An Advanced Collision Avoidance Algorithm considering Ellipsoidal Safety Bubble

Abstract — This paper presents an optimal three-dimensional analytical solution for aircraft non-cooperative collision avoidance, having the capability of avoiding a safety bubble with ellipsoidal shape. Based on an analytical approach, a closed form 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). The proposed algorithm does not require the solution of any programming problem, thus resulting suitable for real-time applications. Moreover, the availability of an analytical solution allows the application of well assessed control analysis and synthesis techniques in order to improve stability and performance robustness. The proposed algorithm performs optimal avoidance maneuvers, by minimizing aircraft deviation from its nominal trajectory. From a practical point of view, the implementation of the proposed algorithm implies that, 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). The effectiveness of the algorithm here described has been proved by means of numerical simulations, where proper conflict scenarios which take into account aircraft dynamics and on-board sensors errors and limitations have been considered.