Autonomous navigation is one of the key requirements for every potential application of mobile robots in the real-world. Besides high-accuracy state estimation, a suitable and globally consistent representation of the 3D environment is indispensable. We present a fully tightly-coupled LiDAR-Visual-Inertial SLAM system and 3D mapping framework applying local submapping strategies to achieve scalability to large-scale environments. A novel and correspondence-free, inherently probabilistic, formulation of LiDAR residuals is introduced, expressed only in terms of the occupancy fields and its respective gradients. These residuals can be added to a factor graph optimisation problem, either as frame-to-map factors for the live estimates or as map-to-map factors aligning the submaps with respect to one another. Experimental validation demonstrates that the approach achieves state-of-the-art pose accuracy and furthermore produces globally consistent volumetric occupancy submaps which can be directly used in downstream tasks such as navigation or exploration.
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