Distributionally Robust Integrated “Decision–Control” Task Assignment for Multiple Unmanned Aerial Systems in Emergency Response Under Stochastic Disturbances

Emergency response missions employing heterogeneous multi-UAVs are challenged by both the tight coupling between task assignment and motion control and the inherent difficulty in obtaining full probability distributions of stochastic disturbances. In practice, only partial moment information—typically the mean, covariance, and support set—can be estimated. To address this, the paper proposes a distributionally robust integrated “decision–control” framework. A bi-level optimization model is established: the upper level minimizes the maximum mission completion time across all platforms, while the lower level solves minimum-time optimal control problems under kinematic constraints, with the two levels coupled through task execution times. Given only the mean, covariance, and support set of disturbances, an ambiguity set is constructed, and by leveraging duality theory and semidefinite programming, the distributionally robust chance constraints on site reachability are equivalently transformed into deterministic safety margins. A two-stage trajectory planning method is further designed to decouple accumulated time estimation from robust constraint enforcement, ensuring computational tractability. Simulation results across multiple disturbance configurations show that, whereas deterministic planning yields an overall mission success rate of only about 0.7%, the proposed framework consistently achieves success rates above 99.9% and effectively balances workload among multiple UAVs. These results validate the practical benefit of the framework in providing reliable emergency response plans under limited distributional information.