A closed-form solution of horizontal maneuver to collision avoidance system for UAVs

A geometric model for the Unmanned Aerial Vehicles (UAVs) is proposed in which horizontal maneuvers are made only by changing speed while keeping the flight direction constant. The calculating formulae for projected horizontal miss distance (HMD) and reserved time (Tau) to the closest point of approach are derived from the model according to the Galilean principle of relativity. The closed-form solution is presented to predict the separation to be achieved with a horizontal collision avoidance maneuver. The influence of speed change time and autopilot´s response delay on the horizontal miss distance and reserved time are also calculated and analyzed. The simulation results indicate that the algorithm for conflict detection and resolution in the horizontal plane can predict not only the horizontal separation at the closest point of approach, but also the reserved time to get to the closest point of approach.