This paper presents a new method to isolate all configurations that a multiloop linkage can adopt. The problem is tackled by means of formulation and resolution techniques that fit particularly well together. The adopted formulation yields a system of simple equations (only containing linear, bilinear, and quadratic monomials, and trivial trigonometric terms for the helical pair only) whose structure is later exploited by a branchand-prune method based on linear relaxations. The method is general, as it can be applied to linkages with single or multiple loops with arbitrary topology, involving lower pairs of any kind, and complete, as all possible solutions get accurately bounded, irrespectively of whether the linkage is rigid or mobile.

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In its original formulation, the motion planning problem considers the search of a robot path from an initial to a goal configuration. The study of motion planning has advanced significantly in recent years, in large part due to the development of highly successful sampling and searching techniques. Recent advances have influenced sampling-based motion planning algorithms to be used in disparate areas such as humanoid robotics, automotive manufacturing, architecture, computational geography, computer graphics, and computational biology. Many of these methods work well on a large set of problems, however, they have weaknesses and limitations. This thesis expands the basic motion planning techniques to include critical concerns that are not covered by the motion planning algorithms that are in widespread use now. The technical approach is organized around three main thrusts: 1) the development of efficient nearest neighbor searching techniques for spaces arising in motion planning; 2) the development of uniform sampling techniques on these spaces to allow resolution completeness in sampling-based planning algorithms; and 3) the development of guided sampling techniques for efficient exploration on such spaces. We show that most of the modern motion planners incorporate one or more of these components; therefore, addressing these core issues in motion planning does not only lead to a more fundamental understanding of the problem, but also to

any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. Modular and Reconfigurable Robots (MRRs) are those designed to address the increasing demand for flexible and versatile manipulators in manufacturing facilities. The term, modularity, indicates that they are constructed by using a limited number of interchangeable standardized modules which can be assembled in different kinematic configurations. Thereby, a wide variety of specialized robots can be built from a set of standard components. The term, reconfigurability, implies that the robots can be disassembled and rearranged to accommodate different products or tasks rather than being replaced. A set of MRR modules may consist of joints, links, and end-effectors. Different kinematic configurations are achieved by using different joint, link, and end-effector modules and by changing their relative orientation. The number of distinct kinematic configurations, attainable by a set of modules, varies with respect to the size of the module set from several tens to several thousands. Although determining the most suitable configuration for a specific task from