  In this work, we propose a method to efficiently compute smooth, time-optimal
trajectories for micro aerial vehicles (MAVs) evading a moving obstacle. Our
approach first computes an n-dimensional trajectory from the start- to an
arbitrary target state including position, velocity and acceleration. It
respects input- and state-constraints and is thus dynamically feasible. The
trajectory is then efficiently checked for collisions, exploiting the piecewise
polynomial formulation. If collisions occur, viastates are inserted into the
trajectory to circumvent the obstacle and still maintain time-optimality. These
viastates are described by position, velocity, and acceleration. The evaluation
shows that the computational demands of the proposed method are minimal such
that obstacle avoidance can begin within few milliseconds. Optimality of
generated trajectories, combined with the ability for frequent online
re-planning from non-hover initial conditions, make the approach well suited
for evasion of suddenly perceived obstacles during fast flight.
