Local randomization in neighbor selection improves PRM roadmap quality

Abstract

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].

A scalable motion planner for high-dimensional kinematic systems

“…In particular, it is shown that a nearly random tree search can perform virtually identically to the well-known RRT algorithm and that removing the workspace decomposition from XXL yields a (nearly) random graph that can perform well in certain instances of planning for R2 and planar kinematic chains. The benefits of randomizing the neighbor selection have been demonstrated previously for the PRM (McMahon et al, 2012), showing that connecting to a random subset of the k -nearest neighbors can result in better connected roadmaps in a variety of planning queries with rigid and articulated systems.…”

Adaptive local learning in sampling based motion planning for protein folding

“…Connecting all possible pairs of samples is computationally unfeasible, and it has been shown that only connecting the k-closest neighbors results in a roadmap of comparable quality [26].…”

The anatomy of a distributed motion planning roadmap

“…This may not be the case if the edges are not unique, a condition which may occur if V is low and k or k is high. Typically, k is a constant and is normally very low compared to V [3], [9], so our assumption is emperically valid. Also, selecting unique random neighbors increases the possibility that the resulting edge connection is unique.…”

“…While selecting closest neighbors is the defacto standard in motion planning algorithms, it is not uncommon to explore random neighbor selection [1], [12], [13]. In fact, some studies have shown that random neighbor selection does improve roadmap quality [9].…”