We envision a scenario with robots moving on a terrain represented by a plane. A mobile robot, called explorer is connected by a communication chain to a stationary base camp. The chain is expected to pass communication messages between the explorer and the base camp. It is composed of simple, mobile robots, called relays.
We are investigating strategies for organizing and maintaining the chain, so that the number of relays employed is minimized and nevertheless the distance between neighbored relays in the chain remains bounded. We are looking for local and distributed strategies employed by restricted relays that have to base their decision (“Where should I go?”) solely on the relative positions of its neighbors in the chain.
We present the Manhattan–Hopper and the Hopper strategy which improve the performance of all known solutions to this problem significantly. They are the first such strategies that are optimal in this setting, i.e., that allow the explorer to move with constant speed, independent of the length of the chain, and keep this length minimum up to a constant factor.
