We consider search in an unknown finite 2D square grid by a metamorphic robotic system consisting of anonymous memory-less modules. Each module autonomously moves while executing a common distributed algorithm and the modules collectively form a robotic system by keeping connectivity. The number of shapes of the metamorphic robotic system grows as the number of modules increases, and a shape of the system serves as its memory and shows its functionality. We present the minimum number of modules for search in a finite 2D square grid. We demonstrate that if the modules agree on the directions, i.e., they are equipped with the global compass, three modules are necessary and sufficient for search from an arbitrary initial shape, otherwise five modules are necessary and sufficient for search from limited initial shapes assuming that all modules share a common handedness.

我们考虑通过由匿名无记忆模块组成的变形机器人系统在未知的有限二维正方形网格中进行搜索。每个模块在执行通用分布式算法的同时自主移动，并且模块通过保持连通性共同形成机器人系统。变形机器人系统的形状数量随着模块数量的增加而增长，系统的形状作为其记忆并显示其功能。我们提出了在有限二维正方形网格中搜索的最小模块数。我们证明，如果模块在方向上一致，即它们配备了全局罗盘，则三个模块对于从任意初始形状进行搜索是必要且充分的，