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

Pages: 1413 - 1422, Issue Special, September 2011

 Abstract        Full Text (834.3K)              

Erik I. Verriest - School of ECE, Georgia Institute of Technology, Atlanta, GA 30332-0250, United States (email)

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.

Received: July 2010;      Revised: March 2011;      Published: October 2011.