  In this paper, the parking problem of a swarm of mobile robots has been
studied. The robots are deployed at the nodes of an infinite grid, which has a
subset of prefixed nodes marked as parking nodes. Each parking node p_i has a
capacity of k_i which is given as input and equals the maximum number of robots
a parking node can accommodate. As a solution to the parking problem, robots
need to partition themselves into groups so that each parking node contains a
number of robots that are equal to the capacity of the node in the final
configuration. It is assumed that the number of robots in the initial
configuration represents the sum of the capacities of the parking nodes. The
robots are assumed to be autonomous, anonymous, homogeneous, identical and
oblivious. They operate under an asynchronous scheduler. They neither have any
agreement on the coordinate axes nor do they agree on a common chirality. All
the initial configurations for which the problem is unsolvable have been
identified. A deterministic distributed algorithm has been proposed for the
remaining configurations, ensuring the solvability of the problem.
