When employing autonomous helicopters, it is desirable to use navigation approaches, which firmly ensure safety. In this paper, we propose and compare two approaches to navigation through environments containing obstacles. The first uses sliding mode boundary following to maintain a prespecified distance to obstacles, and the second uses a model predictive control approach to plan short horizon trajectories around detected objects, while ensuring that the helicopter is brought to a halt within the sensor visibility radius. The navigation approaches are subjected to analysis for robustness, and simulations are carried out with a realistic helicopter model for verification. Additional real-world experiments were performed with a wheeled robot to demonstrate potential for real-time application.