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.
AI 速览：本教程第一部分系统介绍基于数据驱动变形雅可比的可变形物体形状伺服控制的基本要素与完整闭环。
In robotics, shape control (or shape servoing) refers to the automatic manipulation of a deformable object to achieve a desired shape. It involves a feedback loop that exploits the relation between robot motion and changes in the measured shape. This relation, known as the interaction Jacobian or, in this context, the deformation Jacobian, depends on the object's mechanical properties, geometry, and boundary conditions (e.g., where the object is grasped). Because these factors are often difficult to model accurately, the deformation Jacobian can be estimated locally from observed shape changes produced by commanded robot motions, without requiring a fine-tuned mechanical model. This article is the first of a two-part tutorial on data-driven Jacobian-based shape control of deformable objects. It introduces the central elements of the approach: the formulation of the shape-control problem, shape representation, estimation and online update of the deformation Jacobian, and a standard control law from the literature. It then assembles these elements into a complete shape-servoing loop, derives a local stability condition for this loop, and illustrates why some target shapes cannot be reached. Part II covers more advanced topics. Throughout both parts, a simulated planar example in which two robot arms manipulate an elastic rod observed by a camera illustrates the concepts.
Ignacio Cuiral-Zueco, David Hardman, Michele Pierallini, Erfan Shahriari
Dexterous manipulation of rigid objects has reached a level of maturity where grasp stability, control, and planning strategies are successfully applied in industry and logistics. In contrast, manipulating deformable objects (cables, plastic pieces, cloth) remains far more challenging, as rigid-object methods do not account for their additional complexity. This paper identifies semantic failure analysis as a key step toward mature deformable-object manipulation and supports this claim with proof-of-concept experiments. Unlike rigid-object manipulation, where goals are well-defined in terms of criteria such as force balance and slippage, deformable-object manipulation involves a broader variety of failure modes arising from differences in materials, geometry, and behaviour. Typical failures include buckling, plastic deformation, pressure variations, and tearing. These diverse and often hard-to-detect events require distinct corrective strategies, making semantic failure analysis necessary. We define its key components and challenges and present experimental results supporting its potential as a research direction.