Analytical modeling of a 3-D snake robot based on sidewinding locomotion

  • Mohsen Malayjerdi
  • Alireza Akbarzadeh


In this paper, we restrict our attention to sidewinding locomotion and present detailed kinematics and dynamics of a 3-D multi-link snake robot. To obtain kinematics of three-dimensional snake-like robot modeling, first, a virtual structure with an additional six degrees of freedom is attached to the tail of the robot. Denavit–Hartenberg method is next employed to derive the kinematics relationships. A spring and damper model is used to realistically model contacts between ground and the robot. Gibbs–Appell’s method is next utilized to obtain the 3-D robot dynamics. To validate the dynamics equations, SimMechanic software is used. Finally, a 3-D snake robot, referred to as FUM-Snake 5, is constructed and utilized to experimentally show the sidewinding locomotion. The theoretical derived equation in this study can also be used to generate both other 2-D and 3-D snake robot locomotions.


Dynamic analysis Gibbs–Appell 3-D snake-like robot Friction and ground model 


  1. 1.
    Hirose S (1993) Biologically inspired robots: snake-like locomotors and manipulators. Oxford University Press, OxfordGoogle Scholar
  2. 2.
    Hasanzadeh Sh, Tootoonchi AA (2010) Ground adaptive and optimized locomotion of snake robot moving with a novel gait. Auton Robot 28:457–470. CrossRefGoogle Scholar
  3. 3.
    Akbarzadeh A, Kalani H (2012) Design and modeling of a snake robot based on worm-like locomotion. Adv Robot 26:537–560. CrossRefGoogle Scholar
  4. 4.
    Kalani H, Akbarzadeh A, Safehian J (2010) Traveling wave locomotion of snake robot along symmetrical and unsymmetrical body shapes. ISR-Robotik, 7–9 June, MunichGoogle Scholar
  5. 5.
    Saito M, Fukaya M, Iwasaki T (2002) Modeling, analysis, and synthesis of serpentine locomotion with a multilink robotic snake. IEEE Control Syst Mag 22(1):64–81. CrossRefGoogle Scholar
  6. 6.
    Ma S (2001) Analysis of creeping locomotion of a snake-like robot. Adv Robot 15:205–224. CrossRefGoogle Scholar
  7. 7.
    Ma S, Tadokoro N (2006) Analysis of creeping locomotion of a snake-like robot on a slope. Auton Robots 20:15–23. CrossRefGoogle Scholar
  8. 8.
    Wang Z, Ma S, Li B, Wang Y (2011) A unified dynamic model for locomotion and manipulation of a snake-like robot based on differential geometry. Sci China F 54:318–333. MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Ma S, Ohmameuda Y, Inoue K (2004) Dynamic analysis of 3-dimensional snake robots. In: Proceedings of IEEE/RSJ international conference on intelligent robots and systems, Sendai, pp 767–772.
  10. 10.
    Vossoughi G, Pendar H, Heidari Z, Mohammadi S (2008) Assisted passive snake-like robots: conception and dynamic modeling using Gibbs–Appell method. Robotica 26:267–276. CrossRefGoogle Scholar
  11. 11.
    Liljebäck P, Stavdahl Ø, Pettersen KY (2005) Modular pneumatic snake robot: 3-D modelling, implementation and control. In: Proceedings 16th IFAC world congress, Prague, pp 19–24.
  12. 12.
    Liljebäck P, Stavdahl Ø, Pettersen KY (2008) Modular pneumatic snake robot: 3D modelling, implementation and control. Model Identif Control 29(1):21–28. CrossRefGoogle Scholar
  13. 13.
    Transeth AA et al (2008) 3-D snake robot motion: nonsmooth modeling, simulations, and experiments. IEEE Trans Robot 24(2):361–376. CrossRefGoogle Scholar
  14. 14.
    Transeth AA (2007) Modelling and control of snake robots. Dissertation, TrondheimGoogle Scholar
  15. 15.
    Kalani H, Akbarzadeh A, Nabavi SN, Moghimi S (2018) Dynamic modeling and CPG-based trajectory generation for a masticatory rehab robot. Intell Serv Robot 11(2):187–205. CrossRefGoogle Scholar
  16. 16.
    Desoyer K, Lugner P (1989) Recursive formulation for the analytical or numerical application of the Gibbs–Appell method to the dynamics of robots. Robotica 7(4):343–347. CrossRefGoogle Scholar
  17. 17.
    Ginsberg JH (1998) Advanced engineering dynamics. Cambridge University Press, New YorkzbMATHGoogle Scholar
  18. 18.
    Greenwood DT (2003) Advanced dynamics. Cambridge University Press, New YorkCrossRefGoogle Scholar
  19. 19.
    Liljebäck P (2011) Modelling, Development, and Control of Snake Robots. Dissertation, NTNUGoogle Scholar
  20. 20.
    Hatton RL, Choset H (2010) Generating gaits for snake robots: annealed chain fitting and keyframe wave extraction. Auton Robots 28(3):271–281. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center of Excellence on Soft Computing and Intelligent Information Processing, (SCIIP) Mechanical Engineering DepartmentFerdowsi University of MashhadMashhadIran

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