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This paper addresses a phase space partitioning problem in motion planning systems. In a previous study, we developed a kinematic and dynamic motion planning system, known as rapid semi-optimal motion-planning (RASMO), that ensures the optimality of the planned motions with rapid calculations using a partition for the phase space. The shape of the partition determines the optimality of the motion. We propose a state-dispersion-based phase space partitioning (SDPP) method that generates adaptive partitions for RASMO and the same class of motion planning systems. These partitions allow motion planning systems to plan motions with better optimality. To validate SDPP method, we compared the optimality of RASMO in several conditions using a double inverted pendulum model while setting the optimality criterion of RASMO to time. Results show that RASMO with SDPP planned smaller time motions than that obtained RASMO with a uniform partition. Once this method is applied to a machine (e.g. industrial or space robots), the planning system provides better motions with the same calculation cost.