Abstract—This paper presents a computationally tractable, resolution-complete algorithm for generating dynamically feasible trajectories for N interchangeable (identical) aerial robots navigating through cluttered known environments to M goal states. This is achieved by assigning the robots to goal states while concurrently planning the trajectories for all robots. The algorithm minimizes the maximum cost over all robot trajectories. The computational complexity of this algorithm is shown to be cubic in the number of robots, substantially better than the expected exponential complexity associated with planning in the joint state space and the assignment of goals to robots. This algorithm can be used to plan motions and goals for tens of aerial robots, each in a 12-dimensional state space. Finally, experimental trials are conducted with a team of six quadrotor robots navigating in a constrained three-dimensional environment. I
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