Fast Trajectory Planning for Multiple Quadrotors using Relative Safe Flight Corridor

This paper presents a new trajectory planning method for multiple quadrotors in obstacle-dense environments. We suggest a relative safe flight corridor (RSFC) to model safe region between a pair of agents, and it is used to generate linear constraints for inter-collision avoidance by utilizing the convex hull property of relative Bernstein polynomial. Our approach employs a graph-based multi-agent pathfinding algorithm to generate an initial trajectory, which is used to construct a safe flight corridor (SFC) and RSFC. We express the trajectory as a piecewise Bernstein polynomial and formulate the trajectory planning problem into one quadratic programming problem using linear constraints from SFC and RSFC. The proposed method can compute collision-free trajectory for 16 agents within a second and for 64 agents less than a minute, and it is validated both through simulation and indoor flight test.