Partial Differential Equation-Based Trajectory Planning for Multiple Unmanned Air Vehicles in Dynamic and Uncertain Environments

This paper proposes a physics-inspired method for unmanned aerial vehicle (UAV) trajectory planning in three dimensions using partial differential equations (PDEs) for application in dynamic hostile environments. The proposed method exploits the dynamical property of fluid flowing through a porous medium. This method evaluates risk to generate porosity values throughout the computational domain. The trajectory that encounters the highest porosity values determines the trajectory from the point of origin to the goal position. The best trajectory is found using the reaction of the fluid in porous media by the way of streamlines obtained by numerically solving the PDEs representing the fluid flow. Constraints due to UAV dynamics, obstacles, and predefined way points are applied to the problem after solving for the best trajectory to find the optimal and feasible trajectory. This method shows near-optimality and much reduced computational effort when compared to the other typical numerical optimization methods.