Layering algorithm for collision-free traversal using hexagonal self-reconfigurable metamorphic robots

This paper presents an algorithm that deterministically plans the simultaneous, collision-free movement of n hexagonal metamorphic robots (modules) over any contiguous surface composed of modules in a hexagonal grid. A planning stage algorithm identifies narrow passages between surface cells where moving modules will come into contact. After identifying all narrow passages on a surface, our algorithm identifies the cells that can be used to build temporary structures across the entrance to each narrow passage using 1, 2, or 3 modules. The algorithm does not use intermodule message passing at any stage of the traversal, making it suitable for modules with limited communication capabilities. The algorithm maintains optimal spacing between moving modules throughout the traversal. Our current algorithm is an improvement over previous bridging algorithms because the bridging cells are situated such that when they are filled with modules, they do not form narrow passages (pockets) on the surface. In this paper, we also propose a multi-layered technique for finding longer bridges. We discuss the complexity and performance of our algorithms and give an example of the results of simulating them using a discrete event simulator.