arXiv:2410.06819v2 Announce Type: replace-cross Abstract: Generalist robot policies must operate safely and reliably in everyday human environments such as homes, offices, and warehouses, where people and objects move unpredictably. We present Dynamic Neural Potential Field (NPField-GPT), a learning-enhanced model predictive control (MPC) framework that couples classical optimization with a Transformer-based predictor of footprint-aware repulsive potentials. Given an occupancy sub-map, robot footprint, and optional dynamic-obstacle cues, our autoregressive NPField-GPT head forecasts a horizon of differentiable potentials that are injected into a sequential quadratic MPC program via L4CasADi, yielding real-time, constraint-aware trajectory optimization. We additionally study two baselines: (NPField-D1) static-frame decomposition and (NPField-D2) parallel MLP heads for all steps. In dynamic indoor scenarios from BenchMR and on a Husky UGV in office corridors, NPField-GPT produces safer, more conservative trajectories under motion changes, while D1/D2 offer lower latency. We also compare with the CIAO* and MPPI baselines. Across methods, the Transformer+MPC synergy preserves the transparency and stability of model-based planning while learning only the part that benefits from data: spatiotemporal collision risk. Code and trained models are available at https://github.com/CognitiveAISystems/Dynamic-Neural-Potential-Field