We introduce the notion of expansiveness to characterize a family of robot configuration spaces whose connectivity can be effectively captured by a roadmap of randomly-sampled milestones. The analysis of expansive configuration spaces has inspired us to develop a new randomized planning algorithm. This algorithm tries to sample only the portion of the configuration space that is relevant to the current query, avoiding the cost of precomputing a roadmap for the entire configuration space. Thus, it is well-suited for problems where a single query is submitted for a given environment. The algorithm has been implemented and successfully applied to complex assembly maintainability problems from the automotive industry.

... This paper provides foundations for understanding the effect of passages on the connectedness of probabilistic roadmaps. It also proposes a new random sampling scheme for finding such passages. An initial roadmap is built in a "dilated" free space allowing some penetration distance of the robot into the obstacles. This roadmap is then modified by resampling around the links that do not lie in the true free space. Experiments show that this strategy allows relatively small roadmaps to reliably capture the free space connectivity

Abstract — Probabilistic roadmap (PRM) planners have been successful in path planning of robots with many degrees of freedom, but narrow passages in a robot’s configuration space create significant difficulty for PRM planners. This paper presents a hybrid sampling strategy in the PRM framework for finding paths through narrow passages. A key ingredient of the new strategy is the bridge test, which boosts the sampling density inside narrow passages. The bridge test relies on simple tests of local geometry and can be implemented efficiently in high-dimensional configuration spaces. The strengths of the bridge test and uniform sampling complement each other naturally and are combined to generate the final hybrid sampling strategy. Our planner was tested on point robots and articulated robots in planar workspaces. Preliminary experiments show that the hybrid sampling strategy enables relatively small roadmaps to reliably capture the connectivity of configuration spaces with difficult narrow passages. I.

Abstract This paper presents a comparative evaluation of different dis-tance metrics and local planners within the context of probabilistic roadmap methods for motion planning. Both C-space andWorkspace distance metrics and local planners are considered. The study concentrates on cluttered three-dimensionalWorkspaces typical, e.g., of mechanical designs. Our results include recommendations for selecting appropriate combinationsof distance metrics and local planners for use in motion planning methods, particularly probabilistic roadmap methods. Wefind that each local planner makes some connections than none of the others do-- indicating that better connectedroadmaps will beconstructed using multiple local planners. We propose a new local planning method we call rotate-at-s that outperforms the commonstraight-line in C-space method in crowded environments. 1

This paper describes a nev probabilistic roadmap (PRM) path planner that is: (1) single-query instead of pre-computing a roadmap covering the entire free space, it uses the tvo input query configurations as seeds to explore as little space as possible; (2) hi-directional it explores the robotis free space by concur- rently building a roadmap made of tvo trees rooted at the query configurations; (3) adaptive it makes longer steps in opened areas of the free space and shorter steps in cluttered areas; and (4) lazy in checking collision it delays collision tests along the edges of the roadmap until they are absolutely needed. Experimental results shov that this combination of techniques drastically reduces planning times, making it possible to handle difficult problems, including multi-robot problems in geometrically complex environments.

We propose the use of quasi-random sampling techniques for path planning in high-dimensional conguration spaces. Following similar trends from related numerical computation elds, we show several advantages oered by these techniques in comparison to random sampling. Our ideas are evaluated in the context of the probabilistic roadmap (PRM) framework. Two quasi-random variants of PRM-based planners are proposed: 1) a classical PRM with quasi-random sampling, and 2) a quasi-random Lazy-PRM. Both have been implemented, and are shown through experiments to oer some performance advantages in comparison to their randomized counterparts. 1 Introduction Over two decades of path planning research have led to two primary trends. In the 1980s, deterministic approaches provided both elegant, complete algorithms for solving the problem, and also useful approximate or incomplete algorithms. The curse of dimensionality due to high-dimensional conguration spaces motivated researchers from the 199...

This paper describes the foundations and algorithms of a new probabilistic roadmap (PRM) planner that is: single-query -- instead of pre-computing a roadmap covering the entire free space, it uses the two input query configurations to explore as little space as possible; bi-directional -- it explores the robot's free space by building a roadmap made of two trees rooted at the query configurations; and lazy in checking collisions -- it delays collision tests along the edges of the roadmap until they are absolutely needed. Several observations motivated this strategy: (1) PRM planners spend a large fraction of their time testing connections for collision; (2) most connections in a roadmap are not on the final path; (3) the collision test for a connection is most expensive when there is no collision; and (4) any short connection between two collision-free configurations has high prior probability of being collision-free. The strengths of single-query and bi-directional sampling techniques, and those of delayed collision checking reinforce each other. Experimental results

This paper presents a randomized motion planner for kinodynamic asteroid avoidanceproblems, in which a robot must avoid collision with moving obstacles under kinematic, dynamic constraints and reach a specified goal state. Inspired by probabilistic-roadmap (PRM) techniques, the planner samples the state\Thetatime space of a robot by picking control inputs at random in order to compute a roadmap that captures the connectivity of the space. However, the planner does not precompute a roadmap as most PRM planners do. Instead, for each planning query, it generates, on the fly, a small roadmap that connects the given initial and goal state. In contrast to PRM planners, the roadmapcomputed by our algorithm is a directed graph oriented along the time axis of the space. To verify the planner's effectiveness in practice, we tested it both in simulated environments containing many moving obstacles and on a real robot under strict dynamic constraints. The efficiency of the planner makes it possibl...

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Typical high-level directives for locomotion of human-like characters are useful for interactive games and simulations as well as for off-line production animation. In this paper, we present a new scheme for planning natural-looking locomotion of a biped figure to facilitate rapid motion prototyping and task-level motion generation. Given start and goal positions in a virtual environment, our scheme gives a sequence of motions to move from the start to the goal using a set of live-captured motion clips. Based on a novel combination of probabilistic path planning and hierarchical displacement mapping, our scheme consists of three parts: roadmap construction, roadmap search, and motion generation. We randomly sample a set of valid footholds of the biped figure from the environment to construct a directed graph, called a roadmap, that guides the locomotion of the figure. Every edge of the roadmap is associated with a live-captured motion clip. Augmenting the roadmap with a posture transition graph, we traverse it to obtain the sequence of input motion clips and that of target footprints. We finally adapt the motion sequence to the constraints specified by the footprint sequence to generate a desired locomotion.