Probabilistic Roadmaps of Trees for Parallel Computation of Multiple Query Roadmaps

Abstract

Abstract. We propose the combination of techniques that solve multiple queries for motion planning problems with single query planners in a motion planning framework that can be efficiently parallelized. In multiple query motion planning, a data structure is built during a preprocessing phase in order to quickly respond to on-line queries. Alternatively, in single query planning, there is no preprocessing phase and all computations occur during query resolution. This paper shows how to effectively combine a powerful sample-based method primarily designed for multiple query planning (the Probabilistic Roadmap Method -PRM) with sample-based tree methods that were primarily designed for single query planning (such as Expansive Space Trees, Rapidly Exploring Random Trees, and others). Our planner, which we call the Probabilistic Roadmap of Trees (PRT), uses a tree algorithm as a subroutine for PRM. The nodes of the PRM roadmap are now trees. We take advantage of the very powerful sampling schemes of recent tree planners to populate our roadmaps. The combined sampling scheme is in the spirit of the non-uniform sampling and refinement techniques employed in earlier work on PRM. PRT not only achieves a smooth spectrum between multiple query and single query planning but it combines advantages of both. We present experiments which show that PRT is capable of solving problems that cannot be addressed efficiently with PRM or single-query planners. A key advantage of PRT is that it is significantly more decoupled than PRM and sample-based tree planners. Using this property, we designed and implemented a parallel version of PRT. Our experiments show that PRT distributes well and can easily solve high dimensional problems that exhaust resources available to single machines.

GPU-Based Parallel Collision Detection for Real-Time Motion Planning

“…for parallel collision queries in milestone computation and local planning. Some of the prior algorithms perform parallel queries in a simple manner: each thread handles a single collision query in an independent manner [23,22,3,2]. As current multi-core CPUs have the capability to perform multiple-instruction multiple-data (MIMD) computations, these simple strategies can work well on CPUs.…”

Iteratively Locating Voronoi Vertices for Dispersion Estimation

“…They continue this procedure until a Voronoi vertex is found. 1 It is interesting to note the similarities between this approach and Lloyd's algorithm for k-means clustering [19]. In many cases, our algorithm will behave similar to these approaches; however, our method improves upon them in several respects.…”

“…Multiple-query algorithms like PRMs construct graphs which attempt to represent the connectivity of free space [1], [2], [13], [16], [24], [27]; single-query algorithms construct search graphs which attempt to solve a particular motion planning query [12], [14], [15], [21]. Typically, both multiple-and single-query methods build graphs in which the vertices are points in the state space or the configuration space.…”

“…Coverage estimation may be useful for providing deterministic safety guarantees when the safety falsification tool is unable to find an unsafe trajectory. Third, Voronoi vertices can be used to inform multiple-tree planners such as [1], [9], [25]. One of the key questions which multiple-tree algorithms must answer is when (and where) to start a new search tree.…”

Motion Planning for a Six-Legged Lunar Robot

“…A prm planner samples configurations at random, retaining feasible ones as milestones and connecting close milestones if possible with feasible local paths. Its performance depends on fast methods of sampling and local connection, either from scratch across all of configuration space [24] or via perturbation by growing trees from existing milestones [1,22,30]. Closed kinematic chains (athlete has many) make both of these operations harder because there is zero probability that an arbitrary configuration will satisfy the closure constraints.…”