Adaptive Deformation Control for Elastic Linear Objects

This paper addresses the general problem of deformable linear object manipulation. The main application we consider is in the field of agriculture, for plant grasping, but may have interests in other tasks such as human daily activities and industrial production. We specifically consider an elastic linear object where one of its endpoints is fixed, and another point can be grasped by a robotic arm. To deal with the mentioned problem, we propose a model-free method to control the state of an arbitrary point that can be at any place along the object's length. Our approach allows the robot to manipulate the object without knowing any model parameters or offline information of the object's deformation. An adaptive control strategy is proposed for regulating the state of any point automatically deforming the object into the desired location. A control law is developed to regulate the object's shape thanks to the adaptive estimation of the system parameters and its states. This method can track a desired manipulation trajectory to reach the target point, which leads to a smooth deformation without drastic changes. A Lyapunov-based argument is presented for the asymptotic convergence of the system that shows the process's stability and convergence to desired state values. To validate the controller, numerical simulations involving two different deformation models are conducted, and performances of the proposed algorithm are investigated through full-scale experiments.