Local, Self-organizing Strategies for Robotic Formation Problems

We consider a scenario with a set of autonomous mobile robots having initial positions in the plane. Their goal is to move in such a way that they eventually reach a prescribed formation. Such a formation may be a straight line between two given endpoints (Robot Chain Problem), a circle or any other geometric pattern, or just one point (Gathering Problem). In this survey, we assume that there is no central control that guides the robot’s decisions, thus the robots have to self-organize in order to accomplish global tasks like the above-mentioned formation problems. Moreover, we restrict them to simple local strategies: the robots are limited to ”see” only robots within a bounded viewing range; their decisions where to move next are solely based on the relative positions of robots within this range.

We survey recent results on local strategies for short robot chains and gathering, among them the first that come with upper and lower bounds on the number of rounds needed and the maximum distance traveled. Finally we present a continuous local strategy for short robot chains, and present a bound for the ”price of locality”: for every configuration of initial robot positions, the maximum distance traveled by the robots is at most by a logarithmic (in the number of robots) factor away from the maximum distance of the initial robot positions to the straight line.