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Associating Uncertainty With Three-Dimensional Poses for Use in Estimation Problems

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2 Author(s)
Timothy D. Barfoot ; Autonomous Space Robot. Lab., Univ. of Toronto, Toronto, ON, Canada ; Paul T. Furgale

In this paper, we provide specific and practical approaches to associate uncertainty with 4 ×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.

Published in:

IEEE Transactions on Robotics  (Volume:30 ,  Issue: 3 )