  Gathering is a fundamental coordination problem in cooperative mobile
robotics. In short, given a set of robots with arbitrary initial locations and
no initial agreement on a global coordinate system, gathering requires that all
robots, following their algorithm, reach the exact same but not predetermined
location. Gathering is particularly challenging in networks where robots are
oblivious (i.e., stateless) and direct communication is replaced by
observations on their respective locations. Interestingly any algorithm that
solves gathering with oblivious robots is inherently self-stabilizing if no
specific assumption is made on the initial distribution of the robots. In this
paper, we significantly extend the studies of de-terministic gathering
feasibility under different assumptions This manuscript considerably extends
preliminary results presented as an extended abstract at the DISC 2006
conference [7]. The current version is under review at Distributed Computing
Journal since February 2012 (in a previous form) and since 2014 in the current
form. The most important results have been also presented in MAC 2010 organized
in Ottawa from August 15th to 17th 2010 related to synchrony and faults (crash
and Byzantine). Unlike prior work, we consider a larger set of scheduling
strategies, such as bounded schedulers. In addition, we extend our study to the
feasibility of probabilistic self-stabilizing gathering in both fault-free and
fault-prone environments.
