Skip to main content
SpringerLink
Log in

Plane-Parallel Motion of a Snake Robot in the Presence of Anisotropic Dry Friction and a Single Control Input

  • ROBOTICS
  • Published:
Journal of Computer and Systems Sciences International Aims and scope

Abstract

A snake robot moving along a rough plane is considered. Anisotropic dry friction acts at the points of contact with the support. The link joints are passive, but coil springs are installed in them. The following robot configurations are compared: one-, two-, and three-link. The only control action is the torque applied to the flywheel installed in the head link. A control is constructed that ensures the steady motion of the robot, in which the center of mass moves along a serpentine trajectory. The specified configurations with identical dimensions, weight, and control restrictions are compared in terms of the average velocity of the progression of the center of mass and by the width of the path required for movement.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.

Similar content being viewed by others

REFERENCES

  1. F. L. Chernous’ko, “On the motion of a rigid body with movable internal masses,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 33–44 (1973).

  2. V. V. Kozlov and S. M. Ramodanov, “On the motion of a body with a rigid shell and variable mass geometry in a perfect fluid,” Dokl. Phys. 47, 132–135 (2002).

    Article  MathSciNet  Google Scholar 

  3. S. Childress, S. E. Spagnolie, and T. Tokieda, “A bug on a raft: Recoil locomotion in a viscous fluid,” J. Fluid Mech. 669, 527–556 (2011).

    Article  MathSciNet  Google Scholar 

  4. F. L. Chernousko, “Locomotion of multibody robotic systems: Dynamics and optimization,” Theor. Appl. Mech. 45, 17–33 (2018).

    Article  Google Scholar 

  5. L. Yu. Volkova and S. F. Yatsun, “Control of the three-mass robot moving in the liquid environment,” Russ. J. Nonlin. Dyn. 7, 845–857 (2011).

    Google Scholar 

  6. N. N. Bolotnik, T. Yu. Figurina, and F. L. Chernous’ko, “Optimal control of the rectilinear motion of a two-body system in a resistive medium,” J. Appl. Math. Mech. 76, 1–14 (2012).

    Article  MathSciNet  Google Scholar 

  7. M. J. Fairchild, P. M. Hassing, S. D. Kelly, P. Pujari, and P. Tallapragada, “Single-input planar navigation via proportional heading control exploiting nonholonomic mechanics or vortex shedding,” in Proceedings of the Dynamic Systems and Control Conference, Arlington, Virginia, USA, 2011, Vol. 54754, pp. 345–352.

  8. A. A. Kilin, A. I. Klenov, and V. A. Tenenev, “Controlling the movement of the body using internal masses in a viscous liquid,” Komp’yut. Issled. Model. 10, 445–460 (2018).

    Google Scholar 

  9. N. N. Bolotnik, P. A. Gubko, and T. Yu. Figurina, “Possibility of a non-reverse periodic rectilinear motion of a two-body system on a rough plane,” Mech. Solids 53 (1), 7–15 (2018).

    Article  Google Scholar 

  10. F. L. Chernousko, “Two- and three-dimensional motions of a body controlled by an internal movable mass,” Nonlin. Dyn. 99, 793–802 (2020).

    Article  Google Scholar 

  11. T. Yu. Figurina, “Optimal control of system of material points in a straight line with dry friction,” J. Comput. Syst. Sci. Int. 54, 671 (2015).

    Article  MathSciNet  Google Scholar 

  12. F. L. Chernous’ko, “Plane motions of a body controlled by means of a movable mass,” Dokl. Akad. Nauk 494, 69–74 (2020).

    Google Scholar 

  13. E. I. Kugushev, T. V. Popova, and S. V. Sazonov, “On the motion of a system with a moving internal element in the presence of external viscous friction,” Mosc. Univ. Math. Bull. 75 (5), 140–146 (2020).

    Article  Google Scholar 

  14. F. L. Chernousko, “Locomotion of multibody robotic systems: Dynamics and optimization,” Theor. Appl. Mech. 45, 17–33 (2018).

    Article  Google Scholar 

  15. F. L. Chernous’ko, “Control of motion of multilink systems over a rough plane,” Tr. IMM UrO RAN 6, 277–287 (2000).

    Google Scholar 

  16. A. S. Kuleshov, “Further development of the mathematical model of a snakeboard,” Regular Chaot. Dyn. 12, 321–334 (2007).

    Article  MathSciNet  Google Scholar 

  17. S. Derammelaere, C. Copot, M. Haemers, F. Verbelen, B. Vervisch, C. Ionescu, and K. Stockman, “Realtime locomotion control of a snakeboard robot based on a novel model, enabling better physical insights,” Eur. J. Control 45, 57–64 (2019).

    Article  MathSciNet  Google Scholar 

  18. T. Yona and Y. Or, “The wheeled three-link snake model: Singularities in nonholonomic constraints and stick-slip hybrid dynamics induced by coulomb friction,” Nonlin. Dyn. 95, 2307–2324 (2019).

    Article  Google Scholar 

  19. I. A. Bizyaev, A. V. Borisov, and I. S. Mamaev, “Exotic dynamics of nonholonomic roller racer with periodic control,” Regular Chaot. Dyn. 23, 983–994 (2018).

    Article  MathSciNet  Google Scholar 

  20. V. Fedonyuk and P. Tallapragada, “The dynamics of a Chaplygin sleigh with an elastic internal rotor,” Regular Chaot. Dyn. 24, 114–126 (2019).

    Article  MathSciNet  Google Scholar 

  21. B. Pollard and P. Tallapragada, “Passive appendages improve the maneuverability of fishlike robots,” IEEE/ASME Trans. Mechatron. 24, 1586–1596 (2019).

    Article  Google Scholar 

  22. S. D. Kelly, M. J. Fairchild, P. M. Hassing, and P. Tallapragada, “Proportional heading control for planar navigation: The Chaplygin beanie and fishlike robotic swimming,” in Proceedings of the American Control Conference ACC, Montreal, QC Canada (IEEE, 2012), pp. 4885–4890.

  23. I. A. Bizyaev, A. V. Borisov, and I. S. Mamaev, “Dynamics of a Chaplygin sleigh with an unbalanced rotor: Regular and chaotic motions,” Nonlin. Dyn. 98, 2277–2291 (2019).

    Article  Google Scholar 

  24. A. V. Borisov and S. P. Kuznetsov, “Comparing dynamics initiated by an attached oscillating particle for the nonholonomic model of a Chaplygin sleigh and for a model with strong transverse and weak longitudinal viscous friction applied at a fixed point on the body,” Regular Chaot. Dyn. 23, 803–820 (2018).

    Article  MathSciNet  Google Scholar 

  25. A. A. Transeth, K. Y. Pettersen, and P. Liljebäck, “A survey on snake robot modeling and locomotion,” Robotica 27, 999–1015 (2009).

    Article  Google Scholar 

  26. P. Tallapragada and C. Gandra, “A mobile Mathieu oscillator model for vibrational locomotion of a bristlebot,” J. Mech. Robot. 13, 054501 (2021).

  27. M. Z. Dosaev and V. A. Samsonov, “Singularities in Dynamic Systems Involving Elastic Elements and Dry Friction,” Mech. Solids. 56 (8), 1477–1485 (2021).

    Article  Google Scholar 

  28. Y. D. Selyutskiy, A. P. Holub, and M. Z. Dosaev, “Elastically mounted double aerodynamic pendulum,” Int. J. Struct. Stab. Dyn. 19, 1941007 (2019).

  29. A. Zmitrowicz, “Mathematical descriptions of anisotropic friction,” Int. J. Solids Struct. 25, 837–862 (1989).

    Article  Google Scholar 

  30. V. G. Vil’ke, “Anisotropic dry friction and unilateral non-holonomic constraints,” J. Appl. Math. Mech. 72, 3–8 (2008).

    Article  MathSciNet  Google Scholar 

  31. V. V. Kozlov, “Lagrangian mechanics and dry friction,” Russ. J. Nonlin. Dyn. 6, 855–868 (2010).

    Google Scholar 

  32. A. V. Karapetyan and A. A. Shishkov, “Dynamics of Chaplygin skate on a horizontal plane with dry anisotropic friction,” Mosc. Univ. Mech. Bull. 75 (2), 47–49 (2020).

    Article  Google Scholar 

  33. A. Steindl, J. Edelmann, and M. Plochl, “Limit cycles at oversteer vehicle,” Nonlin. Dyn. 99, 313–321 (2020).

    Article  Google Scholar 

  34. M. W. Spong, “Underactuated mechanical systems,” in Control Problems in Robotics and Automation (Springer, Berlin, 1998), pp. 135–150.

    Google Scholar 

  35. A. M. Formalskii, Stabilization and Motion Control of Unstable Objects (Walter de Gruyter, Berlin, 2015).

    Book  Google Scholar 

  36. T. S. Parker and L. O. Chua, Practical Numerical Algorithms for Chaotic Systems (Springer, New York, 1989).

    Book  Google Scholar 

  37. K. Kamiyama, M. Komuro, and T. Endo, “Bifurcation of quasi-periodic oscillations in mutually coupled hard-type oscillators: Demonstration of unstable quasi-periodic orbits,” Int. J. Bifurc. Chaos 22, 1230022 (2012).

  38. L. A. Klimina, “Method for forming autorotations in controllable mechanical system with two degrees of freedom,” J. Comput. Syst. Sci. Int. 59, 817 (2020).

    Article  MathSciNet  Google Scholar 

  39. L. A. Klimina, “Method for constructing asynchronous self-sustained oscillations of a mechanical system with two degrees of freedom,” Prikl. Mat. Mekh. 85, 152–171 (2021).

    MATH  Google Scholar 

  40. A. Y. Aleksandrov and A. A. Tikhonov, “Averaging technique in the problem of Lorentz attitude stabilization of an Earth-pointing satellite,” Aerospace Sci. Technol. 104, 105963 (2020).

Download references

Funding

This work was supported by the Russian Science Foundation, grant no. 22-21-00303.

Author information

Authors and Affiliations

  1. Research Institute of Mechanics, Moscow State University, 119192, Moscow, Russia

    M. Z. Dosaev, L. A. Klimina, V. A. Samsonov & Yu. D. Selyutsky

Authors
  1. M. Z. Dosaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. A. Klimina
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. A. Samsonov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yu. D. Selyutsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. A. Klimina.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dosaev, M.Z., Klimina, L.A., Samsonov, V.A. et al. Plane-Parallel Motion of a Snake Robot in the Presence of Anisotropic Dry Friction and a Single Control Input. J. Comput. Syst. Sci. Int. 61, 858–867 (2022). https://doi.org/10.1134/S1064230722050069

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064230722050069

Search

Navigation