Autonomous drone racing is becoming an excellent platform to challenge quadrotors' autonomy techniques including planning, navigation and control technologies. However, most research on this topic mainly focuses on single drone scenarios. In this paper, we describe a novel time-optimal trajectory generation method for generating time-optimal trajectories for a swarm of quadrotors to fly through pre-defined waypoints with their maximum maneuverability without collision. We verify the method in the Gazebo simulations where a swarm of 5 quadrotors can fly through a complex 6-waypoint racing track in a 35m * 35m space with a top speed of 14m/s. Flight tests are performed on two quadrotors passing through 3 waypoints in a 4m * 2m flight arena to demonstrate the feasibility of the proposed method in the real world. Both simulations and real-world flight tests show that the proposed method can generate the optimal aggressive trajectories for a swarm of autonomous racing drones. The method can also be easily transferred to other types of robot swarms.
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