Geometry and Algorithms for Part Fixturing, Grasping and Manipulation with Modular Fixturing Elements, a New Reconfigurable Gripper and Mobile Robots

This thesis addresses the problem of immobilizing and manipulating parts with devices that have a mixture of discrete and continuous degrees of freedom. Immobilizing an object requires calculating the device parameters that reduce the positions and orientations of the object compatible with the contact constraints to a single point of its conguration space. Likewise, manipulating an object requires identifying the regions of its con guration space where it is free to move under the contact constraints. The kinematic theory of second order mobility of rigid bodies is used, together with the new concept of Inescapable Con guration Space region, to devise e cient algorithms for planning immobilizing xtures, grasps, in-hand manipulation sequences and obstacle avoidance manipulation plans for parts with known geometry. This approach is applied to three di erent mechanisms: a xturing device assembled from standard modular elements, a novel recon gurable gripper, and a team of mobile robots.