Infinite Grid Exploration by Disoriented Robots

Quentin Bramas (1) , Stéphane Devismes (2) , Pascal Lafourcade (3)

1 ICube - Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie
2 VERIMAG - IMAG - VERIMAG
3 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes

We study the infinite grid exploration (IGE) problem by a swarm of autonomous mobile robots. Those robots are opaque, have limited visibility capabilities, and run using synchronous Look-Compute-Move cycles. They all agree on a common chirality, but have no global compass. Finally, they may use lights of different colors that can be seen by robots in their surroundings, but except from that, robots have neither persistent memories, nor communication mean. We show that using only three fixed colors, six robots, with a visibility range restricted to one, are necessary and sufficient to solve the non-exclusive IGE problem. We show that using modifiable colors with only five states, five such robots, with a visibility range restricted to one, are necessary and sufficient to solve the (exclusive) IGE problem. Assuming a visibility range of two, we also provide an algorithm that solves the IGE problem using only seven identical robots without any light.

Domaines: Algorithme et structure de données [cs.DS]; Système multi-agents [cs.MA]

Quentin Bramas, Stéphane Devismes, Pascal Lafourcade. Infinite Grid Exploration by Disoriented Robots. 8th Edition of the International Conference on NETworked and sYStems, NETYS, 2020, Marrakech, Morocco. ⟨hal-02559612⟩