Fast and accurate collision detection based on enclosed ellipsoid

Ju, Ming-Yi; Liu, Jing‐Sin; Shiang, Shen-Po; Chien, Yuh-Ren; Hwang, Kao-Shing; Lee, Wan-Chi

doi:10.1017/s0263574700003295

Cited by 21 publications

(10 citation statements)

References 25 publications

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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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Section: Related Workmentioning

confidence: 99%

Incremental Convex Minimization for Computing Collision Translations of Convex Polyhedra

2007

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“…1(a), for example). In such cases, a nonspherical object such as an ellipsoid or a spheroid can serve as a better approximation for the object (Ju et al 2001;Choi et al 2006Choi et al , 2009. The fuselage of an aeroplane or a submarine are also instances where an ellipsoid can serve as a better bounding box than a sphere.…”

Section: Introductionmentioning

confidence: 99%

Generalization of the collision cone approach for motion safety in 3-D environments

Chakravarthy

Ghose

2011

Auton Robot

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Avoidance of collision between moving objects in a 3-D environment is fundamental to the problem of planning safe trajectories in dynamic environments. This problem appears in several diverse fields including robotics, air vehicles, underwater vehicles and computer animation. Most of the existing literature on collision prediction assumes objects to be modelled as spheres. While the conservative spherical bounding box is valid in many cases, in many other cases, where objects operate in close proximity, a less conservative approach, that allows objects to be modelled using analytic surfaces that closely mimic the shape of the object, is more desirable. In this paper, a collision cone approach (previously developed only for objects moving on a plane) is used to determine collision between objects, moving in 3-D space, whose shapes can be modelled by general quadric surfaces. Exact collision conditions for such quadric surfaces are obtained and used to derive dynamic inversion based avoidance strategies.

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“…Using enclosing ellipsoids, the problems of collision avoidance and detection are studied in [7], [18], [24]. Sohn et al [21] formulate the task of distance computation as a surface-surface intersection problem in the space of lines.…”

Section: Introductionmentioning

confidence: 99%

Oriented bounding surfaces with at most six common normals

Rabl

González-Vega

Jüttler

et al. 2009

2009 IEEE International Conference on Robotics and Automation

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Abstract-We present a new type of oriented bounding surfaces, which is particularly well suited for shortest distance computations. The bounding surfaces are obtained by considering surfaces whose support functions are restrictions of quadratic polynomials to the unit sphere. We show that the common normals of two surfaces of this type -and hence their shortest distance -can be computed by solving a polynomial of degree six. This compares favorably with other existing bounding surfaces, such as quadric surfaces, where the computation of the common normals is known to lead to a polynomial of degree 24.

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Fast and accurate collision detection based on enclosed ellipsoid

Cited by 21 publications

References 25 publications

Incremental Convex Minimization for Computing Collision Translations of Convex Polyhedra

Incremental Convex Minimization for Computing Collision Translations of Convex Polyhedra

Generalization of the collision cone approach for motion safety in 3-D environments

Oriented bounding surfaces with at most six common normals

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