A fast procedure for computing the distance between complex objects in three-dimensional space

Gilbert, Éric; Johnson, Daniel W.; Keerthi, S. Sathiya

doi:10.1109/56.2083

Cited by 1,159 publications

(597 citation statements)

References 24 publications

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“…In those cases, a planner that would return a path with high probability, whenever there exists one that has Figure 2: Robot arm example enough clearance, would be quite satisfactory. 10 Remark also that, if there exists a collision-free path with a clearance greater than some given inf , this path must lie in a subset of C f r e e that is at least -good for an that can be derived 11 from inf . Hence, the assumption of -goodness is realistic as well: for any given value of , our analysis characterizes the probability that the planner nds a path in the subset of C f r e e that is -good.…”

Section: Discussionmentioning

confidence: 99%

A Random Sampling Scheme for Path Planning

Barraquand¹,

Kavraki²,

Latombe³

et al. 1996

Robotics Research

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Several randomized p ath planners have been proposed during the last few years. Their attractiveness stems from their applicability to virtually any type o f r obots, and their empirically observed s u c cess. 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 con guration space. We then describe t w o p r eviously developed planners as instances of planners based on this scheme, but applying very di erent sampling strategies. These planners are p r obabilistically complete: if a path exists, they will nd 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 s p ace, we show that the running time only grows as the absolute value of the logarithm of the probability of failure t h a t w e a r e willing to tolerate. We also show that it increases at a reasonable ra t e a s t h e s p ace g o odness degrades. In the last section we suggest directions for future r esearch.

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Section: Discussionmentioning

confidence: 99%

A Random Sampling Scheme for Path Planning

Barraquand¹,

Kavraki²,

Latombe³

et al. 1996

Robotics Research

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show abstract

“…Early approaches include [14,25,35,48,49,52,53,125,138]. The Gilbert-Johnson-Keerthi algorithm [62] is an early collision detection approach that helped inspire sampling-based motion planning; see [80] and [102] for many early references. In much of the early work, randomization appeared to be the main selling point; however, more recently it has been understood that deterministic sampling can work at least as well while obtaining resolution completeness.…”

Section: Further Readingmentioning

confidence: 99%

Combinatorial Motion Planning

LaValle

2006

Planning Algorithms

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“…In the first case, we will calculate MINMINDIST, since this function returns the distance between two points if the two MBRs have degenerated to two points as shown in the MINMINDIST property. In the second case, we must read the exact geometry of the pair of objects ðO 1 ; O 2 Þ and calculate its distance ObjectDistanceðO 1 ; O 2 Þ, using techniques presented in [7,16].…”

Section: The Sorted Distances Recursive Algorithmmentioning

confidence: 99%

Algorithms for processing K-closest-pair queries in spatial databases

Corral

Manolopoulos

Theodoridis

et al. 2004

Data & Knowledge Engineering

101

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This paper addresses the problem of finding the K closest pairs between two spatial datasets (the socalled, K closest pairs query, K-CPQ), where each dataset is stored in an R-tree. There are two different techniques for solving this kind of distance-based query. The first technique is the incremental approach, which returns the output elements one-by-one in ascending order of distance. The second one is the nonincremental alternative, which returns the K elements of the result all together at the end of the algorithm. In this paper, based on distance functions between two MBRs in the multidimensional Euclidean space, we propose a pruning heuristic and two updating strategies for minimizing the pruning distance, and use them in the design of three non-incremental branch-and-bound algorithms for K-CPQ between spatial objects stored in two R-trees. Two of those approaches are recursive following a Depth-First searching strategy and one is iterative obeying a Best-First traversal policy. The plane-sweep method and the search ordering are used as optimization techniques for improving the naive approaches. Besides, a number of interesting extensions of the K-CPQ (K-Self-CPQ, Semi-CPQ, K-FPQ (the K-farthest pairs query), etc.) are discussed. An extensive performance study is also presented. This study is based on experiments performed with real datasets. A wide range of values for the basic parameters affecting the performance of the algorithms is examined in order to designate the most efficient algorithm for each setting of parameter values. Finally, an experimental study of the behavior of the proposed K-CPQ branch-and-bound algorithms in terms of scalability of the dataset size and the K value is also included.

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A fast procedure for computing the distance between complex objects in three-dimensional space

Cited by 1,159 publications

References 24 publications

A Random Sampling Scheme for Path Planning

A Random Sampling Scheme for Path Planning

Combinatorial Motion Planning

Algorithms for processing K-closest-pair queries in spatial databases

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