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This work focuses on the use of MAVs for industrial inspection tasks. An efficient flight controller based on a model predictive control paradigm is developed. It allows for agile maneuvers in confined spaces while incorporating delays, saturations and inaccurate vehicle state estimates only available at low rate. The fast gradient method is used to solve the optimization problem and meet real-time constraints, given limited computational resources. The vehicle state is estimated from an on-board forward-looking camera system, tightly fused with inertial measurements. Experiments using a realistic industrial mock environment demonstrate the effectiveness, robustness and limitations of the proposed approach. The results show that egomotion estimation is robust under rapid motion, in poorly textured environments and under challenging lighting conditions. When coupled with the model predictive controller, the system requires only limited computational resources and sufficiently tracks an arbitrary trajectory.