Multi-scale Procrustes-based 3D shape control

We developed a novel 3D shape control strategy that does not rely on physical models but rather on a multi-scale shape analysis that allows to prioritise those parts of the objects that not only contribute more to the error metric but also can be influenced by the grippers to an estimated extent. We provided theoretical analysis of local asymptotic stability of the control system and performed several simulations and experiments that validate the system showing robustness and proper error convergence. To the best of our knowledge this is the first 3D shape control framework involving multi-scale geometric analysis of texture-less objects. Regarding future work, an interesting research line would be decoupling the scale at which each gripper is acting, i.e. independently defining an \(r^*\) for each gripper and thus (most likely) achieving more error reduction in certain cases. Note that this is nontrivial as the dimensionality of the problem increases by \(G\) (i.e., \(r_1\times...\times r_G\)).