A geometric method of swarm robot formation controls

According to virtual structures andisomorphic mapping descriptions from initial to goal formation of a swarm robot, a geometric control method of part entire-arrangement formation mapping is presented. In an isomorphic mapping set of all possible formation transformations, a mapping with shortest time is selected in order that the arbitrary formation transformation is time optimal. The stability of formation transformation by the proposed method is proved under time optimal conditions. By mapping characteristic analysis and mapping relation selection, when the number of a swarm robot increases, the computation load of formation control geometrical algorithm will be reduced substantially. Therefore, the problem of fault-tolerant can be further analyzed effectively.