Object-centric task representation and transfer using diffused orientation fields

Curved objects pose a fundamental challenge for task transfer in robotics: Unlike planar surfaces, curved surfaces 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, a smooth representation of local reference frames, for expressing and transferring 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. Our representation is computed online from raw point cloud data using diffusion processes governed by partial differential equations, conditioned on keypoints. We evaluate our method under geometric, topological, and keypoint perturbations and demonstrate successful transfer of tasks requiring continuous physical interaction such as coverage, slicing, and peeling across varied objects.