Parcours continus isotropes et surfaces isotropes de manipulateurs seriels

This thesis deals with serial manipulators as simple opened kinematics chains. These are more precisely the continuous paths, upon which such manipulators always keep an isotropic configuration, that are the subject of the study. The capacity of a manipulator to direct and move its effector is a decisive point in carrying out tasks. Bigger is this capacity better will be the possibility for the manipulator to carry out tasks. The maximal capacity is reached for isotropic configurations. Until recently, the only reachable isotropic configurations by manipulators were isolated configurations, or configurations that we call trivial which means they result from the rotation of the first joint. The contribution of this thesis is to prove the existence of non trivial isotropic paths. Thus, many manipulators can perform tasks on non punctual or non circular paths with an improved dexterity far from singularities.;Not only serials manipulators with contiunous isotropic paths have been found, but also manipulators with isotropic surfaces. These isotropic surfaces are determined for spherical and non spherical manipulators. The isotropy of orientation and isotropy of position are studied separately, then simultaneously.;Through the concept of virtual joints introduced in chapter 4 and 5, this work is also the opportunity to bring a new clarification on the various definitions of manipulators dexterity that have been proposed for more than two decades.;The chapter 2 which ensue from the introduction and related works deals with the conditioning and the isotropy. Most of the expounded results and examples are draged from related papers and aim at showing the importance of these notions which are used as a basis of this research.;The chapter 3 proves an important result: the non existence of non trivial continuous isotropic paths for spherical manipulators with less than 6 joints. It enabled to simplify the work by focusing the research study on spherical manipulators 6R, which enabled to obtain the results of chapter 4 that proves the existence of spherical manipulators having isotropic surfaces, and that even proves the existence of a manipulator which keep an isotropic configuration for all orientation of its effector.;The chapter 5 reveals the existence of an isotropic serial manipulator 4R in position on a sphere. It also compare the dexterity of a manipulator according to criterions based on the conditioning of the jacobian matrix and on the determinant of its product with its transpose: a very interesting analogy was then brought to light. The decoupling between the isotropy of orientation and position was presented through a manipulator being able to have continuous paths around the orientation isotropy and, at the same time, around the singularity in position. It also appears, in contrary to the first impressions, that the isotropy of position is easier to obtain that the isotropy of orientation in the case of a serial manipulator nR.;In this thesis, a lot of results are new and establish interesting prospects on future research study like new situations close to the isotropy in orientation and at the same time close to the singularity in position, and vice-versa. Determination of patterns allowing some specific isotropic continuous paths beforehand setted, can be also considered.;Contributions. This work let us introduce isotropic continuous paths and isotropic surfaces. Some examples of these paths and surfaces were given for spherical and non spherical manipulators. It also enabled to determine the minimum number of needed joints to get isotropic paths. A geometrical resolution of the equations system defining isotropic conditions enabled to determine the general jacobian matrix of a spherical manipulator 5R and can enable the determination of the general jacobian matrix of a spherical manipulator 6R, what an algebraic resolution of the same systems can not perform. The introduction of the virtual joint notion enabled to obtain an estimation mean of the various indexes of dexterity and also to have a better accuracy by performing more accurate calculation using isotropic jacobian matrices.