Geometric Reasoning About Translational Motions

This thesis addresses the problems of planning highly coordinated collision-free translational motions ofmultiple objects (general polygons or polyhedra) and finding sequences of translations that allow for theremoval of one or more objects. These problems are known to be PSPACE-hard in general. Our mainfocus is therefore on the design and analysis of adaptive algorithms that can cope with practically relevantcases such as tightly interlaced placements. Exact and complete algorithms are...