American Institute of Mathematical Sciences

Advanced
2011, 2011(Special): 1413-1422. doi: 10.3934/proc.2011.2011.1413

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, United States

Received  July 2010 Revised  March 2011 Published  October 2011

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: 65K1.
Citation: Erik I. Verriest. Generalizations of Naismith's problem: Minimal transit time between two points in a heterogenous terrian. Conference Publications, 2011, 2011 (Special) : 1413-1422. doi: 10.3934/proc.2011.2011.1413
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