The weapon-target assignment problem is a classic task assignment problem in combinatorial optimization, and its goal is to assign some number of workers (the weapons) to some number of tasks (the targets). Classical approaches for this problem typically use a centralized planner leading to a single point of failure and often preventing real-time replanning as conditions change. This paper introduces a new approach for distributed, autonomous assignment planning executed by the weapons where each weapon is responsible for optimizing over distinct subsets of the decision variables. A continuous, convex relaxation of the associated cost function and constraints is introduced, and a distributed primal-dual optimization algorithm is developed that will be shown to have guaranteed bounds on its convergence rate, even with asynchronous computations and communications. This approach has several advantages in practice due to its robustness to asynchrony and resilience to time-varying scenarios, and these advantages are exhibited in experiments with simulated and physical commercial off-the-shelf ground robots as weapon surrogates that are shown to successfully compute their assignments under intermittent communications and unexpected attrition (loss) of weapons.
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