Cooperative control methods for the weapon target assignment problem
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Weapon target assignment (WTA) is a combinatorial optimization problem in which a set of weapons must selectively engage a set of targets in order to minimize the expected survival value of the targets. In its distributed form, it is also an important problem in autonomous, multi-agent robotics. In this work, distributed methods are explored for a modified weapon target assignment problem in which weapons seek to achieve a specified probability of kill on each target. Three novel cost functions are proposed which, in cases with low agent-to-target ratios, induce behaviors which may be preferable to the behaviors induced by classical cost functions. The performance of these proposed cost functions is explored in simulation of both homogeneous and heterogeneous engagement scenarios using, as an example, airborne autonomous weapons. Simulation results demonstrate that the proposed cost functions achieve the specified desired behaviors in cases with low agent-to-target ratios where efficient use of weapons is particularly important. Additionally, a multi-objective version of the WTA problem is considered in which the quality of an assignment is dependent on both the total effectiveness of the weapons assigned to each target, and the relative timing of agents' arrival at their targets. Such timing constraints may be important in real-world scenarios where a mission planner wishes to enforce an element of surprise on each target. A fourth cost function is presented which couples weapon effectiveness and timing metrics into a combined cost. In cases where weapon-target closing speeds are limited to a certain range, this combined cost allows the inclusion of arrival time constraints in the assignment decision process. The performance of this new cost function is demonstrated through theoretical analysis and simulation. Results show that the proposed cost function balances the dual goals of optimizing effectiveness and arrival time considerations under closing speed limitations, and that a user-defined tuning parameter can be used to adjust the priority of the dual goals of sequenced arrival and achieving the desired probability of kill.