Dexterous grasping is a fundamental yet challenging skill in robotic manipulation, requiring precise interaction between robotic hands and objects. In this paper, we present $\mathcal{D(R,O)}$ Grasp, a novel framework that models the interaction between the robotic hand in its grasping pose and the object, enabling broad generalization across various robot hands and object geometries. Our model takes the robot hand's description and object point cloud as inputs and efficiently predicts kinematically valid and stable grasps, demonstrating strong adaptability to diverse robot embodiments and object geometries. Extensive experiments conducted in both simulated and real-world environments validate the effectiveness of our approach, with significant improvements in success rate, grasp diversity, and inference speed across multiple robotic hands. Our method achieves an average success rate of 87.53% in simulation in less than one second, tested across three different dexterous robotic hands. In real-world experiments using the LeapHand, the method also demonstrates an average success rate of 89%. $\mathcal{D(R,O)}$ Grasp provides a robust solution for dexterous grasping in complex and varied environments. The code, appendix, and videos are available on our project website at https://nus-lins-lab.github.io/drograspweb/.

翻译：灵巧抓取是机器人操作中一项基础但具有挑战性的技能，需要机器人手与物体之间进行精确交互。本文提出$\mathcal{D(R,O)}$ Grasp，这是一个新颖的框架，用于建模机器人手在其抓取姿态下与物体之间的交互，从而能够广泛泛化到不同的机器人手和物体几何形状。我们的模型以机器人手的描述和物体点云作为输入，高效地预测运动学上有效且稳定的抓取，展现出对不同机器人具身形态和物体几何形状的强大适应性。在仿真和真实环境中进行的大量实验验证了我们方法的有效性，在多种机器人手上均实现了成功率、抓取多样性和推理速度的显著提升。我们的方法在三种不同的灵巧机器人手上进行测试，在仿真中平均成功率可达87.53%，且推理时间少于一秒。在使用LeapHand进行的真实世界实验中，该方法也实现了89%的平均成功率。$\mathcal{D(R,O)}$ Grasp为复杂多变环境中的灵巧抓取提供了一个鲁棒的解决方案。代码、附录和视频可在我们的项目网站 https://nus-lins-lab.github.io/drograspweb/ 获取。