This paper presents an approach to trajectories optimization for Unmanned Aerial Vehicle (UAV) in presence of obstacles, waypoints, and threat zones such as radar detection regions, using Mixed Integer Linear Programming (MILP). The main result is the linear approximation of a nonlinear radar detection risk function with integer constraints and indicator 0-1 variables. Several results are presented to show that the approach can yields trajectories depending on the acceptable risk of detection.

This paper presents an approach to trajectory generation for Unmanned Aerial Vehicles (UAV) by using Mixed Integer Linear Programming (MILP) and a modification of the A* algorithm to optimize paths in dynamic environments, particularly having pop-ups with a known future probability of appearance. Each pop-up leads to one or several possible evasion maneuvers, characterized with a set of values used as decision making parameters in an Integer Linear Programming (ILP) model that optimizes the final route by choosing the most suitable alternative trajectories, according to the imposed constrains such as maximum fuel consumption and spent time. The model of the system in MILP and A* algorithms is presented, as well as the ILP formulation for decision making. Results and discussions are given to promote future real time implementations.

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