Development of a Bundle Adjustment algorithm for the navigation of an autonomous lunar drone.

Accurate trajectory estimation for unmanned aerial vehicles is considered a formidable challenge, especially in environments where GPS signals are unavailable. This thesis focuses on developing a bundle adjustment algorithm for the Lunar Nano Drone (LuNaDrone), an autonomous spacecraft designed to explore possible entrances to lunar pits and lava tubes. The work centers on implementing a bundle adjustment pipeline that fuses visual and inertial measurements to enhance trajectory accuracy. The LuNaDrone already incorporates an Extended Kalman Filter (EKF) for real-time navigation. However, these filters suffer from accumulated drift and errors when employed for long distances. This will lead to poor trajectory estimation especially in lunar environments where the conditions can be harsh and unpredictable. Therefore, an offline bundle adjustment can be used after each small flight to reconstruct the overall trajectory and obtain a more reliable overall path for the drone. The proposed algorithm leverages a minimal sensor suite (monocular cameras and an IMU), enabling the system to operate in a self-contained manner. Following an overview of bundle adjustment principles, the thesis delves into the mathematical foundations of the navigation algorithm, employing techniques such as Direct Linear Transform (DLT), Levenberg–Marquardt optimization, and the use of the Schur Complement to efficiently reduce the size of the camera system. The framework is further extended by incorporating inertial measurements into the optimization problem, thereby increasing robustness against visual degradation and harsh environmental conditions. To address the computational challenges associated with processing extensive data on resource-constrained platforms like LuNaDrone, a keyframe-based strategy is employed. This approach selectively processes only the most informative frames while preserving high accuracy. Several experiments were conducted to validate the proposed methodology by comparing the reconstructed trajectory against measurements generated from Unreal Engine visual simulations, which can efficiently model the lunar surface terrain providing reliable approximation to real-world conditions on the lunar surface. The results demonstrate that integrating inertial measurements and strategically selecting keyframes significantly enhances both the accuracy and efficiency of trajectory reconstruction, highlighting the effectiveness of the proposed approach for resource-limited platforms in lunar exploration.