FSMI: Fast computation of Shannon mutual information for information-theoretic mapping
Name
1905.02238.pdf
Description
Accepted version
Size
4.08 MB
Format
Adobe PDF
Checksum (MD5)
9ede23aa60d85a61d23f3b753375bded
Author(s)
Zhang, Zhengdong
Henderson, Theia
Karaman, Sertac
Sze, Vivienne
Date Issued
2020
Journal
International Journal of Robotics Research
Publisher
SAGE Publications
Citation
Zhang, Zhengdong, Henderson, Theia, Karaman, Sertac and Sze, Vivienne. 2020. "FSMI: Fast computation of Shannon mutual information for information-theoretic mapping." International Journal of Robotics Research, 39 (9).
Version
Author's final manuscript
Abstract
© The Author(s) 2020. Exploration tasks are embedded in many robotics applications, such as search and rescue and space exploration. Information-based exploration algorithms aim to find the most informative trajectories by maximizing an information-theoretic metric, such as the mutual information between the map and potential future measurements. Unfortunately, most existing information-based exploration algorithms are plagued by the computational difficulty of evaluating the Shannon mutual information metric. In this article, we consider the fundamental problem of evaluating Shannon mutual information between the map and a range measurement. First, we consider 2D environments. We propose a novel algorithm, called the fast Shannon mutual information (FSMI). The key insight behind the algorithm is that a certain integral can be computed analytically, leading to substantial computational savings. Second, we consider 3D environments, represented by efficient data structures, e.g., an OctoMap, such that the measurements are compressed by run-length encoding (RLE). We propose a novel algorithm, called FSMI-RLE, that efficiently evaluates the Shannon mutual information when the measurements are compressed using RLE. For both the FSMI and the FSMI-RLE, we also propose variants that make different assumptions on the sensor noise distribution for the purpose of further computational savings. We evaluate the proposed algorithms in extensive experiments. In particular, we show that the proposed algorithms outperform existing algorithms that compute Shannon mutual information as well as other algorithms that compute the Cauchy–Schwarz quadratic mutual information (CSQMI). In addition, we demonstrate the computation of Shannon mutual information on a 3D map for the first time.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Massachusetts Institute of Technology. Microsystems Technology Laboratories
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DOI of Published Version
https://doi.org/10.1177/0278364920921941
