Robotic manipulation of a rotating chain
This addresses a specific manipulation challenge for robotics, with potential applications to other flexible objects like elastic rods, but it is incremental in scope.
The paper tackles the problem of manipulating a uniformly rotating chain with a robotic arm, proving that its configuration space is homeomorphic to a 2D surface and devising a stable strategy to transition between rotation modes, demonstrated on a physical robot.
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 $\mathbb{R}^3$. 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.