Brief Announcement: The BG-Simulation for Byzantine Mobile Robots

Abstract

Motivation. Robot networks [4] have recently become a challenging research area for distributed computing researchers. At the core of scientific studies lies the characterization of the minimum robots capabilities that are necessary to achieve a certain kind of tasks, such as the formation of geometric patterns, scattering, gathering, etc. The considered robots are often very weak: They are anonymous, oblivious, disoriented, and most importantly dumb. The last property means that robots cannot communicate explicitly by sending messages to one another. Instead, their communication is indirect (or spatial): a robot ‘writes’ a value to the network by moving toward a certain position, and a robot ‘reads’ the state of the network by observing the positions of other robots in terms of its local coordinate system. The problem we consider in this paper is the gathering of fault-prone robots. Given a set of oblivious robots with arbitrary initial locations and no agreement on a global coordinate system, the gathering problem requires that all correct robots reach and stabilize the same, but unknown beforehand, location. A number of solvability issues about the gathering problem are studied in previous work because of its fundamental importance in both theory and practice. One can easily find an analogy of the gathering problem to the consensus problem, and thus may think that its solvability issue are straightforwardly deduced from the known results about the consensus solvability (e.g., FLP impossibility). However, many differences lies between those two problems and the solvability of the gathering problem is still non-trivial. An important witness encouraging the difference is that the gathering problem can be solved in a certain kind of crash-prone asynchronous robot networks [1, 3], while the consensus cannot be solved under the asynchrony and one crash fault.

This work is supported in part by the DIGITEO project PACTOLE, the ANR projects SHAMAN and R-DISCOVER, KAKENHI no. 22700010 and 21500013, and Foundation for the Fusion of Science and Technology (FOST).