Distributed Conflict Detection and Optimal Four-Dimensional Trajectory Resolution Leveraging Polynomial-Based Methods

This paper presents a methodology for distributed conflict detection and resolution of aircraft following time-dependent flight paths. We use parametric fifth-order polynomial splines to define the full, time-based paths of aircraft. This representation can be exploited to rapidly detect conflicts and calculate optimal resolution solutions that minimize deviations from the original path. Conflicts are identified using a Sturm sequencing procedure and resolutions are found using gradient-based optimization techniques. Simulations show the locally optimal resolution of complex multi-aircraft conflicts and large-scale scenarios. Also, a method of fitting the flight- path model to data sets is presented and flight-path trajectories are shown to accurately represent commercial aircraft trajectories from collected automatic dependent surveillance-broadcast data sets.