Bridging Algorithm for Hexagonal Self-Reconfigurable Metamorphic Robots

This paper presents a bridging algorithm that deterministically plans the simultaneous, collision-free movement of n hexagonal metamorphic robots (modules) over any contiguous surface in a hexagonal grid, from the source to the goal end of the surface. Our centralized planning stage algorithm identifies narrow passages between cells in the surface where modules will come into contact. We call such nonconcurrently traversable surface segments “narrow pockets”. After identifying these narrow pockets, our algorithm finds the cells that must be filled by modules to block the pockets and marks these cells in the surface map of each module. Our algorithm does not use message passing between the modules at any stage of the traversal. In this paper we show how our algorithm guarantees a successful traversal of any contiguous surface in a hexagonal grid by building temporary module structures consisting of 1 or 2 modules that we call bridges. We also show that our algorithm identifies and correctly classifies all possible narrow pocket formations and their corresponding bridges. The bridging modules use pre-calculated delays, and in some cases changes of direction, to maintain optimal spacing between modules and to avoid collisions and deadlock throughout the traversal. Our current algorithm is an improvement over previous bridging algorithms [1] because the bridge forming modules do not generate additional narrow pockets. We discuss the results of simulating our algorithms using a discrete event simulator.