This paper addresses the problem of risk in the environment and presents a new stochastic formulation of the UAV task assignment problem. This formulation explicitly accounts for the interaction between the UAVs -displaying cooperation between the vehicles rather than just coordination. As defined in the paper, cooperation entails coordinated task assignment with the additional knowledge of the future implications of a UAV's actions on improving the expected performance of the other UAVs. The key point is that the actions of each UAV can reduce the risk in the environment for all other UAVs; and the new formulation takes advantage of this fact to generate cooperative assignments that achieve better performance. This change in the formulation is accomplished by coupling the failure probabilities for each UAV to the selected missions for all other UAVs. This results in coordinated plans that optimally exploit the coupling effects of cooperation to improve the survival probabilities and expected performance. This allocation is shown to recover real-world air operations planning strategies that provide significant improvements over approaches that do not correctly account for UAV attrition. The problem is formulated as a Dynamic Programming (DP) problem, which is shown to be more computationally tractable than previous MILP solution approaches. Two DP approximation methods (the one-step and two-step look-ahead) are also developed for larger problems. Simulation results show that the one-step look-ahead can generate cooperative solutions very quickly, but the performance degrades considerably. The two-step look-ahead policy generates plans that are very close to (and in many cases, identical to) the optimal solution and the computation time is still significantly lower than the exact DP approach.
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