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Journal of Intelligent & Robotic Systems

, Volume 73, Issue 1–4, pp 665–677 | Cite as

An Approach for Optimal Goal Position Assignment in Vehicle Formations

  • Luis García-Delgado
  • R. Gómez-Fuentes
  • A. García-Juárez
  • A. L. Leal-Cruz
  • D. Berman-Mendoza
  • A. Vera-Marquina
  • A. G. Rojas-Hernández
Article

Abstract

In this paper one methodology to solve the goal position assignment (GPA) problem is developed, this is, to assign the corresponding goal position (desired position) for a group of vehicles, knowing the initial positions and the established formation shape. By using this GPA methodology, it can be guaranteed that the formation will be reached in a minimum period of time and with lower collision risk compared with the other possible combinations of pairs “vehicles-goal position”. Hungarian algorithm was used as combinatorial optimization algorithm, which requires a cost matrix, therefore it is shown the way to compute the cost matrix to obtain the best GPA. In order to show the optimal behavior of the proposed cost matrix, three approaches of cost matrix were evaluated in simulations of quad-rotor formations. Also, the optimal behavior of the proposed GPA is proved with numerical values of some defined parameters to determine optimal performance. The formation control was based on potential functions, while the control law for each vehicle was based on nested saturation.

Keywords

Assignment Vehicle formations Optimization Quad-rotor 

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References

  1. 1.
    Ahsun, U., Miller, D.W.: Dynamics and control of electromagnetic satellite formations. In: Proceedings of the 2006 American Control Conference, pp. 1730–1735 (2006)Google Scholar
  2. 2.
    Alsuwaiyel, M.H.: Algorithms: Design Techniques and Analys (Lecture Notes Series on Computing). World Scientific (1999)Google Scholar
  3. 3.
    Bai, C., Duan, H., Li, C., Zhang, Y.: Dynamic multi-uavs formation reconfiguration based on hybrid diversity-pso and time optimal control. In: IEEE Intelligent Vehicles Symposium (2009)Google Scholar
  4. 4.
    Barnes, L.E., Fields, M.A., Valavanis, K.P.: Swarm formation control utilizing elliptical surfaces and limiting functions. IEEE Trans. Syst. Man Cybern. 39(6), 1434–1445 (2009)CrossRefGoogle Scholar
  5. 5.
    Castillo, P., Lozano, R., Dzul, A.: Stabilization of a mini rotorcraft having four rotors. IEEE Control Syst. Mag. 25(6), 45–55 (2005)CrossRefMathSciNetGoogle Scholar
  6. 6.
    García, L., Dzul, A., Santibáñez, V., Llama, M.: Quad-rotors formation based on potential functions with obstacle avoidance. IET Control Theory Appl. 6(12), 1787–1802 (2012)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Hu, J., Prandini, M., Tomlin, C.: Interesting conjugate points in formation constrained optimal multi-agent coordination. In: 2005 American Control Conference (2005)Google Scholar
  8. 8.
    Lee, T., Leok, M., McClamroch, N.H.: A combinatorial optimal control problem for spacecraft formation reconfiguration. In: 46th IEEE Conference on Decision and Control (2007)Google Scholar
  9. 9.
    Lindhé, M., Ögren, P., Johansson, K.H.: Flocking with obstacle avoidance: a new distributed coordination algorithm based on voronoi partitions. In: 2005 IEEE International Conference on Robotics and Automation (2005)Google Scholar
  10. 10.
    Moon, S., Oh, E., Shim, D.H.: An integral framework of task assignment and path planning for multiple unmanned aerial vehicles in dynamic environments. J. Intell. Robot. Syst. 70(1–4), 303–313 (2013)CrossRefGoogle Scholar
  11. 11.
    Reis, L.P., Lopes, R., Mota, L., Lau, N.: Playmaker: graphical definition of formations and setplays. In: 5th Iberian Conference on Information Systems and Technologies (2010)Google Scholar
  12. 12.
    Teel, A.R.: Global stabilization and restricted tracking for multiple integrators with bounded controls. Syst. Control Lett. 18(3), 165–171 (1992)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Walls, J., Howard, A., Homaifar, A., Kimiaghalam, B.: A generalized framework for autonomous formation reconfiguration of multiple spacecraft. In: 2005 IEEE Aerospace Conference, pp. 397–406 (2005)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Luis García-Delgado
    • 1
  • R. Gómez-Fuentes
    • 1
  • A. García-Juárez
    • 1
  • A. L. Leal-Cruz
    • 1
  • D. Berman-Mendoza
    • 1
  • A. Vera-Marquina
    • 1
  • A. G. Rojas-Hernández
    • 1
  1. 1.Departamento de Investigación en FísicaUniversidad de SonoraHermosilloMéxico

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