ANZIAM J. 47(EMAC2005) pp.C649--C664, 2007.

Methods of aircraft trajectory optimisation in air combat

Istas F. Nusyirwan

Cees Bil

(Received 27 October 2005; revised 5 February 2007)

Abstract

We overview methodologies to optimise an aircraft trajectory in a two-player close air combat scenario. In mathematical terms air combat can be considered as a game. However, due to the highly nonlinear equations of motion involved, the use of classical games theory is difficult to implement in a computer simulation. The search for the saddle point of the game is difficult and therefore an indirect approach is required to search for the best trajectory. At each instance, one player is given the role of evader and the other the pursuer. The evader must find the trajectory that avoids or maximises the time to interception, while the pursuer must find a trajectory that achieves or minimises the time to intercept the evader. An algorithm has been developed and implemented using Evolutionary Programming. Simulations show that the algorithm is able to find good individuals (or solutions) in a limited time.

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Authors

Istas F. Nusyirwan
The Sir Lawrence Wackett Center for Aerospace Design Technology, RMIT University, Australia. mailto:istasfahrurrazi@gmail.com
Cees Bil
The Sir Lawrence Wackett Center for Aerospace Design Technology, RMIT University, Australia. mailto:cees.bil@rmit.edu.au

Published April 9, 2007. ISSN 1446-8735

References

  1. T. Back, D. B. Fogel, and T. Michalewics. Evolutionary Computation 1 : Basic Algorithms and Operators. Institute of Physics Publishing, 2000.
  2. Thomas Back. Evolutionary Algorithms in Theory and Practice. Oxford University Press, New York, 1996.
  3. M. Diehl and R. Findsein. Stability of nonlinear predictive control in the presence of errors due to numerical online optimization. In Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, Dec 2003, 2003.
  4. J. M. Eklund, J. Sprinkle, J. H. Kim, and S. Sastry. Implementing and testing a nonlinear model predictive tracking controller for aerial pursuit/evasion games on a fixed wing aircraft. American Control Conference, 2005.
  5. V. Y. Glizer. Homicidal chauffer with target set in the shape of a circular angular sector: Conditions for existence of a closed barrier. J. Optimization Theory and Applications, 101(3), June 1999.
  6. F. Imado. Some practical approaches to pursuit evasion dynamic games. Cybernetics and Systems Analysis, 38(2), 3, 2002.
  7. Fumiaki Imado and Sachio Uehara. High-g barrel roll maneuvers against proportional navigation from optimal control viewpoint. Journal of Guidance, Control, and Dynamics, 21(6):876--881, 1998.
  8. R. Isaac. Differential Games. R. E. Krieger Pub. Co., 1975.
  9. T. Miloh. A note on three-dimensional pursuit-evasion game with bounded curvature. IEEE Transactions on Automatic Control, 27(3):739--741, 1982.
  10. I. F. Nusyirwan and C. Bil. Stochastic trajectory optimisation for aircraft in air combat. In Proceedings of Simulation Conference and Exhibition Simtect 2005, Sydney, Australia, 9--12 May 2005, Syd, AU, 2005. http://www.SIMTECT.com.
  11. J. Shinar and S. Gutman. Three-dimensional optimal pursuit and evasion with bounded controls. IEEE Transactions on Automatic Control, 1980.
  12. P. H. Zipfel. Modeling and simulation of aerospace vehicle dynamics. AIAA education series, 2000.