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Title: Distance between a point and a convex cone in n-dimensional space: Computation and applications
Authors: Zheng, Y. 
Chew, C.-M. 
Keywords: Closest point
Convex cone
Force closure
Force distribution
Minimum distance
Multicontact robotic system
Issue Date: Dec-2009
Citation: Zheng, Y., Chew, C.-M. (2009-12). Distance between a point and a convex cone in n-dimensional space: Computation and applications. IEEE Transactions on Robotics 25 (6) : 1397-1412. ScholarBank@NUS Repository.
Abstract: This paper presents an algorithm to compute the minimum distance from a point to a convex cone in n-dimensional space. The convex cone is represented as the set of all nonnegative combinations of a given set. The algorithm generates a sequence of simplicial cones in the convex cone, such that their distances to the single point converge to the desired distance. In many cases, the generated sequence is finite, and therefore, the algorithm has finite-convergence property. Recursive formulas are derived to speed up the computation of distances between the single point and the simplicial cones. The superior efficiency and effectiveness of this algorithm are demonstrated by applications to force-closure test, system equilibrium test, and contact force distribution, which are fundamental problems in the research of multicontact robotic systems. Theoretical and numerical comparisons with previous work are provided. © 2009 IEEE.
Source Title: IEEE Transactions on Robotics
ISSN: 15523098
DOI: 10.1109/TRO.2009.2033333
Appears in Collections:Staff Publications

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