## Materials and Methods
### Algorithms
#### 2.4.3 SA Conflict Resolution  
The conflict resolution function is activated once one or more conflicting aircraft have been identified by the conflict detection function, and, therefore, a separation maneuver is automatically elaborated by this function, thus assuring the ownship separation from all the aircraft detected as conflicts. The function, therefore, calculates multi-conflict separation maneuver that aims to avoid cylindrical separation volume infringement for the considered conflict geometry while using separation and the proper prioritization of the channels (longitudinal, lateral, and speed) in which the maneuver is proposed in order to not generate excessive workload for the pilot in evaluating and implementing the maneuver.  
In addition, in order to allow for the integration of the proposed system in regular conventional traffic and to inherently guarantee self-compatibility among aircraft equipped with the ASACAS SA functionality, the maneuver is elaborated in such a way as to comply with the rules of the air.  
Furthermore, the maneuver is elaborated in such a way to be able to resolve all the conflict encounters detected by the conflict detection function while avoiding the insurgence of new conflicts as a consequence of the maneuver itself, thus ensuring the minimum deviation from the ownship nominal trajectory.  
Figure 3: ASACAS nominal separation assurance volume.  
As anticipated above, the conflict resolution maneuver is elaborated according to three different possible strategies, with tuning priority as follows: horizontal resolution maneuver, vertical resolution maneuver, and velocity resolution maneuver. The horizontal resolution maneuver is a planar maneuver based on the modification of the current ownship's track angle; the suggested track angle aimed to resolve the conflict situation is computed in order to avoid a breach of the separation volume while considering the airspace sector from which the conflicting intruder is coming and the applicable right of way. The vertical resolution maneuver is based on the modification of the current ownship's height to avoid breaching the separation volume around the conflicting aircraft while maintaining the track angle. The speed resolution maneuver is calculated to avoid the separation volume breach by only changing the speed magnitude of the ownship. Finally, as a last resort, a full inertial speed vector variation maneuver, consisting of a whole inertial velocity vector modification, is computed if the previous individual ones cannot solve the conflict. The calculated separation maneuver is then suggested to the pilot on the HMI.  
The separation assurance maneuver is considered to be completed when the condition of clear of conflict (CoC) is satisfied, as stated below:  
* No infringement of the assigned separation volumes is detected for any considered vehicle AND
* Ownship distance with respect to all the considered conflicting vehicles is increasing.  
If the separation assurance maneuver was automatically executed (the remote pilot can command the automatic maneuver execution or can execute it manually as he/she prefers), once these conditions are met, the ownship automatically returns to the original course by implementing the automatic capture of the next applicable waypoint (WP) on the flight plan. Otherwise, if the maneuver was executed in manual or in semi-automatic modes, the responsibility of managing the vehicle once cleared of conflict is that of the remote pilot, who is made aware of the clear of conflict through the dedicated symbols on the interfaces.