This paper addresses the problem of robust take-off of a quadrotor unmanned aerial vehicle (UAV) in critical scenarios, such as in the presence of sloped terrains and surrounding obstacles. Throughout the maneuver, the vehicle is modeled as a hybrid automaton whose states reflect the different dynamic behaviors exhibited by the UAV. The original take-off problem is then addressed as the problem of tracking suitable reference signals in order to achieve the desired transitions between different hybrid states of the automaton. Reference trajectories and feedback control laws are derived to explicitly account for uncertainties in both the environment and the vehicle dynamics. Simulation results demonstrate the effectiveness of the proposed solution and highlight the advantages with respect to more standard open-loop strategies, especially for cases in which the slope of the terrain renders the take-off maneuver more critical to achieve.