提出可重构的模块化机器人运动基元，实现任意7个以上模块的全路径可重构。
Reconfiguration-Complete Motion Primitives with Constructive Planning for Deformable Planar Modular Robots
- 用方格抽象建模可变形菱形模块，通过旋转和剪切两种基元保持物理可解释性。
- 证明当模块数≥7时，任意非直线连接构型均可转化为固定阶梯状标准构型。
- 构造性算法直接生成规划器，适合需要完全可重构性的机器人系统设计者。
模块化机器人的连续可变形几何结构使得重新配置规划与分析难以定义固定表示。本文提出一种方格抽象方法，将可变形菱形单元映射为固定尺寸网格单元，同时通过两种运动基元（旋转与剪切）保留局部运动的物理可解释性。在此抽象下，我们证明：对于任意由N≥7个模块构成的非直线边连接构型，均可仅通过允许的基元运动转换为固定的标准阶梯构型。由于这些运动可逆，该类中任意两个构型彼此可重构。证明过程是构造性的，直接导出一个阶梯标准化规划器，可在保持连通性的前提下移动可移除边界模块。为进一步提升效率，引入一种边界到交付的前瞻选择器，用于在不破坏完备性的情况下对高层可行选择进行排序。实验验证了构造性重构过程的有效性，并表明该选择器显著降低规划时间；与现有框架相比，在相同模块数量下规划时间更低。
原文摘要 · Abstract (English)
The continuously deformable geometry of modular robots makes it difficult to define a fixed representation for reconfiguration planning and analysis. This letter introduces a square-cell abstraction that maps deformable rhombus modules to fixed-size grid cells while retaining physically interpretable local motions through two primitives, pivoting and shearing. Under this abstraction, we prove that every non-straight edge-connected configuration with $N \geq 7$ can be transformed to a fixed canonical staircase using only admissible primitive motions. Since these motions are reversible, any two configurations in this class are mutually reconfigurable. The proof is constructive and directly yields a staircase-canonicalization planner that transports removable boundary modules while preserving connectivity. As a practical enhancement, we further introduce a boundary-to-delivery lookahead selector that ranks admissible high level choices without affecting the completeness guarantee. Experiments demonstrate the constructive reconfiguration process and show that the selector substantially reduces planning time, while reference comparisons indicate lower planning times than the prior framework over the shared module counts.
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