this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints.

LAAS-CNRS, 7 avenue du Colonel-Roche, 31077 Toulouse, France Abstract-- This paper presents a variant of Probabilistic Roadmap Methods (PRM) that recently appeared as a promising approach to motion planning. We exploit a free-space structuring of the configuration space into visibility domains in order to produce small roadmaps, called visibility roadmaps. Our algorithm integrates an original termination condition related to the volume of the free space covered by the roadmap. The planner has been implemented within a software platform allowing to address a large class of mechanical systems. Experiments show the efficiency of the approach in particular for capturing narrow passages of collision-free configuration spaces. Key words: Collision-avoidance; path planning; motion planning; global planning; probabilistic roadmaps 1.

The Probabilistic RoadMap planner (PRM) has been applied with success to multiple planning problems involving robots with 3 to 16 degrees of freedom (dof) operating in known static environments. This paper describes the planner and reports on experimental and theoretical results related to its performance. PRM computation consists of a preprocessing and a query phase. Preprocessing, which is done only once for a given environment, generates a roadmap of randomly, but properly selected, collision-free configurations (nodes). Planning then connects any given initial and final configurations of the robot to two nodes of the roadmap and computes a path through the roadmap between these two nodes. The planner is able to find paths involving robots with 10 dof in a fraction of a second after relatively short times for preprocessing (a few dozen seconds). Theoretical analysis of the PRM algorithm provides bounds on the number of roadmap nodes needed for solving planning problems in spaces with certain geometric properties. A number of theoretical results are presented in this paper under a unified framework.

Hierarchical data structures have been widely used to design e cient algorithms for interference detection for robot motion planning and physically-based modeling applications. Most of the hierarchies involve use of bounding volumes which enclose the underlying geometry. These bounding volumes are used to test for interference orcompute distance bounds between the underlying geometry. The e ciency of a hierarchy is directly proportional to the choice ofabounding volume. In this paper, we introduce spherical shells, a higher order bounding volume for fast proximity queries. Each shell corresponds to a portion of the volume between two concentric spheres. We present algorithms to compute tight tting shells and fast overlap between two shells. Moreover, we show that spherical shells provide local cubic convergence to the underlying geometry. As aresult, in many cases they provide faster algorithms for interference detection and distance computation as compared toearlier methods. We also describe an implementation and compare it with other hierarchies. 1

This paper presents a variant of probabilistic roadmap algorithms that recently appeared as a promising approach to motion planning. We exploit a free-space structuring of the configuration space into visibility domains in order to produce small roadmaps. The algorithm has been implemented within a software platform allowing to address a large class of mechanical systems. Experiments show the efficiency of the approach in capturing narrow passages of collision-free configuration spaces. 1 Introduction Due to the continuous increasing power of the computers, probabilistic approaches to motion planning (e.g.,[2, 6, 13, 8, 3]) allow today to solve practical problems which were not addressed few years ago. Apart some attempts aiming to provide formal models of complexity [10, 7, 4, 15], the success of such methods remains better noticed than well understood. This paper proposes a variant of the Probabilistic RoadMap (PRM) algorithm introduced in [6] (and independently in [13] as the Pro...

This paper describes a first step in the direction of solving a variant of the above problem, namely the problem of planning a path for a flexible robot/part. We focus on the case of an elastic metal plate to illustrate our approach and explore some of the issues arising when considering flexible parts

This paper addresses the problem of planning paths for an elastic object from an initial to a final configuration in a static environment. It is assumed that the object is manipulated by two actuators and that it does not touch the obstacles in its environment at any time. The object may need to deform in order to achieve a collision-free path from the initial to the final configuration. Any required deformations are automatically computed by our planner according to the principles of elasticity theory from mechanics. The problem considered in this paper differs significantly from that of planning for a rigid or an articulated object. In the first part of the paper we point out these differences and highlight the reasons that make planning for elastic objects an extremely difficult task. We then present a randomized algorithm for computing collision-free paths for elastic objects under the above-mentioned restrictions of manipulation.

This paper presents a probabilistic planner capable of finding paths for a flexible surface patch. The planner is based on the Probabilistic Roadmap approach to path planning while the surface patch is modeled as a low degree Bézier surface. We assume that we are dealing with an elastic part and define an approximate energy model for the part. The energy function penalizes excessive shear and bending of the part and we assume that low-energy configurations correspond to reversible elastic deformations of the part. The planner captures the connectivity of a space by building a roadmap, a network of simple paths connecting configurations selected in the space using randomized techniques. We report on the implementation of our planner and show experimental results with examples where the surface patch is required to move through a small hole in its workspace. Our work is a first step towards considering the physical properties of parts when planning paths.

This paper describes a new efficient collision checker to test single straight-line segments in c-space, sequences of such segments, or more complex paths. This checker is particularly suited for probabilistic roadmap (PRM) planners applied to manipulator arms and multi-robot systems. Such planners spend most of their time checking local paths between randomly sampled configurations for collision. While commonly used approaches test intermediate configurations on a segment at a prespecified resolution, the checker presented in this paper is exact, i.e., it cannot fail to find an existing collision, even when some robot links and obstacles are very thin. Its efficiency relies on its core algorithm, which dynamically adjusts the required resolution by relating the distances between objects in the workspace to the maximum lengths of the paths traced out by points on these objects. The checker's efficiency is further increased by several additional techniques presented in this paper, which adequately approximate distances between objects and lengths of travelled paths in workspace, and order collision tests to reveal collisions as early as possible. The new checker has been extensively tested, first on segments randomly generated in c-space, next as part of an existing PRM planner, and finally as part of a path smoother/optimizer. These experiments show that the checker is faster than a resolution-based approach (with suitable resolution), with the enormous advantage that it never returns an incorrect answer. The checker also admits a number of straightforward extensions. For example, it can monitor a minimum workspace distance between each robot link and other objects (e.g., obstacles, links of other robots).

This paper reports on our current effort for applying probabilistic path planning techniques to logistics and operation in huge industrial installations (e.g., power plants). We show how the specific domain constraints impose a dedicated software architecture to take advantage of the generality of probabilistic approaches. In addition, such an architecture should be compatible with existing CAD systems making critical the interface issues. We conclude on three study cases currently under development within the European project MOLOG. 1 Introduction Today CAD systems are widely used in manufacturing and more generally to help the operation of complex systems and complex tasks. They are supported by powerful dedicated software including 3D visualization possibilities, geometric tools and friendly interfaces. In the framework of logistics of industrial installations, CAD systems provide tools for the manipulation and storage of plant layout and design information. Accurate, full color ...