Journal
IEEE TRANSACTIONS ON ROBOTICS
Volume 30, Issue 3, Pages 679-693Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TRO.2014.2298059
Keywords
Exponential maps; homogeneous points; matrix Lie groups; pose uncertainty; transformation matrices
Categories
Funding
- Natural Sciences and Engineering Research Council of Canada
- EU [269916]
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In this paper, we provide specific and practical approaches to associate uncertainty with 4 x 4 transformation matrices, which is a common representation for pose variables in 3-D space. We show constraint-sensitive means of perturbing transformation matrices using their associated exponential-map generators and demonstrate these tools on three simple-yet-important estimation problems: 1) propagating uncertainty through a compound pose change, 2) fusing multiple measurements of a pose (e.g., for use in pose-graph relaxation), and 3) propagating uncertainty on poses (and landmarks) through a nonlinear camera model. The contribution of the paper is the presentation of the theoretical tools, which can be applied in the analysis of many problems involving 3-D pose and point variables.
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