This paper introduces a motion planning method for a rapid mobile manipulator using an inverted pendulum model. We design a linear quadratic optimal controller to stabilize ZMP. The two kinds of ZMP stabilization strategies (Reverse action ZMP and Flex ZMP) are proposed. The highly geared manipulator is controlled by a Cartesian computed torque (CCT) control for compliant motion. A rapid mobile manipulator called KDMR-1 has been developed for its application. The high acceleration and speed performances of the proposed methods are shown by a rapid maneuvering experiment.