Mars robot puzzle (a multiagent approach to the Dijkstra problem)

We continue our study of multiagent algorithms for a problem that we call the Mars Robot Puzzle. This problem could be considered as a special case of a graph-theoretic problem (Discrete Mathematics), as a combinatorial geometry problem (Computer Science), or as a very special case of a path-planning problem (Artificial Intelligence). Our algorithms grew up from a local search (heuristic) solution of the problem suggested by E. W. Dijkstra. In the paper we present a series of new multiagent algorithms solving the problem, prove (manually) their correctness, model check some of these algorithms, and discuss further research topics. All our algorithms are multiagent in contrast to “centralized” graph and combinatorial algoritms; correctness of our algorithms is formally proven, while the testing is used for validation of path-planning algorithms.