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A Matrix Information-Geometric Method for Change-Point Detection of Rigid Body Motion
Xiaomin Duan1, Huafei Sun2, Xinyu Zhao3
1School of Science, Dalian Jiaotong University, Dalian 116028, China.
Abstract:
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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