Precision airdrop transition altitude optimization via the one-in-a-set traveling salesman problem

Mission planning for ballistic precision airdrop (PAD) operations has traditionally focused on determining the optimal computed air release point (CARP) to release the payloads that minimizes the circle error average (CEA) of the payload impact pattern on the ground. More recent work has introduced the idea of varying the drogue-to-main parachute transition altitude of the ballistic payloads in order to improve airdrop accuracy and reduce bundle dispersion. By varying the transition altitude of the payload, its impact location can be controlled to lie anywhere on a finite 1D curve on the ground. The exact shape of this curve is defined by the system properties and the local wind field. Previous work has demonstrated the usage of these curves for determining the optimal transition altitudes that minimize the CEA. This paper discusses the limitations of optimizing the transition altitudes based on the ground impact CEA. An alternative cost function is proposed that explicitly represents the risk encountered when retrieving the payloads on the ground and returning them to a base location. This cost function is the solution to the traveling salesman problem (TSP). Additionally, an algorithm is introduced that models this PAD optimization problem as a one-in-a-set TSP. Established techniques from the TSP literature are then utilized to determine the transition altitudes. This cost function and algorithm is compared to CEA-based optimization for a scenario with complex terrain. The resulting TSP-based solution results in a 43% reduction in risk encountered when retrieving and returning the supplies to a base when compared to the CEA-based solution. Here, risk is modeled as the total distance traveled during the retrieval process; however, alternative models for risk can easily be considered within this solution framework.