  This paper presents a framework for controlled emergency landing of a
quadcopter, experiencing a rotor failure, away from sensitive areas. A complete
mathematical model capturing the dynamics of the system is presented that takes
the asymmetrical aerodynamic load on the propellers into account. An
equilibrium state of the system is calculated around which a linear
time-invariant control strategy is developed to stabilize the system. By
utilizing the proposed model, a specific configuration for a quadcopter is
introduced that leads to the minimum power consumption during a
yaw-rate-resolved hovering after a rotor failure. Furthermore, given a 3D
representation of the environment, an optimal flight trajectory towards a safe
crash landing spot, while avoiding collision with obstacles, is developed using
an RRT* approach. The cost function for determining the best landing spot
consists of: (i) finding the safest landing spot with the largest clearance
from the obstacles; and (ii) finding the most energy-efficient trajectory
towards the landing spot. The performance of the proposed framework is tested
via simulations.
