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An open-access, university-level educational tutorial and reference module on Simultaneous Localization and Mapping (SLAM) for mobile robotics and autonomous systems.

This learning module breaks down the circular dependency of autonomous spatial awareness through rigorous probabilistic formulations and modern computational frameworks:- Probabilistic Problem Formulation: Deriving joint state-map estimation, Bayes' theorem applications, and first-order Markov factorization for Full and Online SLAM.- Kinematics and Measurement Models: Non-linear state transition dynamics for differential-drive platforms, Jacobian linearizations, and range-bearing polar sensor models.- Classical vs. Modern Estimation Paradigms: Comparative analysis of Extended Kalman Filter SLAM (EKF-SLAM) covariance scaling bottlenecks versus sparse non-linear least squares optimization in modern Factor Graphs.- Spatial Integrity Mechanisms: Mahalanobis distance feature correspondence, Joint Compatibility Branch and Bound (JCBB), and place-recognition loop closure for global trajectory drift elimination.

Includes built-in interactive self-assessment checkpoints, conceptual thought experiments, a comprehensive technical FAQ, and 12 worked numerical engineering problems with step-by-step solutions (differential drive propagation, EKF matrix sizing, information matrix sparsity, and occupancy grid memory footprints).

Permanent citable archive available via Zenodo DOI: 10.5281/zenodo.22844053.

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