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

arXiv: https://arxiv.org/abs/1805.04973 · HTML: https://mlsanity.com/paper/1805.04973/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 May 2018.

## Built on by (most cited first, 1 of 1)

- [Deep learning methods for inverse problems using connections between proximal operators and Hamilton-Jacobi equations](https://mlsanity.com/paper/2512.23829/) (2025)

## Abstract (arXiv)

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.