  One of the keys to flying quadrotors is to optimize their trajectories within
the set of collision-free corridors. These corridors impose nonconvex
constraints on the trajectories, making real-time trajectory optimization
challenging. We introduce a novel numerical method that approximates the
nonconvex corridor constraints with time-triggered convex corridor constraints.
This method combines bisection search and repeated infeasibility detection. We
further develop a customized C++ implementation of the proposed method, based
on a first-order conic optimization method that detects infeasibility and
exploits problem structure. We demonstrate the efficiency and effectiveness of
the proposed method using numerical simulation on randomly generated problem
instances as well as indoor flight experiments with hoop obstacles. Compared
with mixed integer programming, the proposed method is about 50--200 times
faster.
