Using Task Symmetry for Human-Robot Collaborative Manipulation of Deformable Objects Without Modeling Deformation

I. INTRODUCTION We present a symmetry-based method that allows humans and robots to collaboratively manipulate deformable objects. The method does not require modeling and simulating deformation. Our method is based on the concept of diminishing rigidity, which we use to quickly compute an approximation to the Jacobian of the deformable object without using simulation. This Jacobian is used to drive the points within the deformable object towards a set of targets. For collaborative tasks, these targets are derived from the human's " side " of the task, i.e. the robot seeks to preserve symmetry of the deformable object as the human is manipulating it. However, this method alone is insufficient to avoid stretching the object beyond its allowed length and to avoid gripper collision with obstacles. Thus a key part of our approach is incorporating techniques to avoid collision and excessive stretching. Our experiments show how to perform a folding task with a two-dimensional deformable object, where the robot and a user simultaneously manipulate the deformable object. Our experiments are conducted in simulation but we emphasize that our method does not have access to the model of the deformable object used by the simulator, although we assume we are able to sense the geometry of the object (though sensing may be noisy). While our method is local (i.e. a controller), we find that it is quite versatile in the range of tasks it can perform, especially since it has no knowledge of the model of the deformable object. Our method can be applied to surgical tasks where the human and robot control separate manipulators to accomplish a common task; for instance for retracting tissue. The primary challenge of manipulating deformable objects is that they are very difficult to model and simulate. Many models and simulation methods have been proposed [1], [2], [3], [4], [5], [6]. Even if it were possible to obtain a perfect model of the deformable object, simulating that model is time-consuming and often very sensitive to simulation parameters. Given the difficulties of deformable object modeling and simulation, we seek to explore the practicality of manipulating deformable objects without explicitly modeling and simulating them. Our hypothesis is that model-free deformable manipulation like this can be accomplished by exploiting a property we call diminishing rigidity – i.e. that the effect of gripper motion along the deformable object diminishes as the