In this paper, we present a distributed algorithm to generate collision-free trajectories for a group of quadrotors flying through a common workspace. In the setup adopted, each vehicle replans its trajectory, in a receding horizon manner, by solving a small-scale optimization problem that only involves its own individual variables. We adopt the Voronoi partitioning of space to derive local constraints that guarantee collision avoidance with all neighbors for a certain time horizon. The obtained set of collision avoidance constraints explicitly takes into account the vehicle's orientation to avoid infeasiblity issues caused by ignoring the quadrotor's rotational motion. Moreover, the resulting constraints can be expressed as Bézier curves, and thus can be evaluated efficiently, without discretization, to ensure that collision avoidance requirements are satisfied at any time instant, even for an extended planning horizon. The proposed approach is validated through extensive simulations with up to 100 drones. The results show that the proposed method has a higher success rate at finding collision-free trajectories for large groups of drones compared to other Voronoi diagram-based methods.
Keywords: Voronoi diagram; distributed trajectory generation; multi-drone applications; real-time replanning.