{"references": ["A.Tayebi, S.Mcgilvray, 2004 \"Attitude stabilisation of a four rotor aerial robot\", IEEE conference on decision and control, December 14- 17, Atlantis Paradise Island, Bahamas 1216-1217.", "Derafa L. Madani t. and Benallegue A, 2006 \u00ab dynamic modelling and experimental identification of four rotor helicopter parameters \u00bb ICIT Mumbai, India.", "Guenard N. Hamel t. Moreau V, 2004 \u00ab mod\u00e9lisation et \u00e9laboration de commande de stabilisation de vitesse et de correction d-assiette pour un drone \u00bbCIFA.", "Hamel T. Mahoney r. Lozano r. Et Ostrowski j, 2002. \"Dynamic modelling and configuration stabilization for an X4-flyer.\" In the 15\u00e9me IFAC world congress-, Barcelona, Spain.", "Olfati. S, 2001 \"nonlinear control of under actuated mechanical systems with application to robotics and aerospace vehicles \u00bb, PhD thesis, MIT.", "P. Pounds, R.Mahony, 2002 \"Design of a four rotor \"ICRA, Auckland.", "R.Lozano, P.Castillo, and A.Dzul, 2004 \"global stabilization of the PVTOL: real time application to a mini aircraft\" International Journal of Control, Vol 77, Number 8, pp 735-740, may.", "S. Bouabdellah, P.Murrieri and R.Siegwart, 2004 \"Design and control of an indoor micro quadrotor\" ICRA 2004, New Orleans (USA), April.", "S. Bouabdellah and R.Siegwart, 2005 \"Backstepping and sliding mode techniques applied to an indoor micro quadrotor\" Proceeding of the 2005 IEEE, ICRA, Barcelona, Spain, April.\n[10] S.Bouabdellah, A.Noth and R.Siegwart, 2004 \"modelling of the (OS4) quadrotor\" modelling course, EPFL, may.\n[11] S. Yazir, M. Mekki and T. Chettibi, 2007 \"Mod\u00e9lisation dynamique directe et inverse d-un quadrotor\u00bb Accepted in CGE, Algiers, Algeria, April.\n[12] W.Khalil, Dombre, 2002 \"modelling, identification and control of robots\" HPS edition.\n[13] A.Benchaib, F.Boudjema and A.Rachid\"sliding mode flux observer based on backstepping approach for induction motor\" World Automation congress WAC-98, Alaska, USA, may 1998.\n[14] A.Mokhtari, A.Benallegue and A.Belaidi \"polynomial linear quadratic Gaussian and sliding mode observer for a quadrotor unmanned aerial vehicle\" Journal of Robotics and Mechatronics Vol.17 No.4, 2005.\n[15] A.Mokhtari, N.K.M-sirdi, K.Meghriche and A.Belaidi \"feedback linearization and linear observer for a quadrotor unmanned aerial vehicle\" Advanced Robotics, Vol.20, No.1, pp. 71-91, 2006."]}

In this paper; we are interested principally in dynamic modelling of quadrotor while taking into account the high-order nonholonomic constraints in order to develop a new control scheme as well as the various physical phenomena, which can influence the dynamics of a flying structure. These permit us to introduce a new state-space representation. After, the use of Backstepping approach for the synthesis of tracking errors and Lyapunov functions, a sliding mode controller is developed in order to ensure Lyapunov stability, the handling of all system nonlinearities and desired tracking trajectories. Finally simulation results are also provided in order to illustrate the performances of the proposed controller.