Planification de trajectoire pour manipulateurs seriels redondants: Application au controleur KALI

Abstract

Ce memoire presente une serie d'algorithmes permettant la commande d'un manipulateur redondant a 7 degres de liberte de type SARCOS par le logiciel KALI. Un algorithme permettant de calculer la chai ne cinematique resultant du blocage d'une articulation d'un manipulateur seriel arbitraire est d'abord presente. Ensuite le cas particulier associe au manipulateur SARCOS est aussi demontre. Lors du blocage d'une de ses articulations, le manipulateur SARCOS devient un manipulateur a 6 d.d.l., decouplable ou non selon l'articulation qui est bloquee. Des algorithmes permettant de resoudre le probleme geometrique inverse sont donc presentes pour les deux cas. Un algorithme d'exploitation de la redondance developpe en vue de maximiser l'efficacite numerique est aussi presente. Cet algorithme repose sur l'utilisation des equations de vitesse et permet donc de calculer la solution iterativement. A l'aide des reflexions de Householder, une solution a norme mimmale et une solution dans le noyau de la matrice Jacobienne sont trouvees. Cette derniere permet d'utiliser le degre de liberte supplementaire du manipulateur SARCOS afin d'eviter les limites articulaires. Finalement, quelques exemples de trajectoires (obtenus a l'aide d'un simulateur developpe dans le cadre de ce projet) sont donnes.

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This thesis presents a series of algorithms allowing the control of a redundant manipulator with 7 degrees of freedom of the SARCOS type by the KALI software. An algorithm allowing to calculate the kinematic chain resulting from the blocking of a joint of an arbitrary serial manipulator is first presented. Then the special case associated with the SARCOS manipulator is also demonstrated. When one of its joints is blocked, the SARCOS manipulator becomes a 6 d.d.l. manipulator, decouplable or not depending on the joint that is blocked. Algorithms for solving the inverse geometric problem are therefore presented for both cases. A redundancy exploitation algorithm developed to maximize digital efficiency is also presented. This algorithm is based on the use of velocity equations and therefore makes it possible to calculate the solution iteratively. Using Householder reflections, a solution with mimmal norm and a solution in the kernel of the Jacobian matrix are found. The latter makes it possible to use the additional degree of freedom of the SARCOS manipulator in order to avoid articular limits. Finally, some examples of trajectories (obtained using a simulator developed within the framework of this project) are given.