We propose a new formulation for the multi-robot task planning and allocation problem that incorporates (a) precedence relationships between tasks; (b) coordination for tasks allowing multiple robots to achieve increased efficiency; and (c) cooperation through the formation of robot coalitions for tasks that cannot be performed by individual robots alone. In our formulation, the tasks and the relationships between the tasks are specified by a task graph. We define a set of reward functions over the task graph's nodes and edges. These functions model the effect of robot coalition size on the task performance, and incorporate the influence of one task's performance on a dependent task. Solving this problem optimally is NP-hard. However, using the task graph formulation allows us to leverage min-cost network flow approaches to obtain approximate solutions efficiently. Additionally, we explore a mixed integer programming approach, which gives optimal solutions for small instances of the problem but is computationally expensive. We also develop a greedy heuristic algorithm as a baseline. Our modeling and solution approaches result in task plans that leverage task precedence relationships and robot coordination and cooperation to achieve high mission performance, even in large missions with many agents.

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