Reachability analysis on optimal trim state for aerial docking

Aerial refueling is an important capability to increase the endurance and flight range of aircraft, but it often suffers from a low success rate. The altitude and speed of the tanker aircraft in the docking phase play a great role in the docking success rate. According to this, the optimal trim state, namely the optimal speed and altitude of the tanker aircraft, is investigated through the reachability analysis method in this paper. The optimal problem is transformed to find the trim state corresponding to the maximum volume of the reachable set. First, a relative motion model of the receiver aircraft with respect to the drogue is proposed. Then, based on reachability analysis, an optimization problem is formulated and a solution procedure is given in detail. In the simulation, the volumes of reachable sets are plotted with respect to the given discrete speeds and altitudes, based on which the optimal trim state of the docking phase is determined. Finally, the determined optimal trim state is verified by using numerous docking control simulations and the degree of controllability from another aspect. The effectiveness of the proposed method is demonstrated.