提出可三角剖分图，实现大变形充气机器人的多样化构型设计
Triangle-Decomposable Graphs for Isoperimetric Robots
- 基于图论优化算法，判断任意图是否可分解为唯一三角形
- 枚举了9个节点以内的最小刚性图（共7个三角形）及其工作空间
- 通过拼接已三角剖分子图，扩展构建更大复杂度机器人构型
等周机器人是大规模、无缆的充气机器人，能发生大幅形变，但此前仅实现过八面体一种3D形态。这类机器人由独立三角形构成，可通过调整关节相对位置改变形状，同时保持边长不变。本文提出一种优化方法，用于判断任意图能否被分解为唯一的三角形组合，从而可构造为等周机器人系统。我们枚举了最多含9个节点（7个三角形）的最小刚性图，并刻画了每类机器人中单个节点的工作空间。此外，还提出一种构建更大可三角剖分图的方法：将已成功三角剖分的子图进行组装。该方法显著拓展了等周机器人可能的构型种类。
原文摘要 · Abstract (English)
Isoperimetric robots are large scale, untethered inflatable robots that can undergo large shape changes, but have only been demonstrated in one 3D shape -- an octahedron. These robots consist of independent triangles that can change shape while maintaining their perimeter by moving the relative position of their joints. We introduce an optimization routine that determines if an arbitrary graph can be partitioned into unique triangles, and thus be constructed as an isoperimetric robotic system. We enumerate all minimally rigid graphs that can be constructed with unique triangles up to 9 nodes (7 triangles), and characterize the workspace of one node of each these robots. We also present a method for constructing larger graphs that can be partitioned by assembling subgraphs that are already partitioned into triangles. This enables a wide variety of isoperimetric robot configurations.
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