This paper presents the Flying Lidar (Flydar) aerial robot for simultaneous localization and mapping (SLAM). The Flydar integrates a single laser and capitalizes on the rotating dynamics of a nature-inspired aerial robot for omnidirectional scanning. This paper presents a 2.5D SLAM approach using the Flydar and does not assume that the Flydar's hovering plane, and thus the laser scan, is parallel to the ground plane, which is a key assumption in our previous work. A quaternion-based filter performs active correction of the Flydar's laser scan due to its transient attitude. A dual-accelerometer approach was incorporated to estimate the Flydar's scan rate during high angular rates flight beyond the gyroscope dynamic range. The proposed attitude filter output was experimentally evaluated statically on a bench-top setup and dynamically in flight, with an rms inclination estimate error of up to 1.1 o and 0.38 o respectively. The attitudecorrected lidar scan was used to estimate the robot pose for 2.5D SLAM. The 2.5D SLAM was experimentally validated on the Flydar and demonstrated to be superior to pure 2D SLAM in loop closure, position estimate drift, and rms error. Significantly, the 2.5D SLAM using the Flydar reports a low rms Euclidean error of up to 0.083 m, which is a 32.0% error reduction compared with our previous work, which uses 2D SLAM.