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We aim to solve the problem of data-driven collision-distance estimationgiven 3-dimensional (3D) geometries. Conventional algorithms suffer from lowaccuracy due to their reliance on limited representations, such as pointclouds. In contrast, our previous graph-based model, GraphDistNet, achieveshigh accuracy using edge information but incurs higher message-passing costswith growing graph size, limiting its applicability to 3D geometries. Toovercome these challenges, we propose GDN-R, a novel 3D graph-based estimationnetwork.GDN-R employs a layer-wise probabilistic graph-rewiring algorithmleveraging the differentiable Gumbel-top-K relaxation. Our method accuratelyinfers minimum distances through iterative graph rewiring and updating relevantembeddings. The probabilistic rewiring enables fast and robust embedding withrespect to unforeseen categories of geometries. Through 41,412 random benchmarktasks with 150 pairs of 3D objects, we show GDN-R outperforms state-of-the-artbaseline methods in terms of accuracy and generalizability. We also show thatthe proposed rewiring improves the update performance reducing the size of theestimation model. We finally show its batch prediction and auto-differentiationcapabilities for trajectory optimization in both simulated and real-worldscenarios.

Graph-based 3D Collision-distance Estimation Network with Probabilistic Graph Rewiring