Abstract: Manipulation of deformable objects is an important set of open problems in the field of robotics. Application areas include robotic surgery, household robotics, manufacturing, logistics, 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 paper, we start by providing a tutorial on foundational aspects of models of shape and on models of shape dynamics. Subsequently, we use this as the basis for a survey review of existing work for learning and estimation of these models and for motion planning and control to achieve desired deformations. We also suggest future lines of work.
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