Visual Tracking Control of Deformable Objects with a FAT- based Controller

Automatic manipulation of deformable objects is a challenging problem. Improper operations, such as excessive stretching, collision, are easy to cause damages to the deformable objects. Thus, not only the final configuration but also the trajectory of the deformation is supposed to be controlled during the process of interaction. In this paper, a model-free method to control the trajectory of the deformation in the unknown environment is proposed. We design an adaptive dynamic controller that adaptively estimates the deformation Jacobian matrix (DJM) online based on function approximation techniques (FAT), which approximates nonlinear functions with an arbitrary small error, avoiding modeling for compliant objects. Besides, we introduce a virtual force to improve the manipulability and robustness of the method. The stability of the proposed adaptive algorithm and the boundedness of internal signals are proved by Lyapunov theory whenever the approximation error is non-negligible or negligible. Experiment results validate the efficiency of the algorithm proposed.