  High-speed trajectory planning through unknown environments requires
algorithmic techniques that enable fast reaction times while maintaining safety
as new information about the operating environment is obtained. The requirement
of computational tractability typically leads to optimization problems that do
not include the obstacle constraints (collision checks are done on the
solutions) or use a convex decomposition of the free space and then impose an
ad-hoc time allocation scheme for each interval of the trajectory. Moreover,
safety guarantees are usually obtained by having a local planner that plans a
trajectory with a final "stop" condition in the free-known space. However,
these two decisions typically lead to slow and conservative trajectories. We
propose FASTER (Fast and Safe Trajectory Planner) to overcome these issues.
FASTER obtains high-speed trajectories by enabling the local planner to
optimize in both the free-known and unknown spaces. Safety guarantees are
ensured by always having a feasible, safe back-up trajectory in the free-known
space at the start of each replanning step. Furthermore, we present a Mixed
Integer Quadratic Program formulation in which the solver can choose the
trajectory interval allocation, and where a time allocation heuristic is
computed efficiently using the result of the previous replanning iteration.
This proposed algorithm is tested extensively both in simulation and in real
hardware, showing agile flights in unknown cluttered environments with
velocities up to 3.6 m/s.
