An offline geometric model for controlling the shape of elastic linear objects

We propose a new approach to control the shape of deformable objects with robots. Specifically, we consider a fixed-length elastic linear object lying on a 2D workspace. Our main idea is to encode the object's deformation behavior in an offline constant Jacobian matrix. To derive this Jacobian, we use geometric deformation modeling and combine recent work from the fields of deformable object control and multirobot systems. Based on this Jacobian, we then propose a robotic control law that is capable of driving a set of shape features on the object toward prescribed values. Our contribution relative to existing approaches is that at run-time we do not need to measure the full shape of the object or to estimate/simulate a deformation model. This simplification is achieved thanks to having abstracted the deformation behavior as an offline model. We illustrate the proposed approach in simulation and in experiments with real deformable linear objects.