Planification et exécution de mouvements pour un robot bi-guidable: une approche basée sur la platitude différentielle

http://emotion.inrialpes.fr/bibemotion/2003/Her03/ voir basilic Inst. Nat. Polytechnique de GrenobleGrenoble (FR)This dissertation addresses the problem of planning and executing motions for a special class of four-wheel robot with double steering axles: we call bi-steerable car a vehicle capable of steering its rear wheels in function of the front steering angle. The differential equations describing the control system set new problems of motion planning and control in mobile robotics. The methodology employed to solve these problems is framed within the theory of Nonlinear Control and in particular differential flatness. The objective is to find state and control transformations, putting the system in normal forms with structural properties convenient for control design purposes. This dissertation shows first that the bi-steerable car is flat. For these systems, effective solutions can be found in the literature and resort to the structural properties of the flat or linearizing output. Notwithstanding, the major difficulty, and open problem in the general case, is to find transformations yielding a flat output of the system. Hence we first establish theoreticalresults framed in the theory of Pfaffian systems and in particular those concerned by the Engel's theorem. For such systems, we propose a systematic approach leading to a necessary condition on the coordinates transformations yielding a linearizing output. We apply this approach to the bi-steerable car. We consider the symmetries of our problem in order to effectively compute a flat output. We make this result effective by proposing the first complete motion planner for this kind of mechanical structure. We next establish results in the framework of flatness and feedback linearization regarding the bi-steerable car. This allowed us to fully linearize the system and to synthesize a simple control law to solve the trajectory tracking problem. Experimental results validate these theoretical issues.Aucu