Risk-sensitive mean-field control of large-scale UAV Swarms for stochastic disaster tracking and robust first response

This paper proposes a risk-sensitive mean field optimal control framework for large-scale multi-UAV disaster tracking, guidance, and first response operations in the presence of stochastic uncertainty and communication limitations. As opposed to existing heuristic, clustering approaches, and swarm-based optimization techniques, which are frequently risk neutral and based on deterministic propagation models, the new approach takes into account the stochastic nature of the disaster field, a risk-sensitive performance function of exponential form, and a modified Riccati recursion. Although the backward Riccati recursion is computed offline in a centralized fashion, the real-time computations become fully distributed, whereby each UAV calculates its own control gain using communication with its neighboring UAVs only. Computational complexity is decoupled from the cardinality of the swarm using a mean-field approximation. In addition, entropy-dual formulation guarantees distribution robustness, which takes into account the worst-case disturbance realizations within a bounded Kullback-Leibler divergence ball, irrespective of, and also complementary to, the distributed online computing structure in which each UAV only interacts with its nearest neighbors. Theoretical results on closed-loop Schur stability, risk-admissibility limits, convergence to a mean-field equilibrium, and consistency of distributed consensus algorithms have been rigorously proved and numerically verified. The simulations carried out on a wide range of urban obstacles have shown that the proposed algorithm performs better compared to other methods in terms of efficiency in coverage, mission time, energy consumption, connectivity preservation, path length, and robustness to increased variances in disturbances. The suggested framework is, to the best knowledge of the authors, the first integrated approach to the problem of risk-sensitive mean-field control, entropy-dual distributionally robust optimization, and communication-constrained distributed consensus in the context of disaster relief operations with UAVs.