Fast and precise approximation of Minkowski sum of two rotational ellipsoids with a superellipsoid

In this paper, we propose a fast and accurate method for approximating the Minkowski sum of two rotational ellipsoids with a superellipsoid. The Minkowski sum is used in a variety of applications such as robot motion planning and particle flow simulation requiring collision detection. Many of them a...

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Bibliographic Details
Published in:The Visual computer 2024-07, Vol.40 (7), p.4609-4621
Main Authors: Yamada, Ryunosuke, Tsuji, Tokuo, Hiramitsu, Tatsuhiro, Seki, Hiroaki, Nishimura, Toshihiro, Suzuki, Yosuke, Watanabe, Tetsuyou
Format: Article
Language:English
Subjects:
Approximation
Artificial Intelligence
Collisions
Computation
Computer Graphics
Computer Science
Ellipsoids
Euclidean space
Exponents
Flow simulation
Image Processing and Computer Vision
Motion planning
Robot dynamics
Sums
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Summary:In this paper, we propose a fast and accurate method for approximating the Minkowski sum of two rotational ellipsoids with a superellipsoid. The Minkowski sum is used in a variety of applications such as robot motion planning and particle flow simulation requiring collision detection. Many of them are computed based on Minkowski sum, whose accuracy and processing time depend on how the mesh is created. We approximate Minkowski sum with a superellipsoid function. The superellipsoid has various shapes with the value of the exponents, and the computation of the parameters including the exponents is an algebraic computation with the time complexity O ( 1 ) . As a result, approximation error is small and computation is fast in all combinations of rotational ellipsoids. In addition, collision is quickly detected by solving the inequality of superellipsoid.
ISSN:0178-2789
1432-2315
DOI:10.1007/s00371-024-03445-9