Subdimensional expansion for multirobot path planning

Planning optimal paths for large numbers of robots is computationally expensive. In this paper, we introduce a new framework for multirobot path planning called subdimensional expansion, which initially plans for each robot individually, and then coordinates motion among the robots as needed. More specifically, subdimensional expansion initially creates a one-dimensional search space embedded in the joint configuration space of the multirobot system. When the search space is found to be blocked during planning by a robot–robot collision, the dimensionality of the search space is locally increased to ensure that an alternative path can be found. As a result, robots are only coordinated when necessary, which reduces the computational cost of finding a path. We present the M⁎M⁎ algorithm, an implementation of subdimensional expansion that adapts the A⁎A⁎ planner to perform efficient multirobot planning. M⁎M⁎ is proven to be complete and to find minimal cost paths. Simulation results are presented that show that M⁎M⁎ outperforms existing optimal multirobot path planning algorithms.