Optimal Human Navigation in Steep Terrain: a Hamilton-Jacobi-Bellman Approach
Christian Parkinson, D. J. Arnold, Andrea Louise Bertozzi, Yat Tin Chow, Stanley Osher · eScholarship (California Digital Library) · 2018
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.