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Abstract
Le travail de recherche presente ici a porte sur la planification de trajectoires de manipulateurs robotiques. Son but est de construire des algorithmes assurant au manipulateur (i) un mouvement lisse et continu tout le long d'une trajectoire et (ii) accroitre son adaptabilite et sa flexibilite dans le cas ou son environnement est encombre d'obstacles. Le premier point cite porte sur la planification de trajectoires pour les operations de transfert et les trajectoires continues imposees. Des solutions polynomiales articulaires d'ordre minimal et non minimal assurant la continuite jusqu'a la derivee troisieme ont ete presentees. Elles apportent des solutions aux problemes engendres par celles qui assurent la continuite jusqu'a la derivee seconde et qui sont utilisees jusqu'a date. Par ailleurs, en ce qui concerne les trajectoires continues imposees, des expressions permettant de faire passer des entites d'ordre superieur de l'espace cartesien a l'espace articulaire ont ete developpees ce qui conduira a planifier la trajectoire directement dans l'espace articulaire. Le second point, concerne la detection d'obstacles qui encombrent l'espace de travail du manipulateur. Le domaine interdit caracterisant la zone dans laquelle il n'est pas permis au manipulateur d'evoluer a ete defini analytiquement ce qui permet de detecter les collisions a l'aide de simples inegalites. Deux strategies basees sur les equations parametriques du contour de l'obstacle et sur sa forme particuliere (circulaire) conduisant aux memes resultats ont ete definies. Elles ont ete testees sur un manipulateur plan a deux degres de liberte puis etendues au manipulateur a trois degres de liberte.
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The research work presented here focuses on the planning of trajectories of robotic manipulators. Its goal is to build algorithms ensuring the manipulator (i) a smooth and continuous movement all along a trajectory and (ii) increasing its adaptability and its flexibility in the case where its environment is cluttered with obstacles. The first point mentioned relates to trajectory planning for transfer operations and imposed continuous trajectories. Joint polynomial solutions of minimal and non-minimal order ensuring continuity up to the third derivative have been presented. They bring solutions to the problems generated by those which ensure continuity until the second derivative and which are used until date. Moreover, with regard to the imposed continuous trajectories, expressions allowing to pass entities of higher order from the Cartesian space to the articular space have been developed which will lead to plan the trajectory directly in the articular space. . The second point concerns the detection of obstacles that clutter the manipulator's workspace. The forbidden domain characterizing the zone in which the manipulator is not allowed to evolve has been defined analytically, which makes it possible to detect collisions using simple inequalities. Two strategies based on the parametric equations of the contour of the obstacle and on its particular shape (circular) leading to the same results have been defined. They were tested on a planar manipulator with two degrees of freedom and then extended to a manipulator with three degrees of freedom.
