  Computationally tractable methods are developed for centralized goal
assignment and planning of collision-free polynomial-in-time trajectories for
systems of multiple aerial robots. The method first assigns robots to goals to
minimize total time-in-motion based on initial trajectories. By coupling the
assignment and trajectory generation, the initial motion plans tend to require
only limited collision resolution. The plans are then refined by checking for
potential collisions and resolving them using either start time delays or
altitude assignment. Numerical experiments using both methods show significant
reductions in the total time required for agents to arrive at goals with only
modest additional computational effort in comparison to state-of-the-art prior
work, enabling planning for thousands of agents.
