Generalizations of Naismith's problem: Minimal transit time between two points in a heterogenous terrian

Erik I. Verriest

doi:10.3934/proc.2011.2011.1413

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2011, Volume 2011: 1413-1422. Doi: 10.3934/proc.2011.2011.1413 open access

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Generalizations of Naismith's problem: Minimal transit time between two points in a heterogenous terrian

Erik I. Verriest^1,

1.
School of ECE, Georgia Institute of Technology, Atlanta, GA 30332-0250

Received: June 30, 2010

Revised: February 28, 2011

Published: August 2017

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Abstract

Naismith obtained a set of empirical rules for the time required to move through a terrain. In this paper we solve the problem of determining the path which minimizes the transit time between two points on a given terrain. We give an interpretation of Naismith’s rule which leads to an elegant geometric construction of the optimal solution. This problem is a paradigm for the navigation of an autonomous vehicle in a heterogenous terrain.

Keywords:

Optimal control,
path planning.

Mathematics Subject Classification: Primary: 49K05, 49K15; Secondary: 65K10.

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