Duan X, Sun H, Zhao X. A Matrix Information-Geometric Method for Change-Point Detection of Rigid Body Motion.
ENTROPY (BASEL, SWITZERLAND) 2019;
21:e21050531. [PMID:
33267245 PMCID:
PMC7515020 DOI:
10.3390/e21050531]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/16/2019] [Revised: 05/09/2019] [Accepted: 05/23/2019] [Indexed: 06/12/2023]
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.
Collapse