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Estimating Rigid Transformation With Correlated Observations

[+] Author Affiliations
Chung-Yen Lin, Masayoshi Tomizuka

University of California, Berkeley, CA

Paper No. DSCC2015-9672, pp. V002T23A002; 9 pages
  • ASME 2015 Dynamic Systems and Control Conference
  • Volume 2: Diagnostics and Detection; Drilling; Dynamics and Control of Wind Energy Systems; Energy Harvesting; Estimation and Identification; Flexible and Smart Structure Control; Fuels Cells/Energy Storage; Human Robot Interaction; HVAC Building Energy Management; Industrial Applications; Intelligent Transportation Systems; Manufacturing; Mechatronics; Modelling and Validation; Motion and Vibration Control Applications
  • Columbus, Ohio, USA, October 28–30, 2015
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-5725-0
  • Copyright © 2015 by ASME


The problem of finding the rotation and the translation between two sets of corresponded points is known as the rigid transformation estimation problem. It plays a crucial role in many robotic applications such as “simultaneous localization and mapping” (SLAM), surface reconstruction, and inertial sensor calibration. The most widely used solution to this problem is based on performing the singular value decomposition (SVD) over a derived data matrix. A drawback of the SVD method is that it is a least-squares method and thus may fail to take into account the anisotropic and/or correlated noises, which often present in practical applications. A natural variation is to add a matrix weight to the least-squares problem to balance the estimation errors in different measurement directions. However, it becomes difficult to write down a closed form solution in this setup. In this paper, an efficient algorithm is presented to estimate the rigid transformation with correlated observations. The effectiveness of the proposed method is experimentally demonstrated on two robotic applications, namely the point set registration and the inertial sensor localization.

Copyright © 2015 by ASME



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