Optimal Human Navigation in Steep Terrain: a Hamilton-Jacobi-Bellman Approach

TL;DR

This paper introduces a novel method for calculating optimal walking paths in steep terrains using Hamilton-Jacobi-Bellman equations, demonstrated through mountainous regions and law enforcement applications.

Contribution

It applies the level set method and optimal control formulation to terrain navigation, providing a new computational approach for path optimization in complex landscapes.

Findings

Successfully computed optimal paths in Yosemite National Park

Demonstrated application for law enforcement patrols

Validated effectiveness of the Hamilton-Jacobi-Bellman approach

Abstract

We present a method for determining optimal walking paths in steep terrain using the level set method and an optimal control formulation. By viewing the walking direction as a control variable, we can determine the optimal control by solving a Hamilton-Jacobi-Bellman equation. We then calculate the optimal walking path by solving an ordinary differential equation. We demonstrate the effectiveness of our method by computing optimal paths which travel throughout mountainous regions of Yosemite National Park. We include details regarding the numerical implementation of our model and address a specific application of a law enforcement agency patrolling a nationally protected area.