Feedback Linearization and High Order Sliding Mode Observer For A Quadrotor UAV A. Benallegue, A. Mokhtari, and L. Fridman Abstract— In this paper, a feedback linearization-based con- troller with a high order sliding mode observer running parallel is applied to a quadrotor unmanned aerial vehicle. The high order sliding mode observer works as an observer and estimator of the effect of the external disturbances such as wind and noise. The whole observer-estimator-control law constitutes an original approach to the vehicle regulation with minimal num- ber of sensors. Performance issues of the controller-observer are illustrated in a simulation study that takes into account parameter uncertainties and external disturbances. I. I NTRODUCTION Small UAV Quadrotors are designed to easily move in different environments while following specific tasks and providing good performance as well as a great autonomy. Affected by aerodynamic forces, the quadrotor dynamics is nonlinear, multivariable, and is subject to parameter un- certainties and external disturbances. In turn, controlling of the quadrotor is required i) to meet the stability, robustness and desired dynamic properties; ii) to be able to handle nonlinearity; iii) to be adaptive to changing parameters and environmental disturbances. Main difficulties of the motion control are thus para- metric uncertainties, unmodeled dynamics, and external dis- turbances [1], which result in further complication in the design of controllers for actual systems [3]. However various advanced control methods such as feedback linearization method [4], have been developed to meet increasing demands on the performance, however, they required full information on the state that may limit their practical utility. Indeed, even if all the state measurements are possible they are typically corrupted by noise. Moreover, the increased number of sensors makes the overall system more complex in imple- mentation and expensive in realization. In order to decrease the number of sensors in [5] the use only a rotational motion sensors is proposed in order to control tilt angles and evaluate translational motion. However, aerodynamic forces still cause difficulties to overcome. Thus motivated, an observer-based feedback design becomes an attractive approach to robotic control. The use of state observers appears to be useful in not only system monitoring and regulation but also detecting as well as identifying failures in dynamic systems. Almost all observer designs are based on the mathematical model of the A. Benallegue is with Robotics Laboratory of Versailles, France. benalleg@robot.uvsq.fr A. Mokhtari is with the University of Science and Technology of Oran, Algeria. mokhtari@robot.uvsq.fr L. Fridman is with the university of Mexico, Mexico. lfridman@servidor.unam.mx plant, is no linearized and has consequently have uncertain inputs. From the other hand the relative degree of the model with respect to the known outputs heavily dependent on the accuracy of the mathematical model of the plant [6]. So the main motivation of the paper are: • Feedback linearization controller of the quadrotor needs the third derivatives of measured states in order to reconstruct tilt angles and to fulfill the controller re- quirement. • When quadrotor is subjected to external disturbances, it would be suitable to compensate them through an observer based controller. • The observers should be robust with respect to external perturbations (wind and noise). • Observers based identification perturbation allow to re- duce the number of sensors required for control design. Methodology. The relative degree of the UAV Quadrotors model w.r.t. to unknown inputs is more than one and the standard necessary and sufficient conditions for observation of the systems with unknown inputs are not fulfilled [2]. To solve the problem of observation for UAV Quadrotors the higher order sliding mode observers will be used. Sliding mode observers (see, for example, the correspond- ing chapters in the textbooks [13], [22], and the recent tutorials [7], [9], [10]) are widely used due to their attrac- tive features: a) insensitivity (more than robustness!) with respect to unknown inputs; b) possibilities to use the values of the equivalent output injection for the unknown inputs identification; c) finite time convergence to exact values of the state vectors. In [14], [22] and [8] a step by step form of sliding mode observers were proposed. Such observers based on the transformation of a given system to a block observable form and the sequential estimation of each state by using of the value of the equivalent output injection. On the one hand, this schemes allows to formulate some observability conditions for linear time invariant systems with unknown inputs. Such conditions were formulated in [22], [8] for the scalar case. From the other hand, realization of this scheme caused obligatory filtration due to the non-idealities. In [18], [19] and [21] a robust exact arbitrary order differen- tiator was designed ensuring finite time convergence to the values of the corresponding derivatives, and applications of higher order sliding algorithms were considered. Basing on the second-order sliding-mode super twisting al- gorithm in [20].an observer for uncertain mechanical systems with only position measurements was proposed ensuring best possible approximation for the velocities. Proceedings of the 2006 International Workshop on Variable Structure Systems Alghero, Italy, June 5-7, 2006 WedC.3 1-4244-0208-5/06/$20 ©2006 IEEE 555 365