Interactive companion

A Tutorial on Shape Servoing of Deformable Objects

These demos accompany the two-part tutorial on data-driven, Jacobian-based shape control. They use its running example (Fig. 1): two robot arms move their grippers in a plane to deform an elastic rod observed by a stationary camera.

The demos follow the order of the tutorial. Part I builds the shape-servoing loop. Part II analyzes the singular value decomposition of the deformation Jacobian, the choice of shape features, and the failure modes of the loop, and extends the loop to time-varying targets, secondary tasks, and three-dimensional objects. Part II demos use a warmer page color. All computations run in your browser, in a JavaScript port of the shape_servoing Python package of the code repository.

How to use the demos Glossary Useful definitions

perception \vs=f(\vy) error \ve=\vs^{*}-\vs control \vu=\alpha\,\vJh^{+}\ve update \vJh_k from (\dq_{k-1},\ds_k)

Left: block diagram of the shape-servoing loop with perception, Jacobian estimation, and controller. Right: two robot arms deform a blue cable in a vertical plane, observed by a camera, toward a dashed target shape. Bottom: the shape of the object approaching the target over time. — **Fig. 1 from Part I of the tutorial that these demos accompany.**

Part IFundamentals

features, the deformation Jacobian, its estimation, the closed loop, and its local stability

Part IIAdvanced concepts

singular value analysis, feature choice, failure modes, extensions, and 3-D objects