Semantic-Integrated Topological Mapping with Factor Graph　Optimization for Small Robots in Unknown Environments

Small, resource-constrained swarm robots require scene understanding that is both semantic and metric, yet most SLAM pipelines either ignore semantics or demand heavy sensors. We propose an online hybrid factor-graph optimisation (FGO) framework that jointly estimates continuous robot poses and discrete terrain labels using only low cost wheel encoder and IMU data. Continuous and discrete variables are modelled as nodes in a single factor graph; maximum-a-posteriori in- ference is carried out by an alternating optimisation scheme executed inside a fixed-size sliding window, allowing constant- time updates on embedded hardware. The method closes three longstanding gaps: (1) a unified probabilistic formulation for hybrid state estimation, (2) an online solver that scales with mission duration, and (3) automatic construction of a dynamic semantic topological map that captures both spatial layout and label transitions. The resulting graph supports high- level navigation and situational awareness without external infrastructure. We validate the approach in a 2D simulation comprising six terrain regions, random walks of 150 steps, and realistic odometry and classification noise. These results demonstrate that hybrid FGO can endow minimalist robots with robust, semantics-aware mapping capabilities, paving the way for long-duration exploration and cooperative task planning in GPS-denied, sensor-limited environments.