This paper introduces a novel approach to motion planning for a rapid mobile manipulator using inverted pendulum models. Our aim was to realize an actual rapid mobile manipulator with high acceleration and speed performance for an object's delivery. In our research, we developed an actual rapid mobile manipulator called KDMR-1. We proposed simple motion planning methods using a single inverted pendulum model (SIPM) and a double inverted pendulum model (DIPM), which are easily adaptable to a real-time system with only a small computational burden. The SIPM was useful for basic movement but did not provide object carrying capability. For that, a DIPM was proposed. In both models, we designed linear quadratic optimal controllers to stabilize the Zero Moment Point (ZMP). Two kinds of ZMP stabilization strategies were proposed, fixed ZMP and relaxed ZMP. Using these strategies, we realized optimal ZMP stabilizations for a real-time rapid mobile manipulator. For decoupled forward and rotational linear DIPM, we designed a centrifugal acceleration compensation model in the manner of feedback linearization. The experimental results showed high acceleration and speed performances during rapid object delivery.