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.

翻译：我们旨在解决基于三维几何结构的数据驱动碰撞距离估计问题。传统方法因依赖点云等有限表征形式而存在精度不足的缺陷。相比之下，我们先前提出的基于图的模型GraphDistNet虽能利用边信息实现高精度估计，但随着图规模扩大导致消息传递成本激增，限制了其在三维几何结构中的适用性。为解决这些挑战，我们提出GDN-R——一种新型三维图估计网络。GDN-R采用逐层概率图重连算法，该算法利用可微分的Gumbel-top-K松弛技术。通过迭代图重连与相关嵌入更新，我们的方法能够精确推断最小距离。概率重连机制使嵌入能够针对未见类别的几何结构实现快速鲁棒的泛化。通过包含150对三维物体的41,412次随机基准测试，我们证明GDN-R在精度与泛化能力上均优于当前最优基线方法。研究还表明，所提出的重连策略通过缩减估计模型规模提升了更新性能。我们最终在仿真与真实场景中验证了其批预测与自动微分能力在轨迹优化中的应用。