zeidis I, Behn C (2009) Mechanics of terrestrial locomotion. Springer, BerlinzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.SISSA – International School for Advanced StudiesTriesteItaly
  2. 2.GSSI – Gran Sasso Science InstituteL’AquilaItaly

Personalised recommendations