A Tutorial on Shape Servoing of Deformable Objects-Part II: Advanced Concepts

Abstract

In robotics, shape control, or shape servoing, refers to the automatic manipulation of a deformable object toward a desired shape. This article is the second of a two-part tutorial on data-driven, Jacobian-based shape control, in which the deformation Jacobian, a local model of how robot motion changes the measured shape, is estimated from measurements. Part I built the shape-servoing loop and derived a local stability condition. This paper starts by using the singular value decomposition of the deformation Jacobian to identify shape changes that can be produced by small robot motions, those that require large robot motions, and those that are locally unavailable. It then analyses how the choice of shape features determines how the controller regulates the object's shape and, therefore, how much the object deforms on its way to the target. It then describes three ways in which the shape control loop can fail: loss of controllability, loss of observability, and occurrence of mechanical instabilities. It closes with shape-control extensions to time-varying targets, secondary tasks, and three-dimensional objects.