Enveloping Multiple Obstacles with Hexagonal Metamorphic Robots

The problem addressed is reconfiguration planning for a metamorphic robotic system composed of any number of hexagonal robots when multiple simple obstacles are embedded in the goal environment. Simple obstacles are defined as obstacles that have even surfaces with no pockets or indentations and that, as a group, form no narrow corridors or isolated areas. We extend our earlier work on filling multiple pockets in an obstacle to the case where the goal may contain several simple obstacles. In this paper, we present algorithms that determine how many obstacles are in the goal by logically grouping the obstacle cells in the goal into distinct connected components, order them lexicographically from north-west to south-east, and then link them by shortest path bridges to form one large obstacle with multiple pockets. We subsequently use techniques presented in our earlier papers to envelop the composite obstacle.