An efficient approach to closed-loop shape control of deformable objects using finite element models

Robots are nowadays faced with the challenge of handling deformable objects in industrial operations. In particular, the problem of shape control, which aims at giving a specific deformation state to an object, has gained interest recently in the research community. Among the proposed solutions, approaches based on finite elements proved accurate and reliable but also complex and computationally-intensive. In order to mitigate these drawbacks, we propose a scheme for shape control that does not require to run a real-time simulation or to solve an implicit optimization problem for computing the control outputs. It is based on a partition of the nodal coordinates that allows deriving a control law directly from tangent stiffness matrices. This formulation is also coupled with the introduction of reduced finite element models. Simulation and experimental results in the context of linear deformable object manipulation demonstrate the interest of the proposed approach.