Fusion-driven geometry-constrained latent flow learning for robust AUV motion anticipation from heterogeneous 3D observations

Reliable motion anticipation for autonomous underwater vehicles (AUVs) is challenging when heterogeneous observations are sparse, asynchronous, corrupted, or intermittently unavailable, and when sensing statistics differ between simulation and real deployment. This paper proposes PIG-Dyn, a reliability-aware geometry-constrained latent flow framework for AUV motion anticipation from heterogeneous 3D observations. Timestamped observations are transformed into a common ego-centric frame and assigned learned reliability scores according to availability, acquisition age, and observation quality. Masked reliability-aware attention then fuses the observations into functionally differentiated latent subspaces representing scene geometry, vehicle–environment interaction, ego-motion, and disturbance-related residuals. In parallel, a local geometric belief field preserves occupancy, free-space, directional, and traversal-risk cues and directly conditions the continuous latent vector field. The latent dynamics employ skew-symmetric conservative and positive-semidefinite dissipative operators within a port-structured parameterization. The conservative term contributes zero power to a learned storage function, whereas dissipation is non-positive in the autonomous unforced case. Control, disturbance, and geometry-conditioned effects are modeled as external ports and softly regulated through a finite-step storage-balance objective. Latent uncertainty is propagated through the discrete transition map using a first-order diagonal Gaussian approximation and decoded into future position, orientation, and velocity. Sim-to-real transfer is encouraged by aligning predictive latent moments and batch-averaged transition sensitivities rather than raw sensor appearance. Experiments on HoloOcean, Aqualoc, and SubPipe demonstrate improved displacement accuracy, uncertainty calibration, collision rate, and cross-domain generalization.