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This paper presents a fault-tolerant control method for a quadrotor UAV using solely on-board sensors. A simultaneous localization and mapping (SLAM) system is developed utilizing a laser rangefinder and an open source SLAM algorithm called GMapping. This system allows for mapping of the surrounding environment as well as localizing the position of the quadrotor, enabling real-time position control. However, the SLAM system using the laser rangefinder may fail in certain degenerate environment like featureless tunnels or straight hallways. In order to compensate for possible faults in the SLAM measurements, a fault detection and fault-tolerant control method is developed. An observer is designed to estimate the translational velocity of the quadrotor using SLAM position measurements. The fault detection residual is defined as the deviation between this SLAM-based velocity estimate and another velocity estimate generated by an optical flow algorithm utilizing measurements provided by a downward facing camera. Real-time experimental results have shown the effectiveness of the fault-tolerant control algorithm.