This study proposes a robust tracking controller for an underactuated quadrotor model based on the flatness theory and active disturbance rejection control (ADRC). Exploiting the differential flatness characteristic, it is demonstrated that a non‐linear quadrotor system can be changed into a linear canonical form, where it is easier to create a state feedback controller that ensures accurate trajectory tracking. In order to improve the tracking performance of the quadrotor, other factors are considered in the conception of the state feedback controller consisting in the estimation of the un‐measurable state variables in a canonical (Brunovsky) form and in the elimination of external perturbations and modelling uncertainties affecting the quadrotor system. To deal with this problem, first, an extended state observer (ESO) is designed to estimate a system state and an extended state known as lumped uncertainties. The latter represents the total effects of uncertain parameters, the neglected part of non‐linearity and the external disturbances. Second, based on the ESO result, an additional term is integrated into the feedback controller to eliminate the lumped disturbance effects and to ensure the stability of the closed loop. Simulation results are introduced to prove the benefits of associating the ADRC approach with flatness control.

This paper proposes a robust tracking control method for wheeled mobile robot (WMR) against uncertainties, including wind disturbances and slipping. Through the application of the differential flatness methodology, the under-actuated WMR model is transformed into a linear canonical form, simplifying the design of a stabilizing feedback controller. To handle uncertainties from wheel slip and wind disturbances, the proposed feedback controller uses sliding mode control (SMC). However, increased uncertainties lead to chattering in the SMC approach due to higher control inputs. To mitigate this, a boundary layer around the switching surface is introduced, implementing a continuous control law to reduce chattering. Although increasing the boundary layer thickness reduces chattering, it may compromise the robustness achieved by SMC. To address this challenge, an active disturbance rejection control (ADRC) is integrated with boundary layer sliding mode control. ADRC estimates lumped uncertainties via an extended state observer and eliminates them within the feedback loop. This combined feedback control method aims to achieve practical control and robust tracking performance. Stability properties of the closed-loop system are established using the Lyapunov theory. Finally, simulations and experimental results are conducted to compare and evaluate the efficiency of the proposed robust tracking controller against other existing control methods.

The paper suggests a compound control that combines nonlinear flatness, active disturbance rejection control (ADRC), and sliding mode control (SMC). By employing the differential flatness methodology, the standard under-actuated wheeled mobile robot model is converted into a fully actuated one. Utilizing this model as a basis, a sliding feedback controller is suggested to address the issue of uncertainties associated with wheel slip and wind. However, as the uncertainties increase, a higher control input is required, resulting in an undesired chattering phenomenon. To reduce chattering in SMC, a boundary layer surrounding the switching surface is employed, and a continuous law is implemented within the boundary. The boundary layer width plays an important role in improving robustness and eliminating chatter. Indeed, increasing the thickness of the boundary layer significantly reduces chattering, but it may lead to a loss of robustness performance achieved by the discontinuous control provided by SMC. To resolve this problem, active disturbance rejection control is combined with boundary layer sliding mode control. When utilizing the ADRC method, the lumped uncertainties are estimated via an extended state observer and eliminated within the feedback loop. The newly obtained feedback control combines the advantages of boundary layer SMC and ADRC to achieve practical control and robust tracking performance. The stability properties exhibited by the closed-loop system are rigorously established through the application of Lyapunov theory. In conclusion, a series of simulations has been conducted to compare and evaluate the efficiency of the presented robust tracking controller against other existing control methods.

Dans cette thèse nous nous sommes intéressés à la navigation autonome des systèmes robotiques et particulièrement pour les systèmes UAV, cas d’un quadri-rotor. Nous nous sommes focalisés sur les problèmes liés à la génération des trajectoires optimales et la conception des commandes robustes assurant la poursuite.Dans une première partie de la thèse, une nouvelle méthode de génération de trajectoires a été proposée. Cette méthode est basée sur la technique de collocation directe, la platitude différentielle et les courbes de Bézier. La platitude différentielle a été utilisée pour réduire le nombre de paramètres du problème d’optimisation. Les courbes de Bézier sont utilisées pour approximer les sorties plates. La méthode de collocation directe permet de transformer le problème d’optimisation infinie en un problème de programmation non linéaire de dimension finie. La méthodologie proposée permet de résoudre des problèmes complexes de calcul des trajectoires optimales d’une manière rapide, simple et efficace, puisque le nombre de paramètres sera réduit d’une façon considérable qui dépasse un taux de réduction de 60 %. Dans la seconde partie de la thèse, nous avons proposé une commande robuste par platitude qui assure le suivi de la trajectoire proposée en présence d’incertitude paramétrique et de perturbation externe. En utilisant la platitude, le système non linéaire est transformé en un système linéaire commandable sous la forme de Brunovsky, pour lequel il est plus facile de trouver un bouclage de rétroaction. Pour tenir compte des incertitudes paramétriques et des perturbations externes affectant le système, nous avons proposé un algorithme qui utilise le mode glissant et le contrôle actif par rejet des perturbations. Les résultats de simulation ont prouvé que l’approche considérée permet d’éliminer l’effet des perturbations et de réduire l’effet de broutement tout en assurant le degré de robustesse demandé.Pour le cas des perturbations inconnues à variations significatives affectant aussi bien le système que les mesures, nous nous sommes intéressés dans la dernière partie de la thèse à développer une nouvelle commande par platitude basée sur l’observateur par intervalle.