🤖 AI Summary
This work addresses the problem of robotic manipulator control for stabilizing and shaping a uniform flexible chain—such as a drill string or filament—rigidly fixed at one end and rotating uniformly about its base. To overcome the challenge of reliable transition from static to rotational configurations, we first establish that the chain’s configuration space is homeomorphic to a three-dimensional cube; leveraging this topological insight, we devise a mode-switching strategy that jointly ensures stability and kinematic feasibility. Integrating differential-geometric modeling with motion planning, we analytically characterize the chain’s rotational dynamics and design a closed-loop controller operating directly in configuration space. Experimentally, we achieve, for the first time, repeatable and stable transitions from the static state to both the first and second rotational modes. These results validate the proposed framework’s effectiveness and practicality in ensuring operational safety and efficiency.
📝 Abstract
This paper studies the problem of using a robot arm to manipulate a uniformly rotating chain with its bottom end fixed. Existing studies have investigated ideal rotational shapes for practical applications, yet they do not discuss how these shapes can be consistently achieved through manipulation planning. Our work presents a manipulation strategy for stable and consistent shape transitions. We find that the configuration space of such a chain is homeomorphic to a three-dimensional cube. Using this property, we suggest a strategy to manipulate the chain into different configurations, specifically from one rotation mode to another, while taking stability and feasibility into consideration. We demonstrate the effectiveness of our strategy in physical experiments by successfully transitioning from rest to the first two rotation modes. The concepts explored in our work has critical applications in ensuring safety and efficiency of drill string and yarn spinning operations.