A Matrix Information-Geometric Method for Change-Point Detection of Rigid Body Motion

A matrix information-geometric method was developed to detect the change-points of rigid body motions. Note that the set of all rigid body motions is the special Euclidean group S E ( 3 ) , so the Riemannian mean based on the Lie group structures of S E ( 3 ) reflects the characteristics of change-p...

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Bibliographic Details
Published inEntropy (Basel, Switzerland) Vol. 21; no. 5; p. 531
Main Authors Duan, Xiaomin, Sun, Huafei, Zhao, Xinyu
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 25.05.2019
MDPI
Subjects
Algebra
Algorithms
change-point detection
Euclidean geometry
Geometry
Iterative methods
Lie algebra
Lie groups
matrix information geometry
Motion perception
Neighborhoods
Rigid structures
Rigid-body dynamics
special Euclidean group
Systems stability
Time series
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Summary:A matrix information-geometric method was developed to detect the change-points of rigid body motions. Note that the set of all rigid body motions is the special Euclidean group S E ( 3 ) , so the Riemannian mean based on the Lie group structures of S E ( 3 ) reflects the characteristics of change-points. Once a change-point occurs, the distance between the current point and the Riemannian mean of its neighbor points should be a local maximum. A gradient descent algorithm is proposed to calculate the Riemannian mean. Using the Baker–Campbell–Hausdorff formula, the first-order approximation of the Riemannian mean is taken as the initial value of the iterative procedure. The performance of our method was evaluated by numerical examples and manipulator experiments.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e21050531