Advertisement

Nonlinear Dynamics

, Volume 85, Issue 4, pp 2611–2627 | Cite as

Formation of multiple groups of mobile robots: multi-timescale convergence perspective

  • Soumic SarkarEmail author
  • Indra Narayan Kar
Original Paper

Abstract

Multiple objects of different shapes combined together build a composite structure in automated industry. To carry those objects of different shapes, different numbers of robots are required to be in the formations which comply with the shapes of those objects. This paper introduces a transformation that separates the combined dynamics of a formation of multiple groups of robots into translational dynamics of centroid, intra-group shape dynamics, and inter-group shape dynamics, using the geometry of a shape. Partitioning the intra-group shape vectors, gives one the freedom to choose the number of groups required in a formation (with multiple groups). On the other hand, the inter-group shape vectors as opposed to the existing literature on single group of robots, extend further the connectivity among the groups. Therefore, they determine the geometric shape of the groups when connected. At first the transformation is applied on the combined dynamics of robots for the purpose of partitioning. Then singular perturbation-based control laws are designed to show through simulation results, that the convergence of different groups, the overall shape of groups combined together, and the tracking occur at different time. This ensures that one dynamics does not need to wait for the convergence of others. This saves time as opposed to sequential completion of various operations of the mission.

Keywords

Formation control Multi-level topology Multi-timescale analysis Singular perturbation Obstacle avoidance 

Supplementary material

Supplementary material 1 (avi 161937 KB)

Supplementary material 2 (avi 263233 KB)

Supplementary material 3 (avi 263233 KB)

References

  1. 1.
    Olfati-Saber, R., Fax, J.A., Murray, R.M.: Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–233 (2007)CrossRefGoogle Scholar
  2. 2.
    Balch, T., Arkin, R.C.: Behaviour-based formation control for multi robot systems. IEEE Trans. Robot. Autom. 14(6), 926–939 (1998)CrossRefGoogle Scholar
  3. 3.
    Desai, J.P., Kumar, V., Ostrowski, J.P.: Modeling and control of formations of nonholonomic mobile robots. IEEE Trans. Robot. Autom. 17(6), 905–908 (2001)CrossRefGoogle Scholar
  4. 4.
    Tanner, H., Pappas, G.J., Kumar, V.: Leader-to-formation stability. IEEE Trans. Robot. Autom. 20(3), 443–455 (2004)CrossRefGoogle Scholar
  5. 5.
    Kwon, J., Kim, J.H., Seo, J.: Multiple leader candidate and competitive position allocation for robust formation against member robot faults. Sensors 15, 10771–10790 (2015)CrossRefGoogle Scholar
  6. 6.
    Ding, Y., He, Y.: Flexible leadership in obstacle environment. In: Proceedings of International Conference on Intelligent Control and Information Processing, Dalian, China, pp. 788–791 (2010)Google Scholar
  7. 7.
    Peng, Z., Wang, D., Li, T., Wu, Z.: Leaderless and leader-follower cooperative control of multiple marine surface vehicles with unknown dynamics. Nonlinear Dyn. 74(1), 95–106 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Li, W., Chen, Z., Liu, Z.: Leader-following formation control for second-order multiagent systems with time-varying delay and nonlinear dynamics. Nonlinear Dyn. 72(4), 803–812 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Leonard, N.E., Fiorelli, E.: Virtual leaders, artificial potentials and coordinated control of groups. In: IEEE international conference on decision and control, Florida, OR, pp. 2968–2973 (2001)Google Scholar
  10. 10.
    Lewis, M.A., Tan, K.H.: High precision formation control of mobile robots using virtual structures. Auton. Robots. 4(4), 387–403 (1997)CrossRefGoogle Scholar
  11. 11.
    Egerstedt, M., Hu, X.: Formation constrained multi-agent control. IEEE Trans. Robot. Autom. 17(6), 947–951 (2001)CrossRefGoogle Scholar
  12. 12.
    Ren, W., Beard, R.W.: Formation feedback control for multiple spacecraft via virtual structures. IEE Proc. Control Theory Appl. 151(3), 357–368 (2004)CrossRefGoogle Scholar
  13. 13.
    Gazi, V.: Swarms aggregation using artificial potentials and sliding mode control. IEEE Trans. Robot. 21(4), 1208–1214 (2005)CrossRefGoogle Scholar
  14. 14.
    Pereira, A.R., Hsu, L.: Adaptive formation control using artificial potentials for Euler–Lagrange agents. In: Proceedings of the 17th IFAC World Congress, pp. 10788–10793 (2008)Google Scholar
  15. 15.
    Zavlanos, M.M., Pappas, G.J.: Potential fields for maintaining connectivity of mobile networks. IEEE Trans. Robot. 23(4), 812–816 (2007)CrossRefGoogle Scholar
  16. 16.
    Olfati-Saber, R., Murray, R.M.: Graph rigidity and distributed formation stabilization of multi-vehicle systems. In: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, pp. 2965–2971 (2002)Google Scholar
  17. 17.
    Tanner, H.G., Jadbabaie, A., Pappas, G.J.: Focking in fixed and switching networks. IEEE Trans. Automat. Contr. 52(5), 863–868 (2007)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Wang, L., Sun, S., Xia, C.: Finite-time stability of multi-agent system in disturbed environment. Nonlinear Dyn. 67(3), 2009–2016 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Aquilanti, V., Cavalli, S.: Coordinates for molecular dynamics: orthogonal local systems. J. Chem. Phys. 85(3), 1355–1361 (1986)CrossRefGoogle Scholar
  20. 20.
    Zhang, F.: Geometric cooperative control of particle formations. IEEE Trans. Automat.Contr. 55(3), 800–804 (2010)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Yang, H., Zhang, F.: Robust control of horizontal formation dynamics for autonomous underwater vehicles. Int. Conf. Robot. Autom. Shanghai, China pp. 3364–3369 (2011)Google Scholar
  22. 22.
    Mastellone, S., Mejia, J.S., Stipanovic, D.M., Spong, M.W.: Formation control and coordinated tracking via asymptotic decoupling for lagrangian multi-agent systems. Automatica 47(11), 2355–2363 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Arrichiello, F., Marino, A., Pierri, F.: Observer-based decentralized fault detection and isolation strategy for networked multirobot systems. IEEE Trans. Contr. Syst. Technol. 23(4), 1465–1476 (2015)CrossRefGoogle Scholar
  24. 24.
    Belta, C., Kumar, V.: Abstraction and control for groups of robots. IEEE Trans. Robot. 20(5), 865–875 (2004)CrossRefGoogle Scholar
  25. 25.
    Cheah, C.C., Hou, S.P., Slotine, J.J.E.: Region based shape control for a swarm of robots. Automatica 45(10), 2406–2411 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Lee, D., Li, P.Y.: Passive decomposition approach to formation and maneuver control of multiple rigid bodies. J. Dyn. Syst. Meas. Control 129(5), 662–677 (2007)CrossRefGoogle Scholar
  27. 27.
    Mas, I., Kittes, C.: Obstacle avoidance policies for cluster space control of nonholonomic multirobot systems. IEEE ASME Trans. Mechatron. 17(6), 1068–1079 (2012)CrossRefGoogle Scholar
  28. 28.
    Oh, K.K., Ahn, H.S.: Distance-based Formation Control Using Euclidean Distance Dynamics Matrix: Three-agent Case. American Control Conference, O’Farrell Street, San Francisco, CA, pp. 4810–4815 (2011)Google Scholar
  29. 29.
    Ailon, A., Zohar, I.: Control strategies for driving a group of nonholonomic kinematic mobile robots in formation along a time-parameterized path. IEEE ASME Trans. Mechatron. 17(2), 326–336 (2012)CrossRefGoogle Scholar
  30. 30.
    Tian, Y., Sarkar, N.: Formation control of mobile robots subject to wheel slip. In: IEEE International Conference on Robotics and Automation, pp. 4553–4558 (2012)Google Scholar
  31. 31.
    Kumar, M., Garg, D.P., Kumar, V.: Segregation of heterogeneous units in a swarm of robotic agents. IEEE Trans. Automat. Contr. 55(3), 743–748 (2010)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Lima, P.U., Ahmad, A., Dias, A., Conceio, A.G.S., Moreirab, A.P., Silva, E., Almeidad, L., Oliveira, L., Nascimento, T.P.: Formation control driven by cooperative object tracking. Rob. Auton. Syst. 63, 68–79 (2015)CrossRefGoogle Scholar
  33. 33.
    Nascimento, T.P., Moreira, A.P., Conceio, A.G.S.: Multi-robot nonlinear model predictive formation control: moving target and target absence. Rob. Auton. Syst. 61(12), 1502–1515 (2015)CrossRefGoogle Scholar
  34. 34.
    Chao, Z., Ming, L., Shaolei, Z., Wenguang, Z.: Collision-free UAV formation flight control based on nonlinear MPC. In: International Conference on Electronics, Communications and Control (ICECC), pp. 1951–1956 (2011)Google Scholar
  35. 35.
    Penders, J., Alboul, L.: Emerging robot swarm traffic. Int. J. Intell. Comput. Cybern. 5(3), 312–319 (2012)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Chen, Y., Tian, Y.: Coordinated path following control of multi-unicycle formation motion around closed curves in a time-invariant flow. Nonlinear Dyn. 81(1), 1005–1016 (2013)MathSciNetGoogle Scholar
  37. 37.
    Sun, X., Ge, S.S.: Adaptive neural region tracking control of multi-fully actuated ocean surface vessels. IEEE CAA J. Autom. Sin. 1(1), 77–83 (2014)CrossRefGoogle Scholar
  38. 38.
    de Marina, Garcia H., Cao, M., Jayawardhana, B.: Controlling rigid formations of mobile agents under inconsistent measurements. IEEE Trans. Robot. 31(1), 31–39 (2015)CrossRefGoogle Scholar
  39. 39.
    Miao, Z., Wang, Y., Fierro, R.: Collision-free consensus in multi-agent networks: a monotone systems perspective. Automatica 64, 217–225 (2016)Google Scholar
  40. 40.
    Hou, S.P., Cheah, C.C.: Dynamic compound shape control of robot swarm. IET Contr. Theory Appl. 6(3), 454–460 (2012)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Haghighi, R., Cheah, C.C.: Multi-group coordination control for robot swarms. Automatica 48(10), 2526–2534 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Yan, X., Chen, J., Sun, D.: Multilevel-based topology design and shape control of robot swarms. Automatica 48(12), 3122–3127 (2012)Google Scholar
  43. 43.
    Sarkar, S., Kar, I.N.: Formation control of multiple groups of robots. In: IEEE International Conference on Decision and Control, Florence, Italy, pp. 1466–1471 (2013)Google Scholar
  44. 44.
    Smith, S.L., Broucke, M.E., Francis, B.A.: A hierarchical cyclic pursuit scheme for vehicle networks. Automatica 41(6), 1045–1053 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Fierro, R., Lewis, F.L.: Control of a nonholonomic mobile robot: backstepping kinematics into dynamics. J. Robot. Syst. 14(3), 149–163 (1997)CrossRefzbMATHGoogle Scholar
  46. 46.
    Sarkar, S., Kar, I.N.: Formation control of multiple groups of nonholonomic wheeled mobile robots. In: Proceedings of Conference on Advances In Robotics, Pune, India, pp. 1–6 (2013)Google Scholar
  47. 47.
    Sarkar, S., Kar, I.N.: Three time scale behaviour analysis of the Leader Follower formation of multiple groups of nonholonomic robots. In: IEEE international conference on decision and control, Osaka, Japan, pp. 44–49 (2015)Google Scholar
  48. 48.
    Roncero, S.E.: Three-Time-Scale Nonlinear Control of an Autonomous Helicopter on a Platform. PhD. Thesis, Automation, Robotics and Telematic Engineering, Universidad de Sevilla (2011)Google Scholar
  49. 49.
    Esteban, S., Gordillo, F., Aracil, J.: Three-time scale singular perturbation control and stability analysis for an autonomous helicopter on a platform. Int. J. Robust Nonlinear Contr. 23(12), 1360–1392 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  50. 50.
    Khalil, H.: Nonlinear Systems, 2nd edn. Prentice-Hall, Upper Saddle River, NJ (1995)Google Scholar
  51. 51.
    Kokotovic, P., Khalil, H., Oreilly, J.: Singular Perturbation Methods in Control: Analysis and Design. Society for Industrial Mathematics, Philadelphia (1999)CrossRefGoogle Scholar
  52. 52.
    Kokotovic, P., Khalil, H., OReilly, J.: Singular Perturbation Methods in Control: Analysis and Design. Academic Press, London (1987)Google Scholar
  53. 53.
    Kokotovic, P., Bensoussan, A., Blankenship, G.: Singular Perturbations and Asymptotic Analysis in Control Systems. 90. Springer, Berlin (1987)CrossRefzbMATHGoogle Scholar
  54. 54.
    Vidyasagar, M.: Nonlinear Systems Analysis. Society for Industrial Mathematics, Philadelphia (2002)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Electrical EngineeringIndian Institute of Technology DelhiNew DelhiIndia

Personalised recommendations