A Novel 3D Analytical Algorithm for Autonomous Collision Avoidance considering Cylindrical Safety Bubble

This paper presents an innovative 3D analytical algorithm for the resolution of the pair-wise non-cooperative collision avoidance problem between aircrafts. The proposed algorithm addresses the above described problem by using an innovative approach, based on the consideration of a cylindrical safety bubble, and it is able to obtain an optimal three-dimensional analytical solution for this problem. This novel approach allows different minimum separations on the vertical and horizontal planes with respect to the nominal trajectory to be achieved, so minimizing the impact of the collision avoidance maneuver on surrounding traffic. Moreover, the algorithm has the very interesting feature that it does not require the solution of any non deterministic and/or iterative problem, resulting suitable for real-time applications. This is due to the capability of the algorithm to find a closed form solution for the kinematic optimization problem here considered. The solution of the collision avoidance problem requires the simultaneous change of all control variables (speed module, track and slope angles), aiming to assure a high safety level (i.e. accomplishment of sustainable maneuvers in terms of angular rates and load factors) and, at the same time, to minimize aircraft deviation from the nominal trajectory. The effectiveness of the algorithm here described is proved by numerical simulations, where suitable conflict scenarios, taking into account aircraft dynamics and on-board sensors errors and limitations, are considered. Through further numerical simulations the effectiveness of the algorithm is also proved in cases where both aircrafts are equipped with the proposed collision avoidance algorithm or where both aircrafts are subjected to Visual Flight Rules.