
Parameterization of configuration space obstacles in threedimensional rotational motion planning
This study investigates the exact geometry of the configuration space in...
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On Bounds and Closed Form Expressions for Capacities of Discrete Memoryless Channels with Invertible Positive Matrices
While capacities of discrete memoryless channels are well studied, it is...
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On power chi expansions of fdivergences
We consider both finite and infinite power chi expansions of fdivergenc...
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Efficient Path Planning in Narrow Passages via ClosedForm Minkowski Operations
Path planning has long been one of the major research areas in robotics,...
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A ClosedForm Solution to Local NonRigid StructurefromMotion
A recent trend in NonRigid StructurefromMotion (NRSfM) is to express ...
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Surface and length estimation based on Crofton's formula
We study the problem of estimating the surface area of the boundary of a...
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Bayesian decisiontheoretic design of experiments under an alternative model
Decisiontheoretic Bayesian design of experiments is considered when the...
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ClosedForm Minkowski Sums of Convex Bodies with Smooth Positively Curved Boundaries
This paper proposes a closedform parametric formula of the Minkowski sum boundary for broad classes of convex bodies in ddimensional Euclidean space. With positive sectional curvatures at every point, the boundary that encloses each body can be characterized by the surface gradient. The first theorem directly parameterizes the Minkowski sums using the unit normal vector at each body surface. Although simple to express mathematically, such a parameterization is not always practical to obtain computationally. Therefore, the second theorem derives a more useful parametric closedform expression using the gradient that is not normalized. In the special case of two ellipsoids, the proposed expressions are identical to those derived previously using geometric interpretations. In order to further examine the results, numerical verifications and comparisons of the Minkowski sums between two superquadric bodies are conducted. The application for the generation of configuration space obstacles in motion planning problems is introduced and demonstrated.
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