让复杂物体碰撞检测可微，提升抓取优化效果
Robust Differentiable Collision Detection for General Objects
- 用距离导向的随机平滑实现可微碰撞检测
- 在DexGraspNet和Objaverse上显著优于基线方法
- 适合需要梯度优化的机器人抓取与操控任务
碰撞检测是机器人仿真、控制与规划的核心。传统算法如GJK+EPA虽能计算最近点或穿透最深点，但不可微，阻碍了接触密集场景（如抓取）中的梯度优化。近期工作采用一阶随机平滑实现可微性，但仅限凸物体且对复杂几何鲁棒性差。本文提出一种支持凸凹物体、跨尺度与多构型的鲁棒高效可微碰撞检测框架。引入基于距离的一阶随机平滑、自适应采样与等效梯度传输，实现稳定且信息丰富的梯度计算。在DexGraspNet和Objaverse的复杂网格上实验显示显著优于现有基线。最后，直接应用于灵巧抓取合成，有效提升抓取质量。代码已开源。
原文摘要 · Abstract (English)
Collision detection is a core component of robotics applications such as simulation, control, and planning. Traditional algorithms like GJK+EPA compute witness points (i.e., the closest or deepest-penetration pairs between two objects) but are inherently non-differentiable, preventing gradient flow and limiting gradient-based optimization in contact-rich tasks such as grasping and manipulation. Recent work introduced efficient first-order randomized smoothing to make witness points differentiable; however, their direction-based formulation is restricted to convex objects and lacks robustness for complex geometries. In this work, we propose a robust and efficient differentiable collision detection framework that supports both convex and concave objects across diverse scales and configurations. Our method introduces distance-based first-order randomized smoothing, adaptive sampling, and equivalent gradient transport for robust and informative gradient computation. Experiments on complex meshes from DexGraspNet and Objaverse show significant improvements over existing baselines. Finally, we demonstrate a direct application of our method for dexterous grasp synthesis to refine the grasp quality. The code is available at https://github.com/JYChen18/DiffCollision.
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