Pattern Formation through Optimum Matching by Oblivious CORDA Robots

Abstract

A (new) geometric pattern formation problem by a set of oblivious, anonymous, asynchronous (i.e., CORDA) robots is investigated in this paper. The conventional pattern formation problem assumes that the target pattern is given as a set of the positions by their coordinates in the global coordinate system, under the assumption that the robots are not aware of it. In the pattern formation problem we discuss in this paper, the points comprising the pattern are assumed to be visible to all robots, like landmarks. However, the robots still cannot obtain their positions in the global coordinate system. This paper shows that this pattern formation problem is solvable by oblivious asynchronous robots through the optimum matching between the robots and the pattern's points. Our study is partly motivated by the state-of-arts of the conventional pattern formation problem by oblivious asynchronous robots; description and correctness proof of a formation algorithm is usually complicated and ambiguous, because of the oblivious and asynchronous natures of the robots. A modular method is thus looked for to describe and prove algorithm in a clearer and more concrete way. Our pattern formation problem and the formation algorithm based on the optimum matching are used as a primitive building block in the modular method.