This paper describes a new approach to probabilistic roadmap planners (PRMs). The overall theme of the algorithm, called Lazy PRM, is to minimize the number of collision checks performed during planning and hence minimize the running time of the planner. Our algorithm builds a roadmap in the configuration space, whose nodes are the user-defined initial and goal configurations and a number of randomly generated nodes. Neighboring nodes are connected by edges representing paths between the nodes. In contrast with PRMs, our planner initially assumes that all nodes and edges in the roadmap are collision-free, and searches the roadmap at hand for a shortest path between the initial and the goal node. The nodes and edges along the path are then checked for collision. If a collision with the obstacles occurs, the corresponding nodes and edges are removed from the roadmap. Our planner either finds a new shortest path, or first updates the roadmap with new nodes and edges, and then searches for a shortest path. The above process is repeated until a collision-free path is returned.

We present, implement, and analyze a spectrum of closely-related planners, designed to gain insight into the relationship between classical grid search and probabilistic roadmaps (PRMs). Building on the quasi-Monte Carlo sampling literature, we have developed deterministic variants of the PRM that use low-discrepancy and low-dispersion samples, including lattices. Classical grid search is extended using subsampling for collision detection and also the dispersion-optimal Sukharev grid, which can be considered as a kind of lattice-based roadmap to complete the spectrum. Our experimental results show that the deterministic variants of the PRM offer performance advantages in comparison to the original, multiple-query PRM and the single-query, Lazy PRM. Surprisingly, even some forms of grid search yield performance that is comparable to the original PRM. Our theoretical analysis shows that all of our deterministic PRM variants are resolution complete and achieve the best possible asymptotic convergence rate, which is shown to be superior to that obtained by random sampling. Thus, in surprising contrast to recent trends, there is both experimental and theoretical evidence that the randomization used in the original PRM is not advantageous.

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

In this paper we consider the motion planning problem for arbitrary articulated structures with one or more closed kinematic chains in a workspace with obstacles. This is an important class of problems and there are applications in many areas such as robotics, closed molecular chains, graphical animation, reconfigurable robots. We use the kinematics-based probabilistic roadmap (kbprm) strategy proposed in [7] that conceptually partitions the linkage into a set of open chains and applies random generation methods to some of the chains and traditional inverse kinematics methods to the others. The efficiency of the method depends critically on how the linkage is partitioned into open chains, and the original method assumed the partition was provided as input to the problem. In this paper, we propose a fully automated method for partitioning an arbitrary linkage into open chains and for determining which should be positioned using the inverse kinematic solver. Even so, the size (number of links) of the closed loops that can be handled by this method is limited because the inverse solver can only be applied to small chains. To handle high dof closed loops, we show how we can use the Iterative Relaxation of Constraints (IRC) strategy [3] to efficiently handle large loops while still only using inverse kinematics for small chains. Our results in 3-dimensional workspace both for planar and spatial linkages show that our framework performs well for general linkage. We also use our planner to simulate an adjustable lamp called Luxo. Using IRC, our planner can handle a single loop of up to 44 links.

Probabilistic roadmap planners have been very successful in path planning for a wide variety of problems, especially applications involving robots with many degrees of freedom. These planners randomly sample the configuration space, building up a roadmap that connects the samples. A major problem is finding valid configurations in tight areas, and many methods have been proposed to more effectively sample these regions. By constructing a skeleton-like subset of the free regions of the workspace, these heuristics can be strengthened. The skeleton provides a concise description of the workspace topology and an efficient means of finding points with maximal clearance from the obstacles. We examine the medial axis as a skeleton, including a method to compute an approximation to it. The medial axis is a twoequidistant surface in the workspace. We form a heuristic for finding difficult configurations using the medial axis, and demonstrate its effectiveness in a planner for rigid objects in a three dimensional workspace.

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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

The probabilistic roadmap approach is one of the leading motion planning techniques. Over the past eight years the technique has been studied by many different researchers. This has led to a large number of variants of the approach, each with its own merits. It is difficult to compare the different techniques because they were tested on different types of scenes, using different underlying libraries, implemented by different people on different machines. In this paper we provide a comparative study of a number of these techniques, all implemented in a single system and run on the same test scenes and on the same computer. In particular we compare collision checking techniques, basic sampling techniques, and node adding techniques. The results should help future users of the probabilistic roadmap planning approach to choose the correct techniques.

Probabilistic roadmap planners have been used with success to plan paths for flexible objects such as metallic plates or plastic flexible pipes. This paper improves the performance of these planners by using the medial axis of the workspace to guide the random sampling. At a preprocessing stage, the medial axis of the workspace is computed using a recent efficient algorithm. Then the flexible object is fitted at random points along the medial axis. The energy of all generated configurations is minimized and the planner proceeds to connect them with low-energy quasi-static paths in a roadmap that captures the connectivity of the free space. Given an initial and a final configuration, the planner connects these to the roadmap and searches the roadmap for a path. Our experimental results show that the new sampling scheme is successful in identifying critical deformations of the object along solution paths which results in a significant reduction of the computation time. Our work on planning for flexible objects has applications in industrial settings, virtual reality environments, and medicine.