One Demonstration Survived a New Object and a Shove

POIL represents the functional part of an object as a set of 3D points used both to transfer a demonstrated trajectory and to control execution. A multimodal model grounds the relevant part, point correspondences transfer the motion across pose and object-category changes, and multi-view tracking closes the loop. The controller projects per-point velocities into one rigid-body twist and carries a convergence argument under a rigid-object assumption. Simulation and real-robot experiments show transfer from one demonstration and recovery from disturbances, within the tested objects and scenes.