Probabilistic Release Point Optimization for Airdrop with Variable Transition Altitude

High-altitude low-opening airdrop is a technique for aerial delivery that has unique operational advantages. The primary decisions that must be made in execution of these missions are the aircraft release heading, package release point, and altitude at which the package transitions from the drogue to the main ballistic parachute. Algorithms have recently been developed to optimize these variables probabilistically to account for uncertainty in winds, package descent rate, and other factors to maximize an expected score function; although, such work optimized the release variables and transition altitude separately. This paper builds on prior work to develop a method to optimize the release point, release heading, and transition altitude in a single, combined framework to achieve a globally optimal solution. The Koopman operator is used to pull back a mission-specific score function through a family of transformations defining the system dynamics with different transition altitudes. The optimal release point, release heading, and transition altitude are selected from a gridded solution space as that which maximizes the expected score. The results show that the combined optimization approach that includes variable transition altitude produces a higher expected score value as compared to cases in which the release variables are optimized by assuming a fixed transition altitude.