A Certified Universal Gathering Algorithm for Oblivious Mobile Robots

Pierre Courtieu (1, 2) , Lionel Rieg (3) , Sébastien Tixeuil (4, 5, 6) , Xavier Urbain (7, 8, 2)

1 GALLIUM - Programming languages, types, compilation and proofs
2 CEDRIC - Centre d'études et de recherche en informatique et communications
3 CdF (institution) - Collège de France
4 NPA - Networks and Performance Analysis
5 LINCS - Laboratory of Information, Network and Communication Sciences
6 IUF - Institut universitaire de France
7 ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise
8 LRI - Laboratoire de Recherche en Informatique

We present a new algorithm for the problem of universal gathering mobile oblivious robots (that is, starting from any initial configuration that is not bivalent, using any number of robots, the robots reach in a finite number of steps the same position, not known beforehand) without relying on a common chirality. We give very strong guaranties on the correctness of our algorithm by proving formally that it is correct, using the COQ proof assistant. To our knowledge, this is the first certified positive (and constructive) result in the context of oblivious mobile robots. It demonstrates both the effectiveness of the approach to obtain new algorithms that are truly generic, and its managability since the amount of developped code remains human readable.

Domaines: Calcul parallèle, distribué et partagé [cs.DC]; Géométrie algorithmique [cs.CG]; Algorithme et structure de données [cs.DS]; Systèmes embarqués; Robotique [cs.RO]; Logique en informatique [cs.LO]

Pierre Courtieu, Lionel Rieg, Sébastien Tixeuil, Xavier Urbain. A Certified Universal Gathering Algorithm for Oblivious Mobile Robots. [Research Report] UPMC, Sorbonne Universites CNRS; CNAM, Paris; College de France; Université Paris Sud. 2015. ⟨hal-01159890⟩