Application of the Laminar Navier-Stokes Equations for Solving 2D and 3D Pathfinding Problems with Static and Dynamic Spatial Constraints: Implementation and Validation in Comsol Multiphysics

Pathfinding problems consist in determining the optimal shortest path, or at least one path, between two points in the space. In this paper, we propose a particular approach, based on methods used in Computational Fluid Dynamics, that intends to solve such problems. In particular, we reformulate pathfinding problems as the motion of a viscous fluid via the use of the laminar Navier-Stokes equations completed with suitable boundary conditions corresponding to some characteristics of the considered problem: position of the initial and final points, a-priori information of the terrain, One-way routes and dynamic spatial configuration. Then, we propose and validate a numerical implementation of this methodology by using Comsol Multiphysics (i.e., a Finite Element Methods software) and by considering various experiments. We compare the obtained results with those returned by a classical pathfinding algorithm. Finally, we perform a sensitivity analysis of the proposed algorithms with respect to some key parameters.