Multi-scale Laplacian-based FMM for shape control

Shape control has become a prominent research field as it enables the automation of tasks in many applications. Overall, deforming an object to a desired target shape by using few grippers is a major challenge. The limited information about the object dynamics, the need to combine small and large deformations in order to achieve certain target shapes and the non-linear nature of most deformable objects are factors that significantly hamper shape control performance. In this paper, we propose a shape control method for multi-robot manipulation of large-strain deformable objects. Our approach is based on multi-scale Laplacian descriptors that feed an FMM (Fast Marching Method) for elastic shape contour matching. The FMM's resulting path and the Laplacian operator are used to define a control strategy for the robot grippers. Simulation experiments carried out with an ARAP (As Rigid As Possible) deformation model provide satisfactory results.