Adam R. Gerlach

Release Point Determination and Dispersion Reduction for Ballistic Airdrops

Physics based models for all phases of an airdrop are presented. These models can be used in conjunction with near real-time wind measurements to optimize an air release point for multi-package bundles in high-altitude low-opening (HALO) airdrops with ballistic drogue and main parachutes. In addition to using the predictive capability of the models to select optimal release points for minimum miss distance, several methods are presented that can reduce multi-package impact dispersion. Variations in a derived wind drift coefficient, which relates the inertial properties of each package to its aerodynamic characteristics, are shown to result in significant dispersion in winds with non-constant direction. Mitigation of this effect through manipulation of the bundle mass or aerodynamic properties is proposed in conjunction with a simulation based aircraft heading and package release order optimization to minimize the overall impact dispersion. Additional optimizations are used to select main parachute deployment altitudes for each package to further reduce the airdrop dispersion. The methods presented are designed to be suitable for real-time implementation on a mobile computer that monitors aircraft flight and wind data and interfaces with ballistic parachute systems. ∗UAS Controls Engineer, Autonomous Control Branch, Power and Control Division, Aerospace Systems Directorate, 2210 Eighth Street, Room 300, Email josiah.vandermey@gmail.com †Principal Aerospace Engineer, Autonomous Control Branch, Power and Control Division, Aerospace Systems Directorate, 2210 Eighth Street, Ste. 21, Email david.doman@us.af.mil, Ph. (937) 713-7003, Fellow AIAA ‡Research Engineer, 1270 North Fairfield Road, Email adam.gerlach.ctr@us.af.mil, Ph. (937) 713-7040

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.

Analytical Solution for Optimal Drogue-to-Main Parachute Transition Altitude for Precision Ballistic Airdrops

During ballistic airdrops, a single discrete control input can be made during the descent of a bundle to counter the effects of unmodeled physics and disturbances that occur before the control event. This control event is the altitude at which the drogue-to-main parachute transition occurs. The ability to vary the transition altitude of a bundle can significantly reduce the miss distance of a bundle to an intended target. The state-of-the-art method for optimizing the transition altitude is computationally burdensome and nondeterministic in time. In this exposition, an analytical solution for optimizing the transition altitude that minimizes the miss distance of an airdropped bundle from a specified ground target is developed. The solution time is deterministic and small enough that it can be implemented in real time on an embedded computer located on the bundle itself. By pairing this bundle-mounted embedded computer with a Global Positioning System sensor, the optimal transition altitude can be recomput...

Probabilistic Algorithm for Ballistic Parachute Transition Altitude Optimization

A probabilistic algorithm for the optimization of drogue-to-main parachute transition altitude is proposed for high-altitude, low-opening ballistic airdrop. In light of the significant effects of w...