Advertisement

Continuum Mechanics and Thermodynamics

, Volume 30, Issue 5, pp 1091–1102 | Cite as

Virtual spring damper method for nonholonomic robotic swarm self-organization and leader following

  • Jakub Wiech
  • Victor A. Eremeyev
  • Ivan Giorgio
Open Access
Original Article
  • 132 Downloads

Abstract

In this paper, we demonstrate a method for self-organization and leader following of nonholonomic robotic swarm based on spring damper mesh. By self-organization of swarm robots we mean the emergence of order in a swarm as the result of interactions among the single robots. In other words the self-organization of swarm robots mimics some natural behavior of social animals like ants among others. The dynamics of two-wheel robot is derived, and a relation between virtual forces and robot control inputs is defined in order to establish stable swarm formation. Two cases of swarm control are analyzed. In the first case the swarm cohesion is achieved by virtual spring damper mesh connecting nearest neighboring robots without designated leader. In the second case we introduce a swarm leader interacting with nearest and second neighbors allowing the swarm to follow the leader. The paper ends with numeric simulation for performance evaluation of the proposed control method.

Keywords

Swarm robots Swarm self-organization Nonholonomic robots Leader following Virtual spring damper mesh 

Notes

References

  1. 1.
    Trianni, V.: Evolutionary Swarm Robotics: Evolving Self-organising Behaviours in Groups of Autonomous Robots. Studies in Computational Intelligence, Vol. 108. Springer, Berlin (2008)Google Scholar
  2. 2.
    Brambilla, M., Ferrante, E., Birattari, M., Dorigo, M.: Swarm robotics: a review from the swarm engineering perspective. Swarm Intell. 7(1), 1–41 (2013)CrossRefGoogle Scholar
  3. 3.
    Sahin, E., Spears, W. M. (Eds).: Swarm Robots. Lecture Notes in Computer Science book series (LNCS, vol. 3342). Springer, Berlin (2005)Google Scholar
  4. 4.
    Moriconi, C. dell’Erb, R.: Social Dependability: a proposed evolution for future Robotics, Sixth IARP-IEEE/RAS–EURON Joint Workshop on Technical Challenges for Dependable Robots in Human Environments May 17–18, (2008), Pasadena, CaliforniaGoogle Scholar
  5. 5.
    Bossi, S., Cipollini, A., dell’Erba, R., Moriconi, C.: Robotics in Italy. Education, Research, Innovation and Economics outcomes. Enea, Rome, (2014)Google Scholar
  6. 6.
    dell’Erba, R., Moriconi, C.: HARNESS: a robotic swarm for environmental surveillance. In 6th IARP Workshop on Risky Interventions and Environmental Surveillance (RISE). Warsaw, Poland, (2012)Google Scholar
  7. 7.
    dell’Erba, R.: Determination of spatial configuration of an underwater swarm with minimum data. Int. J. Adv. Robotic Syst. 12(7), 97–114 (2015)CrossRefGoogle Scholar
  8. 8.
    Urcola, P., Riazuelo, L., Lazaro, M., Montano, L.: Cooperative navigation using environment compliant robot formations. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2008, pp. 2789–2794, IEEE (2008)Google Scholar
  9. 9.
    Shucker, B., Bennett, J.K.: Virtual spring mesh algorithms for control of distributed robotic macrosensors. University of Colorado at Bulder, Technical Report CU-CS-996-05 (2005)Google Scholar
  10. 10.
    Chen, Q., Veres, S.M., Wang, Y., Meng, Y.: Virtual spring, -damper mesh-based formation control for spacecraft swarms in potential fields. J. Guid. Control Dyn. 38(3), 539–546 (2015)ADSCrossRefGoogle Scholar
  11. 11.
    Balkacem, K., Foudil, C.: A virtual viscoelastic based aggregation model for self-organization of swarm robots system. TAROS 2016: Towards Autonomous Robotic Systems, pp. 202–213, Springer (2016)Google Scholar
  12. 12.
    Della Corte, A., Battista, A., dell’Isola, F.: Referential description of the evolution of a 2D swarm of robots interacting with the closer neighbors: perspectives of continuum modeling via higher gradient continua. Int. J. Non-Linear Mech. 80, 209–220 (2016)ADSCrossRefGoogle Scholar
  13. 13.
    Battista, A. et al.: Numerical investigation of a particle system compared with first and second gradient continua: Deformation and fracture phenomena. Math. Mech. Solids,  https://doi.org/10.1177/1081286516657889 (2016)
  14. 14.
    Della Corte, A., Battista, A., dell’Isola, F., Giorgio, I.: Modeling deformable bodies using discrete systems with centroid-based propagating interaction: fracture and crack evolution. In: Mathematical Modelling in Solid Mechanics, pp. 59–88. Springer Singapore, (2017)Google Scholar
  15. 15.
    Pideri, C., Seppecher, P.: A second gradient material resulting from the homogenization of an heterogeneous linear elastic medium. Contin. Mech. Thermodyn. 9(5), 241–257 (1997)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Samuel, F., Sab, K.: Finite-deformation second-order micromorphic theory and its relations to strain and stress gradient models. Math. Mech. Solids. (2017).  https://doi.org/10.1177/1081286517720844
  17. 17.
    Steigmann, D.J.: Theory of elastic solids reinforced with fibers resistant to extension, flexure and twist. Int. J. Non-Lin. Mech. 47, 742–743 (2012)CrossRefGoogle Scholar
  18. 18.
    Turco, E., dell’Isola, F., Cazzani, A., Rizzi, N.L.: Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models. ZAMP 67(4), 1–28 (2016)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Alibert, J.-J., Seppecher, P., dell’Isola, F.: Truss modular beams with deformation energy depending on higher displacement gradients. Math. Mech. Solids 8(1), 51–73 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Buttà, P., De Masi, A., Rosatelli, E.: Slow motion and metastability for a nonlocal evolution equation. J. Stat. Phys. 112(3–4), 709–764 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Cuomo, M., dell’Isola, F., Greco, L., Rizzi, N.L.: First versus second gradient energies for planar sheets with two families of inextensible fibres: investigation on deformation boundary layers, discontinuities and geometrical instabilities. Compos. Part B Eng. 115, 423–448 (2017)CrossRefGoogle Scholar
  22. 22.
    dell’Isola, F., Cuomo, M., Greco, L., Della Corte, A.: Bias extension test for pantographic sheets: numerical simulations based on second gradient shear energies. J. Eng. Math. 103(1), 127–157 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Giergiel, J., Żylski, W.: Description of motion of a mobile robot by Maggie’s equations. J. Theor. Appl. Mech. 43(3), 511–521 (2005)Google Scholar
  24. 24.
    Gutowski R.: Mechanika Analityczna, 1971, PWN, WarszawaGoogle Scholar
  25. 25.
    Madenci, E., Oterkus, E.: Peridynamic Theory and Its Applications. Springer, New York (2014)CrossRefzbMATHGoogle Scholar
  26. 26.
    Born, M., Huang, K.: Dynamical Theory of Crystal Lattices. Clarendon Press, Oxford (1988)zbMATHGoogle Scholar
  27. 27.
    Slepyan, L.I.: Models and Phenomena in Fracture Mechanics. Springer, Berlin (2002)CrossRefzbMATHGoogle Scholar
  28. 28.
    Mishuris, G.S., Movchan, A.B., Slepyan, L.I.: Waves and fracture in an inhomogeneous lattice structure. Waves Random Complex Media 17, 409–428 (2007)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Mishuris, G.S., Movchan, A.B., Slepyan, L.I.: Dynamics of a bridged crack in a discrete lattice. Q. J. Mech. Appl. Math. 61, 151–160 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Slepyan, L.I.: Wave radiation in lattice fracture. Acoust. Phys. 56(6), 962–971 (2010)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Faculty of Mechanical Engineering and AeronauticsPolitechnika Rzeszowska im. Ignacego ŁukasiewiczaRzeszówPoland
  2. 2.Faculty of Civil and Environmental EngineeringGdańsk University of TechnologyGdańskPoland
  3. 3.Department of Mechanical and Aerospace EngineeringUniversity of Rome La SapienzaRomeItaly

Personalised recommendations