As-Rigid-as-Possible Shape Servoing

Abstract

Shape servoing is the problem of controlling the shape of a deformable object via robotic manipulation, exploiting sensory feedback. In many shape servoing scenarios of practical interest, the object has a natural tendency to preserve local rigidity. Motivated by this observation, we propose to use the As-Rigid-As-Possible deformation model for shape servoing. Specifically, we propose a novel control scheme based on a deformation Jacobian computed from this model. The proposed scheme drives the object to a desired 3D shape using as feedback the object’s measured current 3D shape. The scheme is simple to implement, and it avoids some typical requirements in existing work: specifically, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(i)</i> we do not need to know the object’s mechanical deformation parameters, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(ii)</i> we do not use a Jacobian computed from data collected over a time window while the robots move. We test the proposed scheme in bi-arm shape servoing experiments with a variety of deformable objects of different material (paper, rubber, plastic). Tracking of the deformable object’s surface in 3D is performed in our experiments via an algorithm based on monocular vision. The experimental results validate the practicality of our scheme.