Achievable Patterns by an Even Number of Autonomous Mobile Robots

The distributed coordination and control of a set of autonomous, mobile agents/ robots is a widely studied topic in a variety of fields, such as engineering, artificial intelligence, and artificial life. In the majority of the studies, the problem has been approached from an empirical point of view. A different approach to the problem has been introduced in [6], where the authors analyzed the distributed coordination and control of a set of autonomous, mobile robots from a computational point of view. With this purpose, they defined a model where the world was inhabited by a set of totally autonomous, mobile, memoryless entities that were requested to form a generic pattern. From that study, it turned out that whether or not such a task could be accomplished depended on the amount of common knowledge the robots had; in particular, on the direction and orientation of the local coordinate system. Among the issues left open was which kind of patterns a set of such mobile units can form when they are even in number and agree on the orientation and direction of only one axis. This paper answers that question.