In order for a mobile manipulator to be used in areas such as offices and houses, the mobile platform must be small-sized. In the case of a small-sized platform, the mobile manipulator may fall down when moving at high speed, or executing tasks in the presence of disturbances. Therefore, it is necessary to consider both stabilization and manipulation simultaneously while coordinating vehicle motion and manipulator motion. In this paper, we propose a method for coordinating vehicle motion planning considering manipulator task constraints, and manipulator motion planning considering platform stability. Specifically, first, the optimal problem of vehicle motion is formulated, considering vehicle dynamics, manipulator workspace and system stability. Next, the manipulator motion is derived, considering stability compensation and manipulator configuration. Finally, the effectiveness of this method is demonstrated by simulation.