This paper considers the problem of manipulating a uniformly rotating chain: the chain is rotated at a constant angular speed around a fixed axis using a robotic manipulator. Manipulation is quasi-static in the sense that transitions are slow enough for the chain to be always in "rotational" equilibrium. The curve traced by the chain in a rotating plane -- its shape function -- can be determined by a simple force analysis, yet it possesses complex multi-solutions behavior typical of non-linear systems. We prove that the configuration space of the uniformly rotating chain is homeomorphic to a two-dimensional surface embedded in @math . Using that representation, we devise a manipulation strategy for transiting between different rotation modes in a stable and controlled manner. We demonstrate the strategy on a physical robotic arm manipulating a rotating chain. Finally, we discuss how the ideas developed here might find fruitful applications in the study of other flexible objects, such as elastic rods or concentric tubes.
Within the field of robotics, the manipulation of flexible objects is studied along two main directions. A first direction is topological: one is mainly interested in the order and sequence of the manipulation rather than in the precise behavior of the flexible object. Examples include origami folding @cite_14 , laundry folding @cite_1 or rope-knotting @cite_23 @cite_20 .
@cite_20 @cite_14 @cite_1 @cite_23
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Origami, the art of paper sculpture, is a fresh challenge for the field of robotic manipulation, and provides a concrete example of the many difficulties and general manipulation problems faced in robotics. This paper describes our initial exploration, and highlights key problems in the manipulation, modeling, and design of foldable structures. Results include the design of the first origami-folding robot, a complete fold-sequence planner for a simple class of origami, and analysis of the kinematics of more complicated folds, including the common paper shopping bag. We consider the problem of autonomous robotic laundry folding, and propose a solution to the perception and manipulation challenges inherent to the task. At the core of our approach is a quasi-static cloth model which allows us to neglect the complex dynamics of cloth under significant parts of the state space, allowing us to reason instead in terms of simple geometry. We present an algorithm which, given a 2D cloth polygon and a desired sequence of folds, outputs a motion plan for executing the corresponding manipulations, deemed g-folds, on a minimal number of robot grippers. We define parametrized fold sequences for four clothing categories: towels, pants, short-sleeved shirts, and long-sleeved shirts, each represented as polygons. We then devise a model-based optimization approach for visually inferring the class and pose of a spread-out or folded clothing article from a single image, such that the resulting polygon provides a parse suitable for these folding primitives. We test the manipulation and perception tasks individually, and combine them to implement an autonomous folding system on the Willow Garage PR2. This enables the PR2 to identify a clothing article spread out on a table, execute the computed folding sequence, and visually track its progress over successive folds. Here, we propose a planning method for knotting unknotting of deformable linear objects. First, we propose a topological description of the state of a linear object. Second, transitions between these states are defined by introducing four basic operations. Then, possible sequences of crossing state transitions, i.e. possible manipulation processes, can be generated once the initial and the objective states are given. Third, a method for determining grasping points and their directions of movement is proposed to realize derived manipulation processes. Our proposed method indicated that it is theoretically possible for any knotting manipulation of a linear object placed on a table to be realized by a one-handed robot with three translational DOF and one rotational DOF. Furthermore, criteria for evaluation of generated plans are introduced to reduce the candidates of manipulation plans. Fourth, a planning method for tying knots tightly is established because they fulfill their fixing function by tightening them. Finally, we report knotting unknotting manipulation performed by a vision-guided system to demonstrate the usefulness of our approach.