arXiv:2610.12404v1 Announce Type: cross Abstract: Close-proximity multi-arm manipulation requires collision models that are both geometrically accurate and differentiable enough for real-time optimization. Classical geometry checkers provide reliable distances but are difficult to use inside gradient-based model predictive control, while conservative proxy models can restrict tightly coupled motion. We present PI-UDF, a physics-informed unified differentiable framework for body-to-body collision distance prediction between articulated robots. PI-UDF combines analytical forward kinematics with learnable link-geometry embeddings and a shared residual network to predict pairwise inter-arm distances directly from robot configurations. To improve safety-critical fidelity, we combine quota-driven boundary mining with an asymmetric boundary-crossing penalty that emphasizes false-safe sign errors near the collision boundary. The learned distance field is integrated into nonlinear MPC as a differentiable inter-arm clearance term. We validate the framework on a real dual-Franka platform through high-speed close-proximity 14-DoF dual-arm swapping, sustained single-arm dynamic evasion, and dynamic-evasion planning configurations with frozen, predicted, and target-switching treatments of the moving arm. Hardware experiments and offline Drake/FCL replay show that PI-UDF provides a differentiable inter-arm clearance estimate suitable for closed-loop collision-aware collaborative robot motion generation.