Application of planar Randers geodesics with river-type perturbation in search models

TL;DR

This paper explores how to optimize planar search patterns using Randers geodesics under river-like perturbations, applying Finsler geometry to solve the Zermelo navigation problem for improved search efficiency.

Contribution

It introduces a novel approach to modeling search patterns with river-type perturbations using Randers metrics and Finsler geometry, extending Zermelo navigation solutions.

Findings

Derived time-optimal paths under river perturbations

Applied Randers metrics to model search scenarios

Enhanced understanding of navigation in perturbed environments

Abstract

We consider remodeling the planar search patterns, in the presence of the river-type perturbation represented by the weak vector field, basing on the time-optimal paths as Finslerian solutions to the Zermelo navigation problem via Randers metric.