Probabilistic Airdrop Mission Planning

Airdrop missions are playing an increasingly important role in military resupply and humanitarian aid delivery. One important tradeoff that is commonly faced in the airdrop community is use of unguided (or ballistic systems) versus guided systems. Guided airdrop systems typically yield significantly smaller impact dispersion and offer a large measure of control over the desired flight path, and are thus attractive in scenarios involving complex terrain or extreme accuracy requirements. At the same time, guided systems are expensive and are typically impractical for large-scale aerial delivery missions involving tens or hundreds of airdrop packages. For this reason, much effort has focused on improving the accuracy of the large number of unguided ballistic parachutes currently in Army inventory through enhanced techniques for calculating the Computed Air Release Point (CARP). The CARP is the location at which a ballistic parachute should be dropped in order to achieve the desired point of impact. The CARP is a function of the wind, air density profile, transient and steady-state parachute dynamics, and the position, heading, altitude, and velocity of the drop aircraft.

Uncertainty in winds, drop location, air density, payload mass, and parachute drag all contribute to impact dispersion in actual airdrop scenarios. Historically, the CARP has been computed by considering only the mean values of each of these variables and largely ignoring the magnitude of uncertainty associated them. The premise of this work is that the CARP location determined from only a mean-value (or deterministic) analysis is different from the CARP that would be chosen when uncertainty is considered. This work seeks to derive new probabilistic mission planning algorithms that provide the CARP, aircraft flight path, and optimal parachute deployment altitudes conditioned on all sources of uncertainty affecting the airdrop problem. This comprehensive, rigorous probabilistic analysis is expected to yield noticeable improvements in drop accuracy and the ability to shape the impact dispersion pattern in non-trivial ways. Specifically, this work makes use of the Stochastic Liouville Equation (SLE), a specific form of the Fokker-Planck-Kolmogorov equation, for explicit nonlinear uncertainty propagation. A desired impact distribution is defined, and the SLE is used to propagate this probability density backward in time to the airdrop altitude. Knowledge of this time-varying joint probability density is extremely powerful from a mission planning perspective and can be used to optimize the CARP location, aircraft heading, and the altitudes at which the main parachute should deploy. This work is being performed in close collaboration with the US Air Force Research Laboratory in Dayton, OH.

Diagram of PDF Propagation

Diagram of Trajectory Solutions and Selected Joint Probability Densities.

Plot of Propagated Joint Probability Densities

References: A. Leonard, J. Rogers, A. Gerlach, “Probabilistic Release Point Optimization for Airdrop with Variable Transition Altitude,” Journal of Guidance, Control, and Dynamics, Vol. 43, No. 8, 2020, pp. 1-11.