  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.
