Robotic manipulation of a rotating chain

TL;DR

This paper studies how a robotic arm can manipulate a rotating chain in a stable, controlled manner by analyzing its complex equilibrium configurations and proposing a manipulation strategy based on the chain's configuration space.

Contribution

It introduces a novel homeomorphic representation of the rotating chain's configuration space and develops a manipulation strategy for mode transitions.

Findings

Successfully demonstrated manipulation strategy on a physical robot

Proved the configuration space is a 2D surface in 3D space

Discussed potential applications to elastic rods and concentric tubes

Abstract

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.