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.

翻译：碰撞检测是机器人学中仿真、控制与规划等应用的核心组件。传统算法如 GJK+EPA 可计算见证点（即两物体间最近或最深穿透点对），但其本质不可微，阻碍了梯度流动，限制了在抓取与操作等接触密集型任务中基于梯度的优化。近期研究引入高效的一阶随机平滑方法以实现见证点的可微性，然而其基于方向的表述仅限于凸体，对复杂几何形状缺乏鲁棒性。本文提出一种鲁棒且高效的可微碰撞检测框架，支持不同尺度与配置下的凸体与凹体。我们的方法引入了基于距离的一阶随机平滑、自适应采样及等效梯度传输，以实现鲁棒且信息丰富的梯度计算。在 DexGraspNet 与 Objaverse 的复杂网格数据集上的实验表明，本方法较现有基线有显著提升。最后，我们展示了该方法在灵巧抓取合成中的直接应用，以优化抓取质量。代码发布于 https://github.com/JYChen18/DiffCollision。