An excretion care support robot, which can reduce the burden of caregivers, has been developed for bedridden persons. Because the excretion care support robot needs to move between its stop position and the caregiving room, which typically requires navigating a narrow and complex route, the robot must precisely follow a predefined path to avoid colliding with obstacles or falling over. However, different floor conditions in different rooms cause a wide range of time-varying friction, which has a serious effect on the motion accuracy of the robot motion system. To address this issue, a digital acceleration controller is designed to enable the excretion care support robot to accurately follow the predefined path. The digital acceleration controller is a special control algorithm that compensates for friction and can be designed without a priori friction information. Simulations and experiments are conducted under different friction conditions and the results demonstrate that this control method can effectively deal with the friction problem. Therefore, the excretion care support robot can safely move to the user's side when needed.