A Pursuit-evasion Game Between Unmanned Aerial Vehicles

Alexander Alexopoulos, Tobias Schmidt, Essameddin Badreddin

Abstract

In this paper the problem of two-player pursuit-evasion games with unmanned aerial vehicles (UAVs) in a three-dimensional environment is solved. A game theoretic framework is presented, which enables the solution of dynamic games in discrete time based on dynamic programming. The UAV agents taking part in the pursuit-evasion game are two identical quad-rotors with the same non-linear state space model, while the evaders’ absolute velocity is smaller than the pursuers’. The convergence of the pursuit-evasion game is shown in numerical simulations. Finally, the approach is simulated on an embedded computer and tested for real-time applicability. Hence, the implementation and real-time execution on a physical UAV system is feasible.

References

  1. Alexopoulos, A., Kandil, A. A., Orzechowski, P., and Badreddin, E. (2013). A comparative study of collision avoidance techniques for unmanned aerial vehicles. In SMC, pages 1969-1974.
  2. Bas¸ar, T. and Olsder, G. J. (1999). Dynamic Noncooperative Game Theory (Classics in Applied Mathematics). Soc for Industrial & Applied Math, 2 edition.
  3. Beatty, M. (2006). Principles of Engineering Mechanics: Volume 2 Dynamics - The Analysis of Motion. Mathematical Concepts and Methods in Science and Engineering. Springer.
  4. Bellman, R. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ, USA, 1 edition.
  5. Bouabdallah, S. and Siegwart, R. (2007). Advances in Unmanned Aerial Vehicles, chapter Design and Control of a Miniature Quadrotor, pages 171-210. Springer Press.
  6. Chatterjee, B. (2009). An optimization formulation to compute nash equilibrium in finite games. In Methods and Models in Computer Science, 2009. ICM2CS 2009. Proceeding of International Conference on, pages 1- 5.
  7. Chatterjee, B. (2010). n-person game. www.mathworks.com/matlabcentral/fileexchange/ 27837-n-person-game.
  8. Chung, T. H., Hollinger, G. A., and Isler, V. (2011). Search and pursuit-evasion in mobile robotics. Autonomous Robots, 31(4):299-316.
  9. CubieTech Ltd. (2014). Cubieboard - A series of open ARM miniPCs. www.cubieboard.org.
  10. Isaacs, R. (1965). Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization. John Wiley and Sons, Inc., New York.
  11. Johnson, S. G. (2013). The nlopt nonlinear-optimization package. http://ab-initio.mit.edu/nlopt.
  12. Kraft, D. (1988). A software package for sequential quadratic programming. Technical Report DFVLRFB 88-28, DFVLR, Cologne, Germany.
  13. Kraft, D. (1994). Algorithm 733: Tompfortran modules for optimal control calculations. ACM Transactions on Mathematical Software, 20(3):262-281.
  14. Krstic, M., Kokotovic, P. V., and Kanellakopoulos, I. (1995). Nonlinear and Adaptive Control Design. John Wiley & Sons, Inc., New York, NY, USA, 1st edition.
  15. LaValle, S. M. and Hutchinson, S. A. (1993). Game theory as a unifying structure for a variety of robot tasks. In Proceedings of 8th IEEE International Symposium on Intelligent Control, pages 429-434. IEEE.
  16. Littlewood, J. E. (1986). Littlewood's Miscellany. Cambridge University Press.
  17. MikroKopter (2014). MK-QuadroKopter / L4-ME. http:// www.mikrokopter.de/ucwiki/MK-Quadro.
  18. Nahin, P. J. (2012). Chases and Escapes: The Mathematics of Pursuit and Evasion (Princeton Puzzlers). Princeton University Press.
  19. Nash, J. F. (1950). Non-cooperative Games. PhD thesis, Princeton University, Princeton, NJ.
  20. Raspberry Pi Foundation (2014). www.raspberrypi.org.
  21. Sgall, J. (2001). Solution of david gale's lion and man problem. Theoretical Computer Science, 259(1-2):663- 670.
  22. Texas Instruments Inc. (2014a). Beagleboard.org. www.bealgeboard.org.
  23. Texas Instruments Inc. (2014b). BeagleBone Black. www.beagleboard.org/Products/BeagleBone Black.
  24. Thomas, L. C. (1984). Games, Theory and Applications. Dover Books on Mathematics. Dover Publications.
  25. Vieira, M., Govindan, R., and Sukhatme, G. (2009). Scalable and practical pursuit-evasion. In Robot Communication and Coordination, 2009. ROBOCOMM 7809. Second International Conference on, pages 1-6.
  26. von Neumann, J. and Morgenstern, O. (2007). Theory of Games and Economic Behavior (60th-Anniversary Edition). Princeton University Press.
  27. Voos, H. (2009). Entwurf eines flugreglers für ein vierrotoriges unbemanntes fluggerät (control systems design for a quadrotor uav). Automatisierungstechnik, 57(9):423-431.
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Paper Citation


in Harvard Style

Alexopoulos A., Schmidt T. and Badreddin E. (2014). A Pursuit-evasion Game Between Unmanned Aerial Vehicles . In Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO, ISBN 978-989-758-040-6, pages 74-81. DOI: 10.5220/0005038600740081


in Bibtex Style

@conference{icinco14,
author={Alexander Alexopoulos and Tobias Schmidt and Essameddin Badreddin},
title={A Pursuit-evasion Game Between Unmanned Aerial Vehicles},
booktitle={Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},
year={2014},
pages={74-81},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005038600740081},
isbn={978-989-758-040-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,
TI - A Pursuit-evasion Game Between Unmanned Aerial Vehicles
SN - 978-989-758-040-6
AU - Alexopoulos A.
AU - Schmidt T.
AU - Badreddin E.
PY - 2014
SP - 74
EP - 81
DO - 10.5220/0005038600740081