Curved objects pose a fundamental challenge for skill transfer in robotics: unlike planar surfaces, they do not admit a global reference frame. As a result, task-relevant directions such as "toward" or "along" the surface vary with position and geometry, making object-centric tasks difficult to transfer across shapes. To address this, we introduce an approach using Diffused Orientation Fields (DOF), a smooth representation of local reference frames, for transfer learning of tasks across curved objects. By expressing manipulation tasks in these smoothly varying local frames, we reduce the problem of transferring tasks across curved objects to establishing sparse keypoint correspondences. DOF is computed online from raw point cloud data using diffusion processes governed by partial differential equations, conditioned on keypoints. We evaluate DOF under geometric, topological, and localization perturbations, and demonstrate successful transfer of tasks requiring continuous physical interaction such as inspection, slicing, and peeling across varied objects. We provide our open-source codes at our website https://github.com/idiap/diffused_fields_robotics

翻译：曲面物体对机器人技能迁移提出了根本性挑战：与平面不同，曲面无法建立全局参考坐标系。因此，诸如“朝向”或“沿着”表面等任务相关方向会随位置和几何形状变化，导致跨形状的物体中心化任务迁移困难。为解决此问题，我们提出采用扩散方向场（DOF）——一种局部参考系的平滑表示方法——实现曲面物体间的任务迁移学习。通过在连续变化的局部坐标系中表达操作任务，我们将跨曲面物体的任务迁移问题简化为建立稀疏关键点对应关系。DOF通过基于关键点约束的偏微分方程扩散过程，从原始点云数据在线计算生成。我们在几何形变、拓扑变化和定位扰动条件下评估DOF性能，并成功演示了跨不同物体的检测、切割、剥离等需要连续物理交互的任务迁移。开源代码发布于 https://github.com/idiap/diffused_fields_robotics