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数据驱动的碰撞距离估计问题。传统算法因依赖点云等有限表征，导致精度较低。相比之下，我们先前提出的基于图的模型GraphDistNet利用边信息实现了高精度，但随着图规模增大，其消息传递成本显著增加，限制了在三维几何场景中的适用性。为克服这些挑战，我们提出GDN-R——一种新型三维图估计网络。该网络采用基于可微Gumbel-top-K松弛方法的逐层概率图重连算法，通过迭代图重连与相关嵌入更新，精确推断最小距离。概率重连机制使嵌入对未见几何类别具有快速鲁棒性。在包含150对三维物体的41,412个随机基准测试中，GDN-R在精度与泛化能力上均优于现有最优基线方法。实验表明，所提重连方法通过缩小估计模型规模提升了更新性能。最后，我们验证了该网络在仿真与真实场景轨迹优化中的批预测与自动微分能力。