Gathering of Robots on Meeting-Points

We consider the gathering problem of oblivious and asynchronous robots moving in the plane. When n>2 robots are free to gather anywhere in the plane, the problem has been solved in [Cieliebak et al., SIAM J. on Comput., 41(4), 2012]. We propose a new natural and challenging model that requires robots to gather only at some predetermined points in the plane, herein referred to as meeting−points. Robots operate in standard Look-Compute-Move cycles. In one cycle, a robot perceives the robots’ positions and the meeting-points (Look) according to its own coordinate system, decides whether to move toward some direction (Compute), and in the positive case it moves (Move). Cycles are performed asynchronously for each robot. Robots are anonymous and execute the same distributed and deterministic algorithm. In the new proposed model, we fully characterize when gathering can be accomplished. We design an algorithm that solves the problem for all configurations with n>0 robots but those identified as ungatherable.