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19
Path Planning Using Lazy PRM
 In IEEE Int. Conf. Robot. & Autom
, 2000
"... 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 configu ..."
Abstract

Cited by 189 (14 self)
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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 userdefined 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 collisionfree, 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 collisionfree path is returned.
3D Collision Detection: A Survey
 Computers and Graphics
, 2000
"... Many applications in Computer Graphics require fast and robust 3D collision detection algorithms. These algorithms can be grouped into four approaches: spacetime volume intersection, swept volume interference, multiple interference detection and trajectory parameterization. While some approaches ar ..."
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Cited by 84 (3 self)
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Many applications in Computer Graphics require fast and robust 3D collision detection algorithms. These algorithms can be grouped into four approaches: spacetime volume intersection, swept volume interference, multiple interference detection and trajectory parameterization. While some approaches are linked to a particular object representation scheme (e.g., spacetime volume intersection is particularly suited to a CSG representation), others do not. The multiple interference detection approach has been the most widely used under a variety of sampling strategies, reducing the collision detection problem to multiple calls to static interference tests. In most cases, these tests boil down to detecting intersections between simple geometric entities, such as spheres, boxes aligned with the coordinate axes, or polygons and segments. The computational cost of a collision detection algorithm depends not only on the complexity of the basic interference test used, but also on the ...
Incremental algorithms for collision detection between solid models
 IEEE Transactions on Visualization and Computer Graphics
, 1995
"... solid models ..."
A Random Sampling Scheme for Path Planning
 INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH
, 1996
"... Several randomizod path planners have been proposed during the last few years. Their attractiveness stems from their applicability to virtually any type of robots, and their empirically observed success. In this paper we attempt to present a unifying view of these planners and to theoretically expla ..."
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Cited by 82 (26 self)
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Several randomizod path planners have been proposed during the last few years. Their attractiveness stems from their applicability to virtually any type of robots, and their empirically observed success. In this paper we attempt to present a unifying view of these planners and to theoretically explain their success. First, we introduce a general planning scheme that consists of randomly sampling the robot' s configuration space. We then describe two previously developed planners as instances of planners based on this scheme, but applying very different sampling strategies. These planners are probabilistically complete: if a path exists, they will find one with high probability, if we let them run long enough. Next, for one of the planners, we analyze the relation between the probability of failure and the running time. Under assumptions characterizing the "goodness" of the robot's free space, we show that the running time only grows as the absolute value of the logarithm of the probability of failure that we are willing to tolerate. We also show that it increases at a reasonable rate as the space goodness degrades. In the last section we suggest directions for future research.
Contact Constraint Analysis and Determination of Geometrically Valid Contact Formations from Possible Contact Primitives
 IEEE Transactions on Robotics and Automation
, 1997
"... A complete, precise, and systematic analysis on the geometrical nature of contacts between two arbitrary polygons and derivation of the geometric contact constraints between two such polygons are provided. Based on the results, a general algorithm is presented to identify the geometrically valid con ..."
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Cited by 17 (5 self)
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A complete, precise, and systematic analysis on the geometrical nature of contacts between two arbitrary polygons and derivation of the geometric contact constraints between two such polygons are provided. Based on the results, a general algorithm is presented to identify the geometrically valid contact formations (CFs) from a given set S pc of possible principal contacts (PCs) between two polygonal objects with location uncertainties. For any (nonempty) subset of S pc , the algorithm tests if the PCs in the set form a possible CF by verifying the geometrical contact constraints. The obtained set of geometrically valid CFs can serve as input to an additional verifier based on force sensing which can extract the actual CF from the set. The notion of equivalent CFs is introduced to describe those contact situations constraining the relative location between two objects to the same region. This concept proves to be extremely useful to the completeness of the analysis and efficiency of th...
Towards Obtaining All Possible Contacts  Growing a Polyhedron By . . .
 IEEE TRANS. ON ROBOTICS AND AUTOMATION
, 1996
"... A large number of robotic tasks require precision and thus the dealing with uncertainties. The effects of various uncertainties often manifest to location (i.e., position and orientation) uncertainties of objects. Thus, an important problem that often arises is how to assess the region that an ob ..."
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Cited by 13 (4 self)
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A large number of robotic tasks require precision and thus the dealing with uncertainties. The effects of various uncertainties often manifest to location (i.e., position and orientation) uncertainties of objects. Thus, an important problem that often arises is how to assess the region that an object may occupy in the presence of uncertainties. This paper addresses the problem by describing how to grow exactly an arbitrary polyhedral object in the threedimensional Cartesian space by its position and/or orientation uncertainties. Three types of related regions for the object are described: (1) the grown regions# regions possibly occupied by the object due to uncertainties in its position# orientation# or both# #2# the grown shell regions# regions possibly occupied by the boundary #surfaces# of the object due to uncertainties in its position# orientation or both# and #3# the core regions# regions #which could be empty# definitely occupied by the object in spite of uncertainty. The exact representations introduced in this paper can serve as benchmarks against which efficient but approximate algorithms may be evaluated. A particularly important application of the grown shell regions is in obtaining the set of all possible topological contacts among polyhedral objects due to location uncertainties. Such a set can serve as a basis from which more precise contact information can be extracted by additional sensing means# such as vision and force/moment sensing. The approach for this application and its implementation is introduced and discussed.
Collision Detection Algorithms for Motion Planning
 LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES, 229
, 1998
"... ..."
An approach to the movers problem that combines oriented matroid theory and algebraic geometry
 In Proc. IEEE Int. Conf. on Robotics and Automation (Nagoya (J
, 1995
"... This paper investigates the partition of the configuration space induced by basic contacts between polyhedra, using their combinatorial interpretation in terms of oriented matroids. It is shown that solving motion planning problems using this cellular decomposition can be analytically expressed in t ..."
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Cited by 6 (6 self)
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This paper investigates the partition of the configuration space induced by basic contacts between polyhedra, using their combinatorial interpretation in terms of oriented matroids. It is shown that solving motion planning problems using this cellular decomposition can be analytically expressed in terms of invariants, without explicit use of artificial coordinate frames. One ofthe main aims of this paper is to draw the attention of the reader to some results from the Theory of Matroids which are directly applicable to path planning, and many other geometric problems arising in Robotics. In particular, the relevance of the concept of mutation in the context of collisionfree path planning is highlighted. Moreover, it is proved that the set of mutations contains the walls of a given cell in configuration space, and that this set, as one moves from one cell to a neighbor one, can be updated in linear time with the number of vertices. This provides a simple way to detect a large amount of redundant constraints from purely combinatorial considerations, without relying on the manipulation of algebraic equations.
An Efficient Algorithm (FAPRIC) for Finding the Principal Contacts Possibly Established due to Uncertainties
 Proc. IEEE ICRA
, 1995
"... An implemented algorithm is presented for finding all principal contacts possibly established between two surface features (i.e., faces, edges, or vertices) of two polyhedral objects due to location (i.e., position and orientation) uncertainties. The algorithm FAPRIC (for Finding All PRIncipal Conta ..."
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Cited by 5 (3 self)
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An implemented algorithm is presented for finding all principal contacts possibly established between two surface features (i.e., faces, edges, or vertices) of two polyhedral objects due to location (i.e., position and orientation) uncertainties. The algorithm FAPRIC (for Finding All PRIncipal Contacts) requires as inputs: the estimated locations of the two objects, the geometric models of the objects, and the bounds on position and orientation uncertainties. The algorithm is based on checking intersections between the grown regions of the objects by location uncertainties [12] with the Stope model [5]. It is very efficient and apt for realtime processing. The information obtained can serve as a guide for more accurate extraction and further reasoning of the contact data, possibly with additional sensors. As the surface of an arbitrary object can be approximated by planar patches, the algorithm can also be applied to general objects. The work is motivated by the need for automaticall...
Fast Algorithms for Penetration and Contact Determination Between NonConvex Polyhedral Models
 IEEE Int. Conf. on Robotics and Automation
, 1994
"... This paper presents fast algorithms for penetration and contact determination between general polyhedral models in dynamic environments. The main contribution is an extension of an earlier expected constant time algorithm between convex polytopes to detect penetrations and contacts. For each pair of ..."
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Cited by 5 (1 self)
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This paper presents fast algorithms for penetration and contact determination between general polyhedral models in dynamic environments. The main contribution is an extension of an earlier expected constant time algorithm between convex polytopes to detect penetrations and contacts. For each pair of nonconvex polyhedral models, the algorithm uses the convex hull of each object to determine which regions of the objects are colliding. After identifying these regions, it uses a new dynamic technique, sweep and prune, to overcome the bottleneck of O(n 2 ) pairwise feature checks of these regions. The resulting algorithm has been implemented and in practice its performance in dynamic environments is O(n +m), where m corresponds to the number of feature pairs close to each other. 1 Introduction The problem of determining whether objects are penetrating or separated is of great importance in many areas. It has been extensively studied in robotics, molecularbased modeling, computational ...