Choosing Good Paths for Fast Distributed Recon£guration of Hexagonal Metamorphic Robots

The problem addressed is the distributed recon£guration of a metamorphic robot system composed of any number of two dimensional robots (modules) from speci£c initial to speci£c goal con£gurations. The initial con£guration we consider is a straight chain of modules, while the goal con£guration satis£es a simple admissibility condition. Recon£guration of the modules depends on £nding a contiguous path of cells, called a substrate path, that spans the goal con£guration. Modules £ll in this substrate path and then move along the path to £ll in the remainder of the goal without collision or deadlock. In this paper, we examine the problem of £nding the substrate path most likely to result in fast parallel recon£guration, drawing on results from our previous papers [12, 13, 14]. Admissible goal con£gurations are represented as directed acyclic graphs (DAGs). We present a combination graph traversal-weighting algorithm that traverses all paths in the rooted DAG and use this algorithm to determine the best substrate path. We extend our de£nition of admissible substrate paths to consider admissible obstacle surfaces for recon£guration when obstacles are present in the environment.