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Cooperative Multiple Pursuers against a Single Evader

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Abstract

This paper considers a pursuit-evasion game for non-holonomic systems where a group of pursuers attempts to capture an evader in a bounded connected domain. The problem is challenging because all vehicles have the same maneuvering capability in terms of speed and turn radius constraint. The paper initially discusses a simple approach for holonomic systems that is based on the minimization of the safe-reachable area (the area containing the set of points to where an evader can travel without being caught). This idea is then extended to develop a pursuit-evasion strategy for non-holonomic systems. However, solving such a problem is computationally intractable. Therefore, we propose a computationally efficient algorithm to obtain approximate solutions. This paper also proposes an alternative approach to obtain a simple yet effective solution to the cooperative pursuit problem that is based on missile guidance laws. As there is no analytical proof of capture, we empirically evaluate the performance of the algorithms and perform a comparative study using solutions obtained from umpteen simulations. A total of four different cooperative pursuit strategies and three different evader strategies are taken into account for the comparative study. In the process, an evader strategy which is superior to that based on the optimization of safe-reachable area is also identified.

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References

  1. Conway, B.A., Pontani, M.: Numerical solution of the three-dimensional orbital pursuit-evasion game. J. Guid. Control Dyn. 32(2), 474–487 (2009). doi:10.2514/1.37962

  2. Dubins, L.E.: On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. Am. J. Math. 79(3), 497–516 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  3. Evans, L., Souganidis, P.: Differential games and representation formulas for solutions of hamilton-jacobi-isaacs equations. Indiana Univ. Math. J. 33(5), 773–797 (1984). doi:10.1512/iumj.1984.33.33040

  4. Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence, volume 158 of Studies in Computational Intelligence. In: Gavrilova, M. (ed.) Springer-Verlag (2008)

  5. George, J.M., Sujit, P.B., Sousa, J.B., Pereira, F.L.: Coalition formation with communication ranges and moving targets. In: Proceedings of the American Control Conference (ACC), pp. 1605–1610. IEEE, Baltimore, USA (2010). doi:10.1109/ACC.2010.5531604

  6. Huang, H., Zhang, W., Ding, J., Stipanovic, D.M., Tomlin, C.J.: Guaranteed decentralized pursuit-evasion in the plane with multiple pursuers. In: Proceedings of the Fiftieth IEEE Conference on Decision and Control and European Control Conference, pp. 4835–4840. IEEE, Orlando, FL (2011). doi:10.1109/CDC.2011.6161237

  7. Isaacs, R.: Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization (1965)

  8. Jarmark, B., Hillberg, C.: Pursuit-evasion between two realistic aircraft. J. Guid. Control Dyn. 7(6), 690–694 (1984). doi:10.2514/3.19914

  9. Kothari, M., Manathara, J.G., Postlethwaite, I.: A cooperative pursuit-evasion game for non-holonomic systems. In: Proceedings of the Ninteenth IFAC World Congress, pp. 1977–1984, Cape Town, South Africa (2014). doi:10.3182/20140824-6-ZA-1003.01992

  10. Manathara, J.G., Sujit, P.B., Beard, R.W.: Multiple uav coalitions for a search and prosecute mission. J. Intell. Robot. Syst. 62(1), 125–158 (2011)

    Article  MATH  Google Scholar 

  11. Pachter, M., Yavin, Y.: Simple-motion pursuit-evasion differential games, part 1: Stroboscopic strategies in collision-course guidance and proportional navigation. J. Optim. Theory Appl. 51(1), 95–127 (1986). doi:10.1007/BF00938604

  12. Rajan, N., Prasad, U.R., Rao, N.J.: Pursuit-evasion of two aircraft in a horizontal plane. J. Guid. Control Dyn. 3(3), 261–267 (1980). doi:10.2514/3.55982

  13. Ramana, M.V., Kothari, M.: A cooperative pursuit-evasion game of a high speed evader. In: Proceedings of the IEEE Fifty-Fourth Annual Conference on Decision and Control (CDC), pp. 2969–2974. IEEE, Osaka, Japan (2015). doi:10.1109/CDC.2015.7402668

  14. Ramana, M.V., Kothari, M.: A cooperative pursuit strategy for a high speed evader. In: Proceedings of the AIAA Guidance, Navigation, and Control Conference. AIAA Paper 2016-2103, San Diego, CA (2016). doi:10.2514/6.2016-2103

  15. Shneydor, N.A.: Missile guidance and pursuit: Kinematics, Dynamics and control. Horwood Series in Engineering Science. Horwood Publishing Limited, Chichester, England (1998)

    Book  Google Scholar 

  16. Takei, R., Huang, H., Ding, J., Tomlin, C.J.: Time-optimal multi-stage motion planning with guaranteed collision avoidance via an open-loop game formulation. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pp. 323–329. IEEE, Saint Paul, MN (2012). doi:10.1109/ICRA.2012.6225074

  17. Zarchan, P.: Tactical and Strategic Missile Guidance, volume 239 of Progress in Astronautics and Aeronautics, 6th edn. American Institute of Aernautics and Astronautics (2012)

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Authors and Affiliations

  1. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    Mangal Kothari

  2. Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, 600036, India

    Joel G. Manathara

  3. CEO, Dean (Singapore), Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom

    Ian Postlethwaite

Authors
  1. Mangal Kothari
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  2. Joel G. Manathara
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  3. Ian Postlethwaite
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Correspondence to Mangal Kothari.

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Kothari, M., Manathara, J.G. & Postlethwaite, I. Cooperative Multiple Pursuers against a Single Evader. J Intell Robot Syst 86, 551–567 (2017). https://doi.org/10.1007/s10846-016-0423-3

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  • DOI: https://doi.org/10.1007/s10846-016-0423-3

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