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34
RapidlyExploring Random Trees: Progress and Prospects
 Algorithmic and Computational Robotics: New Directions
, 2000
"... this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints. ..."
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Cited by 228 (25 self)
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this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints.
Probabilistic Roadmaps for Robot Path Planning
, 1998
"... 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 perfo ..."
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Cited by 54 (5 self)
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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, collisionfree 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.
Visibilitybased probabilistic roadmaps for motion planning
 Journal of Advanced Robotics
, 2000
"... LAASCNRS, 7 avenue du ColonelRoche, 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 freespace structuring of the configuration space into visibility domains in or ..."
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Cited by 54 (16 self)
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LAASCNRS, 7 avenue du ColonelRoche, 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 freespace 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 collisionfree configuration spaces. Key words: Collisionavoidance; path planning; motion planning; global planning; probabilistic roadmaps 1.
Spherical shell: A higher order bounding volume for fast proximity queries
 In Proc. of Third International Workshop on Algorithmic Foundations of Robotics
"... Hierarchical data structures have been widely used to design e cient algorithms for interference detection for robot motion planning and physicallybased modeling applications. Most of the hierarchies involve use of bounding volumes which enclose the underlying geometry. These bounding volumes are u ..."
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Cited by 46 (9 self)
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Hierarchical data structures have been widely used to design e cient algorithms for interference detection for robot motion planning and physicallybased 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
Visibility Based Probabilistic Roadmaps
, 1999
"... This paper presents a variant of probabilistic roadmap algorithms that recently appeared as a promising approach to motion planning. We exploit a freespace structuring of the configuration space into visibility domains in order to produce small roadmaps. The algorithm has been implemented within a ..."
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Cited by 44 (1 self)
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This paper presents a variant of probabilistic roadmap algorithms that recently appeared as a promising approach to motion planning. We exploit a freespace 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 collisionfree 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...
Planning Paths for Elastic Objects Under Manipulation Constraints
 International Journal of Robotics Research
, 2001
"... 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 ..."
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Cited by 38 (7 self)
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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 collisionfree 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 collisionfree paths for elastic objects under the abovementioned restrictions of manipulation.
Planning Paths for a Flexible Surface Patch
 Proc. IEEE Int. Conf. on Robotics and Automation
, 1998
"... 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 def ..."
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Cited by 36 (7 self)
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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 lowenergy 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.
Towards Planning for Elastic Objects
 ROBOTICS: THE ALGORITHMIC PERSPECTIVE
, 1998
"... This paper investigates the problem of path planning for a thin elastic plate. The underlying geometric model for the plate is provided by a Bezier representation. The geometric model is augmented by a realistic mechanical model. The latter permits the computation of the shape of the plate with resp ..."
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Cited by 35 (6 self)
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This paper investigates the problem of path planning for a thin elastic plate. The underlying geometric model for the plate is provided by a Bezier representation. The geometric model is augmented by a realistic mechanical model. The latter permits the computation of the shape of the plate with respect to a set of grasping constrints by minimizing the elastic energy of the deformation. We use a probabilistic roadmap planner to compute paths for the plate and we present a number of experimental results to illustrate our approach. Our work is a first step towards considering the physical properties of objects when planning.
Exact Collision Checking Of Robot Paths
, 2002
"... This paper describes a new efficient collision checker to test single straightline segments in cspace, sequences of such segments, or more complex paths. This checker is particularly suited for probabilistic roadmap (PRM) planners applied to manipulator arms and multirobot systems. Such planners ..."
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Cited by 28 (6 self)
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This paper describes a new efficient collision checker to test single straightline segments in cspace, sequences of such segments, or more complex paths. This checker is particularly suited for probabilistic roadmap (PRM) planners applied to manipulator arms and multirobot 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 cspace, 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 resolutionbased 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).
Adaptive dynamic collision checking for single and multiple articulated robots in complex environments
 IEEE Tr. on Robotics
, 2005
"... Abstract — Static collision checking amounts to testing a given configuration of objects for overlaps. In contrast, the goal of dynamic checking is to determine whether all configurations along a continuous path are collisionfree. While there exist effective methods for static collision detection, ..."
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Cited by 19 (0 self)
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Abstract — Static collision checking amounts to testing a given configuration of objects for overlaps. In contrast, the goal of dynamic checking is to determine whether all configurations along a continuous path are collisionfree. While there exist effective methods for static collision detection, dynamic checking still lacks methods that are both reliable and efficient. A common approach is to sample paths at some fixed, prespecified resolution and statically test each sampled configuration. But this approach is not guaranteed to detect collision whenever one occurs, and trying to increase its reliability by refining the sampling resolution along the entire path results in slow checking. This paper introduces a new method for testing path segments in cspace or collections of such segments, that is both reliable and efficient. This method locally adjusts the sampling resolution by comparing lower bounds on distances between objects in relative motion with upper bounds on lengths of curves traced by points of these moving objects. Several additional techniques and heuristics increase the checker’s efficiency in scenarios with many moving objects (e.g., articulated arms and/or multiple robots) and high geometric complexity. The new method is general, but particularly well suited for use in probabilistic roadmap (PRM) planners, where it is critical to determine as quickly as possible whether given path segments collide, or not. Extensive tests, in particular on randomly generated path segments and on multisegment paths produced by PRM planners, show that the new method compares favorably with a fixedresolution approach at “suitable ” resolution, with the enormous advantage that it never fails to detect collision.