Manipulation of deformable objects has given rise to an important set of open problems in the field of robotics. Application areas include robotic surgery, household robotics, manufacturing, logistics, and agriculture, to name a few. Related research problems span modeling and estimation of an object's shape, estimation of an object's material properties, such as elasticity and plasticity, object tracking and state estimation during manipulation, and manipulation planning and control. In this survey article, we start by providing a tutorial on foundational aspects of models of shape and shape dynamics. We then use this as the basis for a review of existing work on learning and estimation of these models and on motion planning and control to achieve desired deformations. We also discuss potential future lines of work.

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Exploring and modeling heterogeneous elastic surfaces requires multiple interactions with the environment and a complex selection of physical material parameters. The most common approaches model deformable properties from sets of offline observations using computationally expensive forcebased simulators. In this work we present an online probabilistic framework for autonomous estimation of a deformability distribution map of heterogeneous elastic surfaces from few physical interactions. The method takes advantage of Gaussian Processes for constructing a model of the environment geometry surrounding a robot. A fast Position-based Dynamics simulator uses focused environmental observations in order to model the elastic behavior of portions of the environment. Gaussian Process Regression maps the local deformability on the whole environment in order to generate a deformability distribution map. We show experimental results using a PrimeSense camera, a Kinova Jaco2 robotic arm and an Optoforce sensor on different deformable surfaces.

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