Nous proposons une méthode générale et analytique de description des limites de l'espace de travail plan, c'est-à-dire la frontière de la partie de l'espace du plan atteinte par l'extrémité d'un bras humain ou de robot. La méthode proposée est décomposée en trois étapes indépendantes, aucune ne faisant appel à des calculs de dérivées, de déterminants ou de valeurs propres, ou utilisant des méthodes de résolution numérique de problèmes non linéaires, tous souvent utilisés dans la littérature. La première étape, déjà présentée dans des travaux précédents, consiste à interpréter de façon géométrique la nécessaire dégénérescence de la matrice jacobienne de la fonction de position, au bord de l'espace de travail et une condition d'alignement de certaines articulations permet de déterminer une réunion d'arcs de cercle qui contiennent la frontière. Ensuite, pour chacun des arcs de cercle, l'étude de la variation infinitésimale d'un point par rapport à ce cercle permet d'éliminer tout ou partie des arcs de cercle précédemment définis, qui n'est pas sur la frontière. Enfin, un parcours global de la réunion des arcs de cercle permet de déterminer la frontière extérieure ainsi que la frontière intérieure de l'éventuel trou de l'espace de travail qui contient l'origine.
We give a general and analytical description of plan workspace boundaries, i.e. the boundaries of the part of the space that is reached by the extremity of a human or robot arm. The proposed method is decomposed into three independent steps, for which we do not use calculus of derivatives, determinants and eigenvalues, or numerical resolutions of non-linear problems, which are often used in the literature. The first step, already presented in previous works, consists in interpreting geometrically the necessary Jacobian rank deficiency of the position function at the boundary, and an alignment condition of some joints allows us to determine a union of arcs of circle, which contains the boundary. Then, for all arc of circle, the study of the infinitesimal displacement of a point with regard to this circle allows one to eliminate all or a part of arcs of circle, previously defined, which is not on the boundary. Finally, a global course of the arcs of circle allows us to determine the outer boundary and the inner boundary of the possible void that contains the origin.
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Keywords: Robotics, Workspace, Boundary, Arm, Joints, Biomechanics
@article{CRMECA_2018__346_1_13_0,
author = {J\'er\^ome Bastien},
title = {Description analytique compl\`ete des limites de l'espace de travail pour un manipulateur en s\'erie plan},
journal = {Comptes Rendus. M\'ecanique},
pages = {13--25},
publisher = {Elsevier},
volume = {346},
number = {1},
year = {2018},
doi = {10.1016/j.crme.2017.10.004},
language = {fr},
}
Jérôme Bastien. Description analytique complète des limites de l'espace de travail pour un manipulateur en série plan. Comptes Rendus. Mécanique, Volume 346 (2018) no. 1, pp. 13-25. doi : 10.1016/j.crme.2017.10.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.10.004/
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Commentaires - Politique
Jérôme Bastien; Pierre Legreneur; Karine Monteil
C. R. Méca (2007)