Computation of a penetration measure between 3D convex polyhedral objects for collision detection

This paper presents algorithms to compute the generalized distance between two separated or penetrating compact convex sets, which is defined as the minimum or maximum scale factor of a given gauge set such that the scaled gauge set intersects or is contained in the Minkowski difference of the two sets. The traditional Euclidean distance is a special case where the origincentered unit ball is used as the gauge set. While the generalized distance was proposed almost a decade ago, the only practical method for its computation has been general-purpose numerical optimization, which is computationally expensive. In contrast, our geometry-based algorithms are efficient and guarantee globally optimal solutions. Important applications of the algorithms in robotics include collision detection and grasp planning. The algorithm for computing the penetration distance also provides an accurate and efficient approach to flatness error evaluation, which is a fundamental problem in manufacturing. We demonstrate that our algorithms possess superior efficiency and accuracy in these applications. space such as [6]-[8], we focus on the distance measures and computation in arbitrary n-dimensional space. A. Previous Work 1552-3098

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“…It can also be treated as a special case of computing d − Q (A, B) as will be discussed in Section III-B. Indeed, (16) can be rewritten as…”

Section: ) Iteration Process: Seementioning

confidence: 99%

“…Some algorithms are specific to 3-D polyhedra [7], [8], while an algorithm for general compact convex sets was proposed in [15]. To facilitate the evaluation of penetration depth, other metrics, such as the one-norm and the infinity-norm, were used to define a distance measure [2], [16] such that the global minimum is easier to attain.…”

Section: Introductionmentioning

confidence: 99%

Generalized Distance Between Compact Convex Sets: Algorithms and Applications

Zheng

Yamane

2015

IEEE Trans. Robot.

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“…When the grown objects are larger than the original objects, this growth measures separation; when they are smaller, they measure penetration. Similarly, using two different object representations, half-spaces and edge lists , different classes of measures for the penetration of different representations of three-dimensional convex polyhedrons along a single axis can be defined [101]. These penetration measurements, when combined with a minimum Euclidean distance measure, can also be used to detect collisions.…”

Section: Simulation and Graphics Collisionsmentioning

confidence: 99%

A Cross-Domain Survey of Metrics for Modelling and Evaluating Collisions

Marvel

Bostelman

2014

International Journal of Advanced Robotic Systems

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This paper provides a brief survey of the metrics for measuring probability, degree, and severity of collisions as applied to autonomous and intelligent systems. Though not exhaustive, this survey evaluates the state-of-the-art of collision metrics, and assesses which are likely to aid in the establishment and support of autonomous system collision modelling. The survey includes metrics for 1) robot arms; 2) mobile robot platforms; 3) nonholonomic physical systems such as ground vehicles, aircraft, and naval vessels, and; 4) virtual and mathematical models.

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“…Several algorithms proposed in the literature apply to convex models, a typical choice as basic objects components, e.g. [9], [10], [11], [12], [13]. In the usual case of convex polytopes, the best asymptotic bound for various proximity problems (intersection detection, collision detection, distance, depth of collision) is the O(log 2 n) worst-case bound attained by exploiting the hierarchical representations of polyhedra with O(n) vertices, [14], [15].…”

Section: Related Workmentioning

confidence: 99%

Incremental Convex Minimization for Computing Collision Translations of Convex Polyhedra

2007

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Abstract-The subject of this paper is an asymptotically fast and incremental algorithm for computing collision translations of convex polyhedra, where the problem at hand is reduced to determining collision translations of pairs of planar sections and minimizing a bivariate convex function. There are two main reasons, in our view, why the algorithm is worth consideration. On the one hand, the addressed proximity measure, namely collision translation, is not as widely studied as distance. On the other, its peculiar computation strategy may be interesting in itself, being well suited to work without initialization and also endowed with an inherently embedded mechanism to exploit spatial coherence. After outlining the main ideas of this novel approach and providing an estimation of the computational costs, we summarize a broad set of numerical experiments meant to explore extensively the behavior of the algorithm, both without and with initialization. Finally, in order to assess the efficacy and the potential of the approach under analysis, the attained performances are contrasted with those of other popular algorithms designed to compute distances between polyhedra. A thorough comparison of the reported query times and, more significantly, of the corresponding trends shows that the behavior of the collision translation algorithm is quite interesting, especially when used without initialization or under variable coherence, which should encourage further work on this approach.

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Computation of a penetration measure between 3D convex polyhedral objects for collision detection

Cited by 5 publications

References 9 publications

Generalized Distance Between Compact Convex Sets: Algorithms and Applications

Generalized Distance Between Compact Convex Sets: Algorithms and Applications

A Cross-Domain Survey of Metrics for Modelling and Evaluating Collisions

Incremental Convex Minimization for Computing Collision Translations of Convex Polyhedra

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