In this paper, we propose ContactSDF, a method that uses signed distance functions (SDFs) to approximate multi-contact models, including both collision detection and time-stepping routines. ContactSDF first establishes an SDF using the supporting plane representation of an object for collision detection, and then uses the generated contact dual cones to build a second SDF for time-stepping prediction of the next state. Those two SDFs create a differentiable and closed-form multi-contact dynamic model for state prediction, enabling efficient model learning and optimization for contact-rich manipulation. We perform extensive simulation experiments to show the effectiveness of ContactSDF for model learning and real-time control of dexterous manipulation. We further evaluate the ContactSDF on a hardware Allegro hand for on-palm reorientation tasks. Results show with around 2 minutes of learning on hardware, the ContactSDF achieves high-quality dexterous manipulation at a frequency of 30-60Hz. Project page https://yangwen-1102.github.io/contactsdf.github.io/

翻译：本文提出ContactSDF方法，该方法利用符号距离函数（SDF）来近似多接触模型，包括碰撞检测和时间步进程序。ContactSDF首先利用物体的支撑平面表示建立用于碰撞检测的SDF，随后利用生成的接触对偶锥构建第二个SDF，用于下一状态的时间步进预测。这两个SDF共同构成了一个可微分且封闭形式的多接触动力学模型，用于状态预测，从而实现对密集接触操作的模型高效学习与优化。我们通过大量仿真实验验证了ContactSDF在模型学习和灵巧操作实时控制方面的有效性。进一步在Allegro灵巧手硬件平台上对掌上重定向任务进行评估。结果表明，在硬件上经过约2分钟的学习后，ContactSDF能够以30-60Hz的频率实现高质量的灵巧操作。项目页面 https://yangwen-1102.github.io/contactsdf.github.io/