Formation and agreement problems for synchronous mobile robots with limited visibility

We discuss fundamental formation and agreement problems for autonomous, synchronous robots with limited visibility. Each robots is a mobile processor that, at each discrete time instant, observes the relative positions of those robots that are within distance V of itself, computes its new position using the given algorithm, and then moves to that position. The main difference between this work and many of the previous ones is that, here, the visibility of the robots is assumed to be limited to within distance V, for some constant V > 0. The problems we discuss include the formation of a single point by the robots and agreement on a common x-y coordinate system and the initial distribution, and we present algorithms for these problems, except for the problem of agreement on direction (a subproblem of agreement on a coordinate system), which is not solvable even for robots with unlimited visibility. The discussions we present indicate that the correctness proofs of the algorithms for robots with limited visibility can be considerably more complex than those for robots with unlimited visibility.