We address in this work problems of path planning for autonomous robots; we extend this topic by introducing a new definition of a robot formation and we give a parallel treatment of planning and navigation problems for robot formations. In our investigations into problems of multi-robot planning and navigation, we apply rough mereological theory of spatial reasoning to problems of formations of many robots in a rigorous way and we address the planning and navigation problems for formations of many robots.
In approaching those problems, we employ rough mereology – a theory for approximate reasoning based on the notion of a part to a degree. Using the primitive predicate of a rough inclusion, we construct counterparts of classical predicates of elementary geometry as introduced by Alfred Tarski, which serve us in building a description of robot environment.
The software system Player/Stage is employed as the environment in which predicates of rough mereological geometry are implemented as SQL functions and as means of simulation and visualization of robot trajectories to chosen goals.