The concept of programmable matter envisions a very large number of tiny and simple robot particles forming a smart material. Even though the particles are restricted to local communication, local movement, and simple computation, their actions can nevertheless result in the global change of the material's physical properties and geometry. A fundamental algorithmic task for programmable matter is to achieve global shape reconfiguration by specifying local behavior of the particles. In this paper we describe a new approach for shape reconfiguration in the \emph{amoebot} model. The amoebot model is a distributed model which significantly restricts memory, computing, and communication capacity of the individual particles. Thus the challenge lies in coordinating the actions of particles to produce the desired behavior of the global system. Our reconfiguration algorithm is the first algorithm that does not use a canonical intermediate configuration when transforming between arbitrary shapes. We introduce new geometric primitives for amoebots and show how to reconfigure particle systems, using these primitives, in a linear number of activation rounds in the worst case. In practice, our method exploits the geometry of the symmetric difference between input and output shape: it minimizes unnecessary disassembly and reassembly of the particle system when the symmetric difference between the initial and the target shapes is small. Furthermore, our reconfiguration algorithm moves the particles over as many parallel shortest paths as the problem instance allows.

翻译：可编程物质的概念设想由大量微小且简单的机器人粒子构成一种智能材料。尽管粒子间的通信、移动和计算仅限于局部范围，但它们的协同作用仍可实现材料物理属性与几何结构的全局变化。可编程物质的核心算法任务是通过规范粒子的局部行为来实现全局形态重构。本文提出一种在\emph{变形虫}模型中实现形态重构的新方法。变形虫模型是一种分布式模型，其显著限制了单个粒子的存储、计算与通信能力，因此算法挑战在于协调粒子行动以产生全局系统的预期行为。我们的重构算法是首个在任意形态转换过程中不使用规范中间构型的算法。我们为变形虫模型引入新的几何原语，并证明在最坏情况下，利用这些原语可在线性数量的激活轮次内完成粒子系统重构。在实际应用中，本方法通过分析输入与输出形态的对称差几何特征进行优化：当初始形态与目标形态的对称差较小时，可最大限度减少粒子系统不必要的拆解与重组过程。此外，该重构算法能够使粒子沿问题实例所允许的尽可能多的并行最短路径同步移动。