|Abstract:||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 more efficient practical algorithms. Our results include algorithms addressing the issues, theoretical analysis of their performance and experimental evaluation on motion planning problems.