Abstract
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).
The work has been supported in part by the Italian National Group for Scientific Computation (GNCS-INdAM).
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Notes
- 1.
Specific conditions that must be verified in order to start a given task.
- 2.
If the robot with minimum view is on a corner, it is assumed to reside on the clockwise side of \( mbr (R)\).
- 3.
I.e., when the molecule’s projection on \(\ell \) is not obstructed by any other molecule.
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Cicerone, S., Di Fonso, A., Di Stefano, G., Navarra, A. (2022). Molecular Robots with Chirality on Grids. In: Erlebach, T., Segal, M. (eds) Algorithmics of Wireless Networks. ALGOSENSORS 2022. Lecture Notes in Computer Science, vol 13707. Springer, Cham. https://doi.org/10.1007/978-3-031-22050-0_4
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