Advertisement

Solving the Problem of Coordination and Control of Multiple UAVs by Using the Column Generation Method

  • Duc Manh NguyenEmail author
  • Frédéric Dambreville
  • Abdelmalek Toumi
  • Jean-Christophe Cexus
  • Ali Khenchaf
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)

Abstract

In this paper, we consider the problem of autonomous task allocation and trajectory planning for a set of UAVs. This is a bi-level problem: the upper-level is a task assignment problem, subjected to UAV capability constraints; the lower-level constructs the detailed trajectory of UAVs, subjected to dynamics, avoidance and dependency constraints. Although the entire problem can be formulated as a mixed-integer linear program (MILP), and thus it can be solved by available software, the computational time increases intensively. For solving more efficiently this problem we propose an efficient approach based on the column generation method in which the modified dependency constraint will be added into the sub-problem. The performance of our approach is evaluated by comparing with solution given by the CPLEX on different scenarios.

Keywords

Unmanned aerial vehicle Task allocation Trajectory design Column generation Mixed integer linear programming 

Notes

Acknowledgement

The authors would like to thank the DGA (Direction Générale de l’Armement) for the support to this research.

References

  1. 1.
    Barnhart, C., Johnson, E.L., Nemhauser, G.L., Savelsbergh, M.W.P., Vance, P.H.: Branch-and-price: column generation for solving huge integer programs. Oper. Res. 46(3), 316–329 (1998)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bellingham, J., Tillerson, M., Richards, A., How, J.P.: Multi-task allocation and path planning for cooperative UAVs. In: Butenko, S., Murphey, R., Pardalos, P.M. (eds.) Cooperative Control: Models, Applications, and Algorithms, pp. 23–41. Kluwer Academic Publishers (2003)Google Scholar
  3. 3.
    Chandler, P., Pachter, M.: Research issues in autonomous control of tactical UAVs. In: Proceedings of ACC 1998, pp. 394–398 (1998)Google Scholar
  4. 4.
    Chandler, P.R., Pachter, M., Rasmussen, S.R., Schumacher, C.: Multiple task assignment for a UAV team. In: Proceedings of the AIAA Guidance, Navigation and Control Conference (2002)Google Scholar
  5. 5.
    Le, T.H.A., Nguyen, D.M., Pham, D.T.: Globally solving a nonlinear UAV task assignment problem by stochastic and deterministic optimization approaches. Optim. Lett. 6(2), 315–329 (2012)Google Scholar
  6. 6.
    Le, T.H.A., Nguyen, D.M., Pham, D.T.: A DC programming approach for planning a multisensor multizone search for a target. Comput. Oper. Res. 41, 231–239 (2014)Google Scholar
  7. 7.
    Lübbecke, M., Desrosiers, J.: Selected topics in column generation. Oper. Res. 53(6), 1007–1023 (2005)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Nguyen, D.M., Dambreville, F., Toumi, A., Cexus, J.C., Khenchaf, A.: A column generation based label correcting approach for the sensor management in an information collection process. In: Advanced Computational Methods for Knowledge Engineering, pp. 77–89 (2013)CrossRefGoogle Scholar
  9. 9.
    Richards, A., Bellingham, J., Tillerson, M., How, J.: Co-ordination and control of multiple UAVs. In: AIAA Guidance, Navigation, and Control Conference (2002)Google Scholar
  10. 10.
    Schouwenaars, T., DeMoor, B., Feron, E., How, J.: Mixed integer programming for safe multi-vehicle cooperative path planning. In: ECC, Porto, Portugal (2001)Google Scholar
  11. 11.
    Simonin, C., Le Cadre, J.-P., Dambreville, F.: A hierarchical approach for planning a multisensor multizone search for a moving target. Comput. Oper. Res. 36(7), 2179–2192 (2009)CrossRefGoogle Scholar
  12. 12.
    Walker, D.H., McLain, T.W., Howlett, J.K.: Coordinated UAV target assignment using distributed tour calculation. In: Grundel, D., Murphy, R., Pardalos, P.M. (eds.) Theory and Algorithms for Cooperative Systems. Series on Computers and Operations Research, vol. 4, pp. 327–333. Kluwer, Dordrecht (2004)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Duc Manh Nguyen
    • 1
    Email author
  • Frédéric Dambreville
    • 2
  • Abdelmalek Toumi
    • 2
  • Jean-Christophe Cexus
    • 2
  • Ali Khenchaf
    • 2
  1. 1.Hanoi National University of EducationHanoiVietnam
  2. 2.Lab-STICC UMR CNRS 6285, ENSTA BretagneBrest Cedex 9France

Personalised recommendations