La redondance cinématique dans les robots parallèles pour l'augmentation de l'espace de travail en orientation

Authors: Schreiber, Louis Thomas
Advisor: Gosselin, Clément
Abstract: This thesis deals with the use of kinematic redundancy in parallel robots to increase their orientational workspace. Multiple new architectures are introduced and analysed. The emphasis is on purely parallel architectures since serial and hybrid arrangements are already much better known. First, a literature review article positions the project in the current context. This article shows how kinematic redundancy compares to actuation redundancy and other hybrid architectures. The advantages and disadvantages of each are highlighted. This article also sheds light on the type of layout (serial or parallel) of the actuators for the different types of redundancy. The mathematical bases for kinematic modeling of several architectures are also given. In the second article, two architectures of planar mechanisms are presented and analyzed (inverse and forward kinematic problem, singularity analysis, workspace). Planar architectures are used to introduce redundancy management with a simple case (a single redundant degree of freedom). The redundancy management algorithm must define the best configuration of the redundant degree of freedom while respecting the physical limits of the mechanism (speeds, interferences). A four-degree-of-freedom architecture (SCARA movement) with one redundant degree of freedom is then introduced in the third article. This architecture has the particularity of not being limited (neither by mechanical interferences nor by singularities) in terms of rotation. Kinematic and workspace analyses are presented and a prototype demonstrates convincing experimental results. Then, the fourth article introduces a six-degree-of-freedom architecture with three redundant degrees of freedom. This architecture occupies a large part of the work presented in this thesis. It is derived directly from the Gough-Stewart platform. The kinematic model and an analysis of the singularities of the mechanism are presented. A geometric analysis shows the singularity avoidance capabilities and a workspace analysis shows very high platform tilting and twisting capabilities. The fifth article presents two spherical joints that have been developed specifically for the six-degree-of-freedom architecture. The operating principle of these two spherical joints is explained and the large range of motion (tilting angle) is demonstrated. Two prototypes are presented. The sixth article introduces different methods to exploit the redundancy of the six-degreeof- freedom manipulator while respecting the physical limits of the mechanism (mechanical interference as well as the speed limits of the actuators). A first method attempts to use an analytical expression of the determinant of the Jacobian matrix. The second is purely geometric and is inspired from Grassmann geometry. The third uses a complete discretization of the Cartesian trajectories and the space of the redundant degrees of freedom. Finally, the fourth method uses local optimization. The results of the different methods are then compared.
Document Type: Thèse de doctorat
Issue Date: 2019
Open Access Date: 3 February 2021
Grantor: Université Laval
Collection:Thèses et mémoires

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