Optimal grid-free path planning across arbitrarily-contoured terrain with anisotropic friction and gravity effects
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Authors
Rowe, Neil C.
Ross, Ron S.
Subjects
Advisors
Date of Issue
1990-10
Date
October 1990
Publisher
Monterey, California. Naval Postgraduate School
Language
Abstract
Anisotropic (heading-dependent) phenomena arise in the "two-and-one-half-dimensional" path-planning problem of finding
minimum-energy routes for a mobile agent across some hilly terrain. We address anisotropic friction and gravity effects, and
ranges of impermissible-traversal headings due to overturn danger or power limitations. Our method does not require imposition
of a uniform grid, nor average effects in different directions, but reasons about a polyhedral approximation of terrain. It reduces
the problem to a finite but provably-optimal set of possibilities, and then uses A* search to find the cost-optimal path. However,
the possibilities are not physical locations but path subspaces. Our method exploits the surprising insight that there are only four
ways, mathematically simple, to optimally traverse an anisotropic homogeneous region: (1) straight across without braking, the
standard isotropic-weighted-region traversal; (2) straight across without braking but as close as possible to a desired
impermissible heading; (3) making impermissibility-avoiding switchbacks on the path across a region; and (4) straight across
with braking. We prove specific optimality criteria for transitions on the boundaries of regions for each combination of traversal
types. These criteria subsume previously published criteria for traversal of isotropic weighted-region terrain. Our method can
take considerably less computer time and space than previous methods on some terrain; at the same time, we believe it is the first
algorithm to provide truly optimal paths on anisotropic terrain.
Type
Conference Paper
Description
This paper appeared in IEEE Transactions on Robotics and Automation,
6, no. 5 (October 1990), 540-553. The equations were redrawn in 2008.
Series/Report No
Department
Computer Science (CS)
Organization
Identifiers
NPS Report Number
Sponsors
supported in part by the U. S. Army Combat Developments Experimentation Center under MIPR ATEC 88-86
Funding
Format
Citation
Distribution Statement
Approved for public release; distribution is unlimited.