Home Oxygen Therapy (HOT) patients must take the conveyance cart to carry oxygen equipment when they go out. However the equipment is heavy enough to discourage the patients from going out. Therefore, in this study, we attempt to develop a mobile robotic conveyance cart to support HOT patient's going out by applying Force control and Inverted pendulum control which can also prevent the falling over of the cart. In this paper, we describe the control principle of Force control with Inverted pendulum control by several dynamical simulations, and we also show the effectiveness of our proposed control system by several experiments.