  The gathering over meeting nodes problem requires the robots to gather at one
of the pre-defined meeting nodes. This paper investigates the problem with
respect to the objective function that minimizes the total number of moves made
by all the robots. In other words, the sum of the distances traveled by all the
robots is minimized while accomplishing the gathering task. The robots are
deployed on the nodes of an anonymous two-dimensional infinite grid which has a
subset of nodes marked as meeting nodes. The robots do not agree on a global
coordinate system and operate under an asynchronous scheduler. A deterministic
distributed algorithm has been proposed to solve the problem for all those
solvable configurations, and the initial configurations for which the problem
is unsolvable have been characterized. The proposed gathering algorithm is
optimal with respect to the total number of moves performed by all the robots
in order to finalize the gathering.
