Molecular Robots with Chirality on Grids

In the theoretical studies on distributed algorithms for swarm robotics, the complexity and capabilities of the robots are usually reduced to their minimum. Recently, the MOBLOT model has been introduced in order to deal with robots considered silent, anonymous, and oblivious but capable to aggregate into more complex structures, called molecules. We study the case where robots move along a regular square grid and we formally define the Molecular Pattern Formation (MPF) problem where a specific configuration of robots assembled into molecules must be reached. As general result, we provide a necessary condition for its solvability. Then, we actually show that dealing with molecules can resolve in some cases the symmetry breaking issue on grids where otherwise robots cannot. Finally, we introduce and resolve an interesting case study, where molecules are given by tetrominos (aka Tetris blocks).