As unmanned aerial vehicles (UAVs) expand their roles in civilian and military airspace, challenges are arising to develop flight management systems that efficiently guide the aircraft autonomously and avoid potential hazards. Furthermore, with rapidly developing aircraft design, an anticipatory maneuver is necessary to avoid faster-moving, less-predictable vehicles. Thus, this work proposes a system that avoids collisions by predicting potentially hazardous trajectories of other aircraft using worst-case cost function analysis. The results of this analysis are shown in three-dimensional graphic displays, using elliptical representations of each aircraft's maneuvering uncertainty/capability. Both the calculations and displays are updated in real-time so that the UAV maximizes its efficiency in its maneuvers, integrating the potentially hazardous projections with the actual movements of the other aircraft. The system incorporates full mission objectives, with each mission phase's parameters and the UAV's flying characteristics as inputs. However, at any point in the mission, the UAV can declare an emergency and immediately enter a return-home mission phase, possibly with maneuvering restrictions to incorporate any degradation of flying qualities. Additionally, the simulation demonstrates the robustness of the system (as there were no collisions in 100% of the simulation runs) and provides new ways to visualize and evaluate hazards; the simulation's flexibility in addressing different scenarios and flight paths can greatly benefit statistical analysis of aircraft maneuvering, as well as allow testing of maneuvers currently considered too high-risk. Furthermore, the system displays can be easily converted for operational implementation, so that the user can monitor multiple UAVs on varying missions.