Optimization of the ADS Final Turn Maneuver in 2D and 3D

This paper deals with the problem of optimization of the final turn–into-the-wind maneuver of an aerial delivery system with account of the best known winds. The wind model required for the optimization algorithm to work may utilize onboard wind estimates only, incorporate the ground winds provided a priori or on-line by the target ground station, or be based on the winds measured and uplinked by the preceding system. The previous work by the authors took care of the major touchdown error contributor, downwind variation of the winds. The effect of these variations was mitigated by constantly recomputing an optimal reference trajectory to complete a final turn in a given time. This paper presents some modifications of the original optimization routine to accommodate some specific applications including intentional landing with a substantial crosswind component and operating in the mountainous areas with significant variations in the vertical component of the wind (updrafts and downdrafts). Specifically, the paper presents derivation of equations to account for one-, two- and three-dimensional structure of the wind. In addition, adjustments to the optimal control problem using the direct-method-based approach developed earlier for a simple one-dimensional wind model are developed. Abbreviations ADS = Aerial Delivery System AGL = above the ground level BCs = boundary conditions CEP = Circular Error Probable FAC = final approach capture (point) GPS = Global Positioning System TI = turn initiation (point) TPBVP = two-point boundary-value proble