Physical SLAM: Physics-aware Simultaneous Localisation and Mapping

To reconstruct a predictive 4D representation of the physical world from monocular video captured by a moving camera, we jointly reconstruct dynamic Gaussian radiance fields and infer their underlying physical dynamics. This paper proposes Physical SLAM, a physics-aware method for constructing 4D Gaussian fields of deformable objects and predicting their future state when subjected to external actions, given a sequence of RGB-D images. Our method separates the scene into a static background Gaussian field for camera localization and a dynamic object Gaussian field driven by a spring--mass physical model of elastic deformation, inertia, and damping. To integrate visual observations with physical dynamics, we introduce virtual observation forces that gradually pull simulated surface nodes toward observed depth points, avoiding abrupt replacement of simulated node positions. Meanwhile, the physical parameters of the spring--mass model are updated from simulation errors aggregated over the full reconstruction observation window, enabling the reconstructed dynamics to align with observations. To couple appearance, geometry, and physics, we further design a physics-aware Gaussian transformation and surface alignment strategy, where dynamic Gaussians are transformed along the deforming physical surface of the spring--mass model and constrained to remain aligned with the surface during rendering-based optimization. The resulting representation supports observed-frame rendering and action-conditioned simulation, extending SLAM maps to describe how deformable objects respond to manipulation. On the PhysTwin benchmark, our method improves reconstruction and prediction PSNR over PhysTwin by 10.4% and 11.0%, respectively. On the TUM RGB-D benchmark, it reduces average camera tracking error by 20.6%, improves SSIM by 3.6%, and reduces LPIPS by 8.3% compared with 4DGS-SLAM.