NONLINEAR BACKSTEPPING CONTROL WITH OBSERVER DESIGN FOR A 4 ROTORS HELICOPTER L. Mederreg, F. Diaz and N. K. M’sirdi LRV, Laboratory of Robotics of Versailles, Université de Versailles Saint Quentin en Yvelines, 10, avenue de l’Europe 78140, Vélizy, France. mederreg@robot.uvsq.fr, msirdi@lrv.uvsq.fr Abstract: This paper develops a nonlinear observer and controller applied to a helicopter with 4 rotors. We show how to design a powerful nonlinear control law in term of robustness. In addition, this technique allows reducing the number of sensors to be embedded in the flying system by observing non available or non measurable entities. Performances and the stability of the suggested controller are analyzed through simulations carried out on the model (kinematics and dynamic equations). Keywords: System modelling, non linear controller, Backstepping Observes and controllers. 1. INTRODUCTION The miniature and autonomous air machines arouse a growing interest in the civil and military domain. The fields of application of these apparatuses are vast. One can state the ecological exploration mission, air cartography, and arts structure auscultation. The miniature helicopters are particularly suitable for this kind of applications. They are easy to handle, able to make hovering and can take off or land vertically. Moreover, their configuration appears particularly interesting for some applications, where stability, reliability, and the safety of the people and the goods are of primary importance. Indeed, this helicopter has no “head of rotor” and is mechanically very simple. It has also a weak catch with the wind; this increases its stability in disturbed environment. However, due to the complexity of piloting the helicopters under unfavourable climatic conditions obliges to avoid an open loop control. Consequently, to achieve high level missions planned by human operators, it is necessary to design control laws able to track predefined trajectories even in the presence of wind and turbulences. This idea motivates many studies towards the helicopters [1][2][7][5][9]. An exact linearization method has been developed on the kino-dynamic model with four rotors [11] [12]. However, this technique encounters problems of robustness in presence of disturbances and errors of the system parameters estimations. Moreover, it requires measurements of the full system state vector. In order to overcome these disadvantages, we directed our efforts towards an approach of nonlinear control that guarantees the properties of robustness and reduces also the number of required sensors, by observing states of the system which are difficult to measure. The method proposed is based on the Backstepping approch. It consists of the use of a triangular structure of the given model for which the feed back is computed step by step where a gain is added to compensate the errors. 2. THE DYNAMICAL MODEL OF THE HELICOPTER In this section, we develop the kinematics dynamical model of a 4 rotors helicopter. The 4 rotors are horizontal and the configuration is symmetric. The rotors’ speeds can be controlled independently. Two rotors turn in the clock wise direction whereas the two others turn in the opposite direction. This allows avoiding the couple effects on the platform. A forward motion can be obtained by accelerating the speed of the rear rotor and reducing the speed of the front one. The lateral motion can be obtained by the same manner using left and right rotors. The yaw control is obtained by accelerating two “front to front” rotors and slowing the two others. The four rotors helicopter is assumed to be rigid body, having six degrees of freedom, and subject to external efforts. The mathematical model contains kinematics and dynamic equations. The kinematics equations describe the relation between the position and the orientation of the helicopter and its speed. The absolute position of the helicopter is given by the three co-ordinates 0 0 0 ( , , ) x y z of its centre of gravity, with respect to an inertial reference frame attached to the ground and its orientation by the three Euler angles( , , ) ? ? f . These angles are called, the yaw ( ? - p < < p ) , the pitch ( /2 /2) ? - p < < p and the roll angle( /2 /2) f - p < < p , respectively. The derivative......