Abstract-Probabilistic Roadmap Methods (PRMs) are one of the most used classes of motion planning methods. These sampling-based methods generate robot configurations (nodes) and then connect them to form a graph (roadmap) containing representative feasible pathways. A key step in PRM roadmap construction involves identifying a set of candidate neighbors for each node. Traditionally, these candidates are chosen to be the k-closest nodes based on a given distance metric. In this paper, we propose a new neighbor selection policy called LocalRand(k, k ′ ), that first computes the k ′ closest nodes to a specified node and then selects k of those nodes at random. Intuitively, LocalRand attempts to benefit from random sampling while maintaining the higher levels of local planner success inherent to selecting more local neighbors. We provide a methodology for selecting the parameters k and k ′ . We perform an experimental comparison which shows that for both rigid and articulated robots, LocalRand results in roadmaps that are better connected than the traditional k-closest policy or a purely random neighbor selection policy. The cost required to achieve these results is shown to be comparable to k-closest. I. IntroductionThe motion planning problem involves finding a valid path for a movable object (robot) from a start to a goal configuration in a given environment. Motion planning is an important component of many applications, including computer-aided design Sampling-based methods have been able to solve many motion planning problems that exact methods cannot. One of the most common randomized methods is the Probabilistic Roadmap Method, or PRM [19]. This method randomly generates valid samples (nodes) in an environment's configuration space (C-space) and then attempts to connect nearby pairs of nodes using a local planner, a simplified planner whose objective is to generate and validate transitions between the the specified pair of nodes. The resulting graph, or roadmap, encodes representative feasible paths in C-space and can be queried to obtain valid paths in the environment.One of the key steps in PRM construction is node connection. Ideally, roadmap connectivity should reflect the connectivity of the underlying C-space. From this perspective, the best strategy would be to attempt to connect all θ (n 2 ) pairs of nodes. However, the cost of all these connection attempts is not feasible for any but the simplest of problems. Hence, the selection of candidates for local transitions (neighbors) is crucial to both roadmap quality and efficiency.The objective of a good neighbor selection strategy is to identify pairs of configurations that have a high probability of being connectible by the local planner and that are useful in terms of producing good quality roadmaps. The most commonly used method for neighbor selection in PRMs uses nearest-neighbor search to select the k nodes that are closest to the node in question, where k is typically some relatively small, fixed constant, typically between 5 and 25 [10].

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