Multiscale Procrustes-Based 3-D Shape Control

The shape control problem involves deforming a nonrigid object into a desired shape. In this article, we present a new 3-D shape control method that can handle large deformations of texture-less objects. In particular, we use functional maps to generate surface points' correspondences between the current and the desired shape that serve as input for our Procrustes-based multiscale control strategy. The main contribution is a multiscale analysis with a relaxed rigidity assumption that defines scales based on geodesic distances to the grippers. Our method considers that objects may deform at different scales depending on the gripper actions applied to them. For this reason, our multiscale analysis computes shape control actions defined according to gripper influence on particularly convenient scales. We present stability analysis and discuss several simulations and experiments.