Comparative Study for Path Planning Based on the Decomposition of a Co-Safe LTL Specification

This paper is presenting a comparison between two different methods for decomposing a co-safe LTL global specification that must be accomplished by a team of mobile agents by combining our previous work. Both decomposition algorithms are aiming to break the global mission into independent tasks such that synchronizations between members of the robotic team are not required and the sub-formulas obtained can be accomplished by a single agent. Once the split of the LTL formula is performed, trajectories are projected based on an allocation of tasks to robots, which requires two steps. First time, a cost matrix is computed, followed by the calculation of a binary allocation matrix. The latest will dictate which task, or tasks, will be executed by each mobile robot. The comparison is taking into consideration the variation of the size of the robotic team and the complexity of the global LTL mission, while proposed scenarios and simulations are highlighting the advantages and disadvantages of each decomposition method. The quantitative analysis is involving two criteria: a time related one and a trajectory related one.