  We aim to solve the problem of data-driven collision-distance estimation
given 3-dimensional (3D) geometries. Conventional algorithms suffer from low
accuracy due to their reliance on limited representations, such as point
clouds. In contrast, our previous graph-based model, GraphDistNet, achieves
high accuracy using edge information but incurs higher message-passing costs
with growing graph size, limiting its applicability to 3D geometries. To
overcome these challenges, we propose GDN-R, a novel 3D graph-based estimation
network.GDN-R employs a layer-wise probabilistic graph-rewiring algorithm
leveraging the differentiable Gumbel-top-K relaxation. Our method accurately
infers minimum distances through iterative graph rewiring and updating relevant
embeddings. The probabilistic rewiring enables fast and robust embedding with
respect to unforeseen categories of geometries. Through 41,412 random benchmark
tasks with 150 pairs of 3D objects, we show GDN-R outperforms state-of-the-art
baseline methods in terms of accuracy and generalizability. We also show that
the proposed rewiring improves the update performance reducing the size of the
estimation model. We finally show its batch prediction and auto-differentiation
capabilities for trajectory optimization in both simulated and real-world
scenarios.
