An optimal 3D analytical solution for collision avoidance between aircraft

This paper focuses on an optimal three-dimensional analytical solution for aircraft non-cooperative collision avoidance. Based on a geometric approach, an analytical solution to a proper kinematic optimization problem is here derived, which implies the simultaneous change of all control variables (speed module, track and slope angles), thus this approach resulting very suitable for real-time applications. In a pair-wise non-cooperative collision avoidance, the speed vector of the aircraft implementing the proposed control strategy is continuously changed with the aim of skimming the safety bubble surrounding the other aircraft (considered as an intruder). Under certain hypotheses, the proposed solution can be proved to be optimal with respect to the minimization of aircraft deviation from its nominal trajectory. Proper performance indexes have been defined and challenging conflict scenarios, where the other aircraft be haves even a pursuer, have been analyzed.