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Commande Nonlinéaire et Navigation des Véhicules Marins Sous-actionnés

Abstract : This thesis addresses the problem of controlling an underactuated marine vehicle system. The key motivation for this research topic stems from the fact that underactuated systems pose considerable challenges to control system designers since those systems cannot be stabilized by smooth, time-invariant, state-feedback control laws. Furthermore, in spite of the number of methods available for the control of underactuated mechanical systems, few address important practical topics such as the explicit inclusion of dynamics in the control problem formulation and the need to cope with environmental disturbances due to wind and wave currents. This thesis tackles some of this issues, formulates and solves control problems related to dynamic positioning, trajectory tracking and path following, and discusses the application of the new control methodologies derived to marine vehicles like surface vessel-type ships. The first part of the thesis (Chapter3 and4) focuses on showing that the underactuated marine vehicle model does not satisfy Brockett's necessary condition, i.e. it can not be stabilized by a continuous time-invariant state feedback. However, it is possible to achieve stabilization using discontinuous or time varying controllers which makes the purpose of the third chapter. Chapter 4 consists to apply recent results on cascade nonlinear systems to solve the open problem of determining controllers that stabilize the position/heading of the underactuated surface vessel at the origin. Two transformations are introduced to represent the system into a pure cascade form. First we show through some key properties of the model that the global and uniform asymptotic stabilization problem of the resulting cascade system can be reduced to the stabilization problem of a third order chained form. A discontinuous backstepping approach is then employed for the stabilization of the chained form system via a partial state feedback. We show that the proposed control law exponentially stabilizes the reduced model in a defined set, ensuring the uniform local asymptotic stabilization of the underactuated surface vessel model. To ensure the global uniform stability however, a combined backstepping and time varying control approach is therefore employed. Next, we exploit the cascade structure to construct a suitable defined trajectory generated by the dynamic equations of a virtual underactuated ship. We show that we can find a feedback controller that forces the ship to exponentially follow the desired trajectory from any initial conditions. Using a cascade approach, we show that the tracking error dynamics of the ship can be decomposed as a cascade interconnection of one nonlinear system and a third order chained form system with integrator. The second part of the thesis is devoted to the problem of steering the underactuated ship along a desired path with prescribed dynamic. Controller design relies on two different approaches, the former comes from an observation that it is reasonable in practice to steer a vessel such that it is on the reference path, and its total velocity is tangent to the path. It is also realistic to assume that the vessel travels along the path with a constant forward speed controlled by the main thruster control system. The latter approach relaxes this observation to let the desired forward speed, be adjusted on-line. These two problems are resolved in Chapter 5. In Chapter \ref{chap6}, we exploit the path following approach for reason to consider the problem of coordinating a group of marine vehicles that is, we want to steer the motion of each vehicle such that the group's overall motion is governed by a desired behavior. Thus, independent motion is coordinated as a formation according to the behavior decided by the designer. Such control problems have attracted increasing attention during the last decade due to the many benefits of distributed vehicles controlled as a formation. Chapter 6 looks into the formation problem where several marine vehicles are synchronized such that they are controlled as a virtual structure formation. The paths are synchronized such that equal path parameters imply correct vessels configuration. Chapter 7, is devoted to the general problem of output feedback for global partial-state feedback controller for general marine model systems. Our result is facilitated by deriving a coordinate transformation to cancel the velocity cross terms in the marine model system dynamics to design global exponential velocity observers. An application of such observer is applied to the case of path following problem of an underactuated surface vessel. Finally, Chapter 8 contains the conclusions and discusses challenging issues that warrant further research.
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Jawhar Ghommam. Commande Nonlinéaire et Navigation des Véhicules Marins Sous-actionnés. Automatique / Robotique. Ecole Nationale d'Ingénieurs de Sfax, 2008. Français. ⟨tel-00261791⟩

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