An Artin Braid Group Representation of Knitting Machine State with Applications to Validation and Optimization of Fabrication Plans
An Artin Braid Group Representation of Knitting Machine State with Applications to Validation and Optimization of Fabrication Plans
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DOI：
10.1109/icra48506.2021.9562113
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发表时间：
2021-05
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通讯作者：
Jenny Lin;J. McCann
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作者：
Jenny Lin;J. McCann
工业针织机通过操控数百根针上的线圈来制造织物。为这些机器制作花型的一个核心问题是移圈规划——提出一系列底层操作，将线圈移动到合适的针上，以便通过这些线圈针织出正确的最终结构。由于每个线圈都与正在编织的较大织物部分相连，移圈规划不仅要考虑线圈位置，还要考虑纱线股相互缠绕的方式。
我们首次完整、离散地呈现了机器的线圈缠绕过程。我们的呈现方式将阿廷辫子群中的一个辫子与一组明确的线圈位置相结合，以完全捕捉线圈交叉情况。通过将辫子存储为对称标准型，可以快速比较状态，并随着机器操作逐步更新。这种呈现方式可用于验证移圈操作的等效性，为优化针织生产提供了一个重要工具。
我们改进了先前的移圈规划算法方面的工作，这些算法只能解决某些子类问题，并且在制造时间方面常常不是最优的。我们引入了一种新颖的A*搜索启发式方法和状态合并机制，我们表明该方法能为一大型基准组小型移圈规划问题找到最优移圈规划。
Industrial knitting machines create fabric by manipulating loops held on hundreds of needles. A core problem in pattern making for these machines is transfer planning – coming up with a sequence of low-level operations that move loops to the appropriate needles so that knitting through those loops produces the correct final structure. Since each loop is connected to the larger piece in progress, transfer plans must account for not only loop position, but the way strands of yarn tangle around each other.We present the first complete, discrete representation of the machine’s loop-tangling process. Our representation combines a braid from the Artin Braid Group with an array of explicit loop positions to fully capture loop crossings. By storing braids in the Symmetric Normal Form, states can be quickly compared and updated incrementally with machine operations. This representation can be used to verify the equivalence of transfer operations, providing an important tool in optimizing knit manufacturing.We improve on prior work in transfer planning algorithms, which can only solve certain subclasses of problems and are frequently suboptimal in terms of fabrication time, by introducing a novel A* search heuristic and state-collapsing mechanism, which we show finds optimal transfer plans for a large benchmark set of small transfer planning problems.