  A novel multi-robot path planning approach is presented in this paper. Based
on the standard Dijkstra, the algorithm looks for the optimal paths for a
formation of robots, taking into account the possibility of split and merge.
The algorithm explores a graph representation of the environment, computing for
each node the cost of moving a number of robots and their corresponding paths.
In every node where the formation can split, all the new possible formation
subdivisions are taken into account accordingly to their individual costs. In
the same way, in every node where the formation can merge, the algorithm
verifies whether the combination is possible and, if possible, computes the new
cost. In order to manage split and merge situations, a set of constraints is
applied. The proposed algorithm is thus deterministic, complete and finds an
optimal solution from a source node to all other nodes in the graph. The
presented solution is general enough to be incorporated into high-level tasks
as well as it can benefit from state-of-the-art formation motion planning
approaches, which can be used for evaluation of edges of an input graph. The
presented experimental results demonstrate the ability of the method to find
the optimal solution for a formation of robots in environments with varying
complexity.
