Certified Universal Gathering in $R^2$ for Oblivious Mobile Robots
Abstract
We present a unified formal framework for expressing mobile robots models, protocols, and proofs, and devise a protocol design/proof methodology dedicated to mobile robots that takes advantage of this formal framework. As a case study, we present the first formally certified protocol for oblivious mobile robots evolving in a twodimensional Euclidean space. In more details, we provide 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 orientation nor chirality. We give very strong guaranties on the correctness of our algorithm by proving formally that it is correct, using the COQ proof assistant. This result demonstrates both the effectiveness of the approach to obtain new algorithms that use as few assumptions as necessary, and its manageability since the amount of developed code remains human readable.
 Publication:

arXiv eprints
 Pub Date:
 February 2016
 arXiv:
 arXiv:1602.08361
 Bibcode:
 2016arXiv160208361C
 Keywords:

 Computer Science  Distributed;
 Parallel;
 and Cluster Computing;
 Computer Science  Data Structures and Algorithms;
 Computer Science  Logic in Computer Science;
 Computer Science  Robotics
 EPrint:
 arXiv admin note: substantial text overlap with arXiv:1506.01603