High-speed flight in an ergodic forest
Name
Frazzoli_High-speed flight.pdf
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1.17 MB
Format
Adobe PDF
Checksum (MD5)
3150f698f53f6140b30bcbd9848382c1
Author(s)
Karaman, Sertac
Frazzoli, Emilio
Date Issued
May 2012
Journal
2012 IEEE International Conference on Robotics and Automation
Publisher
Institute of Electrical and Electronics Engineers
Citation
Karaman, Sertac, and Emilio Frazzoli. “High-speed flight in an ergodic forest.” In 2012 IEEE International Conference on Robotics and Automation, 14-18 May 2012, St. Paul, MN, pp. 2899-2906. Institute of Electrical and Electronics Engineers, 2012.
Version
Author's final manuscript
Abstract
Inspired by birds flying through cluttered environments such as dense forests, this paper studies the theoretical foundations of high-speed motion through a randomly-generated obstacle field. Assuming that the locations and the sizes of the trees are determined by an ergodic point process, and under mild technical conditions on the dynamics of the bird, it is shown that the existence of an infinite collision-free trajectory through the forest exhibits a phase transition. In other words, if the bird flies faster than a certain critical speed, there is no infinite collision-free trajectory, with probability one, i.e., the bird will eventually collide with some tree, almost surely, regardless of the planning algorithm governing its motion. On the other hand, if the bird flies slower than this critical speed, then there exists at least one infinite collision-free trajectory, almost surely. Lower and upper bounds on the critical speed are derived for the special case of a Poisson forest considering a simple model for the bird's dynamics. Moreover, results from an extensive Monte-Carlo simulation study are presented. This paper also establishes novel connections between robot motion planning and statistical physics through ergodic theory and the theory of percolation, which may be of independent interest.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1109/ICRA.2012.6225235
