MPM-based simulation and bounded-error compression of material points for magnetic tactile sensors

Tactile sensing provides critical contact feedback for precision robotic micro-assembly, particularly in visually occluded environments common in 3C (Computer, Communication, and Consumer Electronics) manufacturing. Magnetic tactile sensors are especially promising due to their high sensitivity, fast response, and compact structure. However, the lack of effective physics-based simulation tools remains a key bottleneck for applying magnetic tactile sensing in reinforcement learning-based assembly policy training. To address this limitation, we propose a unified framework that integrates physics-based elastomer simulation, tactile-oriented point-cloud representation learning, and Real-to-Sim cross-modal mapping. This framework establishes a physically grounded intermediate representation for magnetic tactile sensing, enabling unified modeling and alignment across domains. The elastomer deformation is modeled using a particle-based formulation and simulated via the Material Point Method (MPM), achieving 0.02 mm spatial resolution with approximately 1 GB GPU memory. To enable efficient learning on high-dimensional tactile data, we propose Point-PAMAE, a masked point-cloud autoencoder with grid-based partitioning, a multi-scale dynamic graph convolutional encoder, and a position-aware decoder. The proposed method reduces partitioning overhead by 43.54% and achieves over 88% compression with a Chamfer Distance of 0.015. Furthermore, a latent-space Real-to-Sim mapping model is developed to project real magnetic signals into the simulated deformation feature space. Experimental results demonstrate that the mapped representations preserve contact-relevant geometric structures and enable reliable cross-domain tactile alignment. These results indicate that the proposed framework provides an efficient representation for magnetic tactile sensing, supporting future Sim-to-Real deployment in precision robotic assembly.