Modeling an Optimal Control Problem for the Navigation of Mobile Robots in an Ocduded Environment Application to Unmanned Aerial Vehicles

1. Slotine, J.-J.E., Li, W.: Applied Nonlinear Control. Prentice Hall, Englewood Cliffs (1991)

   MATH  Google Scholar 

2. Wise, K.A., Sedwick, J.L., Eberhardt, R.L.: Nonlinear control of missiles McDonnell Douglas Aerospace Report MDC 93B0484, October 1993

   Google Scholar 

3. Ehrler, D., Vadali, S.R.: Examination of the optimal nonlinear regulator problem. In: Proceedings of the AIAA Guidance, Navigation, and Control Conference, Minneapolis, MN (1988)

   Google Scholar 

4. Beard, R., et al.: Autonomous vehicle technologies for small fixed-wing UAVs. AIAA J. Aerosp. Comput. Inf. Commun. 2, 92–108 (2005)

   Article  Google Scholar 

5. Guo, W., Gao, X., Xiao, Q., Multiple UAV cooperative path planning based on dynamic Bayesian network. In: Control and Decision Conference (CCDC), pp. 2401–2405, July 2008

   Google Scholar 

6. Mechirgui, M.: Commande Optimale minimisant la consommation d’énergie d’un Drone, Relai de communication, Maîtrise en Génie Eléctrique, Montréal, Le 15 Octobre 2014

   Google Scholar 

7. Boudjellal, A.A., Boudjema, F.: Commande par Backstepping basée sur un Observateur Mode Glissant pour un Drone de type Quadri-rotor. In: ICEE2013 (2013)

   Google Scholar 

8. Hull, D.G.: Optimal Control Theory for Applications. Springer, Heidelberg (2003). https://doi.org/10.1007/978-1-4757-4180-3

   Book  MATH  Google Scholar 

9. Trelat, E.: Contrôle optimal: théorie et applications, Vuibert, collection Mathématiques Concrètes (2005)

   Google Scholar 

10. Sethi, S.P., Thompsonn, G.L.: Optimal Control Theory, Applications to Management Science and Economics, 2nd edn. Kluwer Academic Publishers, Dordrecht (2000)

    Google Scholar 

11. Zaslavski, A.J.: Structure of Approximate Solutions of Optimal Control Problems. Springer, Heidelberg (2013)

    Book  Google Scholar 

12. Akulenko, L.D.: Problems and Methods of Optimal Control. Springer, Heidelberg (1994)

    Book  Google Scholar 

13. Pytlak, R.: Numerical Methods for Optimal Control Problems With State Constraints. Springer, Heidelberg (1999)

    Book  Google Scholar 

14. Demim, F., Louadj, K., Aidene, M., Nemra, A.: Solution of an optimal control problem with vector control using relaxation method. Autom. Control Syst. Eng. J. 16(2) (2016). ISSN 1687–4811

    Google Scholar 

15. Louadj, K., Aidene, M.: Optimization of a problem of optimal control with free initial state. Appl. Math. Sci. 4(5), 201–216 (2010)

    MathSciNet  MATH  Google Scholar 

16. Louadj, K., Aidene, M.: Adaptive method for solving optimal control problem with state and control variables. Math. Probl. Eng. 2012, 15 (2012)

    MathSciNet  MATH  Google Scholar 

17. Louadj, K., Aidene, M.: Direct method for resolution of optimal control problem with free initial condition. Int. J. Differ. Equ. 2012, 18 (2012). Article ID 173634

    Article  MathSciNet  Google Scholar 

18. Louadj, K., Aidene, M.: A problem of optimal control with free initial state. In: Proceedings du Congres National de Mathematiques Appliquees et Industrielles, SMAI 2011, Orleans du 23rd May to au 27th, pp. 184–190 (2011)

    Google Scholar 

19. Titouche, S., Spiteri, P., Messine, F., Aidene, M.: Optimal control of a large thermic. J. Control Syst. 25, 50–58 (2015)

    Google Scholar 

20. Geisert, M., Mansard, N.: Trajectory generation for Quadrotor based systems using numerical optimal control. In: IEEE International Conference on Robotics and Automation (ICRA) Stockholm, Sweden, 16–21 May 2016

    Google Scholar 

21. Fethi, D., Nemra, A., Louadj, K., Hamerlain, M.: Simultaneous localization, mapping, and path planning for unmanned vehicle using optimal control. Adv. Mech. Eng. 10(1), 1–25 (2018)

    Article  Google Scholar 

22. Bonnans, F., Martinon, P., Grélard, V.: Bocop - a collection of examples. Research report RR-8053, INRIA (2012)

    Google Scholar 

23. Louadj, K., Demim, F., Nemra, A., Marthon, P.: An optimal control problem of unmanned aerial vehicle. In: International an Conference on Control, Decision and Information Technologies (CoDIT 2018), Thessaloniki, 10 April 2018–13 April 2018 (2018)

    Google Scholar 

24. Jalel, S.: Optimisation de la navigation robotique. Thesis, Toulouse University (INP) (2016)

    Google Scholar 

25. Atyabi, A., Powers, D.: Review of classical and heuristic based navigation and path planning approaches. Int. J. Adv. Comput. Technol. 5(14), 1–14 (2013)

    Google Scholar 

26. Jalel S., Marthon, P., Hamouda, A.: Optimum path planning for mobile robots is static environments using graph modelling and NURBS Curves. In: WSEAS International Conference on Signal Processing, Robotics and Automation, 20–22 February 2013, Cambridge, UK, pp. 216–221 (2013)

    Google Scholar 

Download references