  Micro aerial vehicles (MAVs), are frequently used for exploration,
examination, and surveillance during search and rescue missions. Manually
piloting these robots under stressful conditions provokes pilot errors and can
result in crashes with disastrous consequences. Also, during fully autonomous
flight, planned high-level trajectories can be erroneous and steer the robot
into obstacles.
  In this work, we propose an approach to efficiently compute smooth,
time-optimal trajectories MAVs that avoid obstacles. Our method first computes
a 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. Afterward, we efficiently check the trajectory for
collisions in the 3D-point cloud, recorded with the onboard lidar. We exploit
the piecewise polynomial formulation of our trajectories to analytically
compute axis-aligned bounding boxes (AABB) to speed up the collision checking
process. If collisions occur, we generate a set of alternative trajectories in
real-time. Alternative trajectories bring the MAV in a safe state, while still
pursuing the original goal. Subsequently, we choose and execute the best
collision-free alternative trajectory based on a distance metric.
  The evaluation in simulation and during a real firefighting exercise shows
the capability of our method.
