Collision and Proximity Queries
01 Jan 2017-pp 1029-1056
TL;DR: In a geometric context, a collision or proximity query reports information about the relative configuration or placement of two objects as mentioned in this paper, and the common examples of such queries include checking whether two objects overlap in space, or whether their boundaries intersect, or computing the minimum Euclidean separation distance between their boundaries.
Abstract: In a geometric context, a collision or proximity query reports information about the relative configuration or placement of two objects Some of the common examples of such queries include checking whether two objects overlap in space, or whether their boundaries intersect, or computing the minimum Euclidean separation distance between their boundaries Hundreds of papers have been published on different aspects of these queries in computational geometry and related areas such as robotics, computer graphics, virtual environments, and computer-aided design These queries arise in different applications including robot motion planning, dynamic simulation, haptic rendering, virtual prototyping, interactive walkthroughs, computer gaming, and molecular modeling For example, a large-scale virtual environment, eg, a walkthrough, creates a model of the environment with virtual objects Such an environment is used to give the user a sense of presence in a synthetic world and it should make the images of both the user and the surrounding objects feel solid The objects should not pass through each other, and objects should move as expected when pushed, pulled, or grasped; see Fig 3901 Such actions require fast and accurate collision detection between the geometric representations of both real and virtual objects Another example is rapid prototyping, where digital representations of mechanical parts, tools, and machines, need to be tested for interconnectivity, functionality, and reliability In Fig 3902, the motion of the pistons within the combustion chamber wall is simulated to check for tolerances and verify the design
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01 Jan 2006
TL;DR: This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms, into planning under differential constraints that arise when automating the motions of virtually any mechanical system.
Abstract: Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.
6,340 citations
TL;DR: In this paper, the authors studied the asymptotic behavior of the cost of the solution returned by stochastic sampling-based path planning algorithms as the number of samples increases.
Abstract: During the last decade, sampling-based path planning algorithms, such as probabilistic roadmaps (PRM) and rapidly exploring random trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g. as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g. showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e. such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.
3,438 citations
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TL;DR: The main contribution of the paper is the introduction of new algorithms, namely, PRM and RRT*, which are provably asymptotically optimal, i.e. such that the cost of the returned solution converges almost surely to the optimum.
Abstract: During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g., as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g., showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e., such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.
2,210 citations
TL;DR: This work surveys current haptic systems and discusses some basic haptic-rendering algorithms, and describes the process by which desired sensory stimuli are imposed on the user to convey information about a virtual haptic object.
Abstract: Haptic rendering allows users to "feel" virtual objects in a simulated environment. We survey current haptic systems and discuss some basic haptic-rendering algorithms. In the past decade we've seen an enormous increase in interest in the science of haptics. Haptics broadly refers to touch interactions (physical contact) that occur for the purpose of perception or manipulation of objects. These interactions can be between a human hand and a real object; a robot end-effector and a real object; a human hand and a simulated object (via haptic interface devices); or a variety of combinations of human and machine interactions with real, remote, or virtual objects. Rendering refers to the process by which desired sensory stimuli are imposed on the user to convey information about a virtual haptic object.
469 citations
14 May 2012
TL;DR: A new collision and proximity library that integrates several techniques for fast and accurate collision checking and proximity computation and is based on hierarchical representations and designed to perform multiple proximity queries on different model representations.
Abstract: We present a new collision and proximity library that integrates several techniques for fast and accurate collision checking and proximity computation. Our library is based on hierarchical representations and designed to perform multiple proximity queries on different model representations. The set of queries includes discrete collision detection, continuous collision detection, separation distance computation and penetration depth estimation. The input models may correspond to triangulated rigid or deformable models and articulated models. Moreover, FCL can perform probabilistic collision checking between noisy point clouds that are captured using cameras or LIDAR sensors. The main benefit of FCL lies in the fact that it provides a unified interface that can be used by various applications. Furthermore, its flexible architecture makes it easier to implement new algorithms within this framework. The runtime performance of the library is comparable to state of the art collision and proximity algorithms. We demonstrate its performance on synthetic datasets as well as motion planning and grasping computations performed using a two-armed mobile manipulation robot.
445 citations
Cites background from "Collision and Proximity Queries"
...The problems of collision detection and distance computations are well studied [6], [7], [16]....
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...At a broad level, they can be classified based on the underlying query or model representation [16], [6]....
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References
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01 Aug 1996
TL;DR: A data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion that can robustly and accurately detect all the contacts between large complex geometries composed of hundreds of thousands of polygons at interactive rates are presented.
Abstract: We present a data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion. The algorithm is applicable to all general polygonal models. It pre-computes a hierarchical representation of models using tight-fitting oriented bounding box trees (OBBTrees). At runtime, the algorithm traverses two such trees and tests for overlaps between oriented bounding boxes based on a separating axis theorem, which takes less than 200 operations in practice. It has been implemented and we compare its performance with other hierarchical data structures. In particular, it can robustly and accurately detect all the contacts between large complex geometries composed of hundreds of thousands of polygons at interactive rates. CR
2,278 citations
"Collision and Proximity Queries" refers background or methods in this paper
...The cost of performing the proximity query is given as [ GLM96 , LGLM99]:...
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...Thecomputationisrobustandworkswellinpractice[ GLM96 ]. Figure35.2.1shows one of the separating axis tests for two rectangles in 2D....
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...theorem(SAT)hasbeenpresentedin[ GLM96 ,Got00]. Itcomputestheprojection ofeachOBBalong15axesin3D.The15axesarecomputedfromthefacenormals of theOBBs(6 face normals) andby taking thecross-productsof the edgesofthe OBBs (9 cross-products)....
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...Itisbased onOBBTreesandusesafastoverlaptestbasedonSeparatingAxisTheoremto check whether two OBBs overlap [ GLM96 ]....
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...These include sphere-trees [Hub95, Qui94], AABB-trees [BKSS90, HKM95, PML97], OBB-trees [ GLM96 , BCG+96, Got00], spherical shell-trees [KPLM98, KGL+98], k-DOP-trees [HKM96, KHM+98], SSVtrees[LGLM99], multiresolution hierarchies [OL03], and convex hull-trees [EL01], as shown in Table 35.2.1....
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01 Apr 1988
TL;DR: An algorithm for computing the Euclidean distance between a pair of convex sets in R/sup m/ has special features which makes its application in a variety of robotics problems attractive.
Abstract: An algorithm for computing the Euclidean distance between a pair of convex sets in R/sup m/ is described. Extensive numerical experience with a broad family of polytopes in R/sup 3/ shows that the computational cost is approximately linear in the total number of vertices specifying the two polytopes. The algorithm has special features which makes its application in a variety of robotics problems attractive. These features are discussed and an example of collision detection is given. >
1,388 citations
"Collision and Proximity Queries" refers methods in this paper
...Enhanced GJK Algorithm: Itisalibraryfordistancecomputationbasedonthe enhancedGJKalgorithm[ GJK88 ]developedbyCameron[Cam97]....
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...time performance in practice has been proposed by Gilbert et al. [ GJK88 ], also knownastheGJKalgorithm....
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...expected time for any positive constant †. Cameron [Cam97] presented an extension to the GJK algorithm [ GJK88 ] to compute upper and lower bounds on the PD between convex polytopes....
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TL;DR: A method for approximating polyhedral objects to support a time-critical collision-detectional algorithm that maintains its real-time performance as objects become more complicated, even as they exceed previouslyreported complexity levels by a factor of more than 10.
Abstract: This article presentsa method for approximatingpolyhedralobjects to support a time-critical collision-detectionalgorithm. The approximationsare hierarchies of spheres, and they allow the time-critical algorithm to progressivelyrefine the accuracy of its detection, stopping as needed to maintain the real-time performanceessential for interactive applications.The key to this approachis a preprocessthat automaticallybuilds tightly fitting hierarchies for rigid and articulatedobjects.The preprocessuses medial-axis surfaces, which are skeletal representations of objects. These skeletonsguide an optimizationtechniquethat gives the hierarchies accuracy properties appropriate for collision detection. In a sample application, hierarchies built this way allow the time-criticalcollision-detectionalgorithmto have acceptableaccuracy, improving significantly on that possible with hierarchies built by previous techniques. The performanceof the time-critical algorithmin this application is consistently 10 to 100 times better than a previous collision-detection algorithm, maintaining low latency and a nearIy constant frame rate of 10 frames per second on a conventional graphics workstation. The time-critical algorithm maintains its real-time performanceas objects become more complicated, even as they exceed previouslyreported complexitylevels by a factor of more than 10.
564 citations
"Collision and Proximity Queries" refers background in this paper
...The problem of performing proximity queries in large environments is typically divided into two parts [ Hub95 , CLMP95]: the broad phase, in which we identify the pair of objects on which we need to perform difierent proximity queries, and the narrow phase, in which we perform the exact pairwise queries....
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...These include sphere-trees [ Hub95 , Qui94], AABB-trees [BKSS90, HKM95, PML97], OBB-trees [GLM96, BCG+96, Got00], spherical shell-trees [KPLM98, KGL+98], k-DOP-trees [HKM96, KHM+98], SSVtrees[LGLM99], multiresolution hierarchies [OL03], and convex hull-trees [EL01], as shown in Table 35.2.1....
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25 Oct 1976
TL;DR: An O(N log N) algorithm is given to determine whether any two intersect and use it to detect whether two simple plane polygons intersect and to show that the Simplex method is not optimal.
Abstract: We develop optimal algorithms for forming the intersection of geometric objects in the plane and apply them to such diverse problems as linear programming, hidden-line elimination, and wire layout. Given N line segments in the plane, finding all intersecting pairs requires O(N2) time. We give an O(N log N) algorithm to determine whether any two intersect and use it to detect whether two simple plane polygons intersect. We employ an O(N log N) algorithm for finding the common intersection of N half-planes to show that the Simplex method is not optimal. The emphasis throughout is on obtaining upper and lower bounds and relating these results to other problems in computational geometry.
473 citations
"Collision and Proximity Queries" refers methods in this paper
...This incrementally computes the AABBs for each object and checks them for overlap by computing the projection of the bounding boxesalongeachdimension,andsortingtheintervalendpointsusinginsertionsort orbubblesort [ MD76 ,Bar92,CLMP95]....
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TL;DR: The Voronoi-clip, or V-Clip, collision detection alogrithm for polyhedral objects specified by a boundary representation is presented, and the theoretical principles and pseudocode description of the algorithm are presented.
Abstract: This article presents the Voronoi-clip, or V-Clip, collision detection alogrithm for polyhedral objects specified by a boundary representation. V-Clip tracks the closest pair of features between convex polyhedra, using an approach reminiscent of the Lin-Canny closest features algorithm. V-Clip is an improvement over the latter in several respects. Coding complexity is reduced, and robustness is significantly improved; the implementation has no numerical tolerances and does not exhibit cycling problems. The algorithm also handles penetrating polyhedra, and can therefore be used to detect collisions between nonvconvex polyhedra described as hierarchies of convex pieces. The article presents the theoretical principles of V-Clip, and gives a pseudocode description of the algorithm. It also documents various test that compare V-Clip, Lin-Canny, and the Enhanced GJK algorithm, a simplex-based algorithm that is widely used for the same application. The results show V-Clip to be a strong contender in this field, comparing favorably with the other algorithms in most of the tests, in term of both performance and robustness.
469 citations
"Collision and Proximity Queries" refers methods in this paper
...Mirtich [ Mir98 ] further optimized this algorithm by proposing a more robust variation that avoids some geometric degeneracies during the local walk, without sacriflcing the accuracy or correctness of the original algorithm....
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