Koopman Operator Approach to Airdrop Mission Planning Under Uncertainty

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Koopman Operator Approach to Airdrop Mission Planning Under Uncertainty

Leonard, Andrew / Rogers, Jonathan / Gerlach, Adam

Mission planning for ballistic airdrop requires the selection of optimal control inputs under uncertainty. While significant uncertainty usually exists in airdrop scenarios, current mission planning algorithms use only nominal parameters to compute a deterministic solution. This paper introduces an optimal control algorithm in which the Koopman operator is used to solve for the probabilistically optimal input in the presence of parametric uncertainty. The proposed approach offers unique computational advantages over alternative uncertainty quantification techniques, providing a practical method to compute a probabilistically optimal input. In the context of the airdrop problem, these inputs are the optimal package release point and aircraft run-in. Given an objective function defined over the drop zone and a joint probability density accounting for uncertainty in the system parameters, the objective function is pulled back to the drop altitude using the Koopman operator, and an expected value is computed with the joint probability density. The optimal release point and run-in is then selected to optimize this expected value. Following a general description of the Koopman operator approach to probabilistic decision making, the airdrop-specific implementation is described. Simulation examples are presented, highlighting the performance of the algorithm in real-world scenarios. Results compare favorably with those achieved through deterministic methods.