In this paper, a control methodology for a mobility assist robot is presented. There are various types of robots that can help persons with disabilities. Among these, mobile robots can help to guide a subject from one place to the other. Broadly, the mobile guidance robots can be classified into active and passive types. From a user’s safety point of view, passive mobility assist robots are more desirable than the active robots. In this paper, a two-wheeled differentially driven mobile robot with a castor wheel is considered the assistive robot. The robot is made to have passive mobility characteristics by a specific choice of control law, which creates damperlike resistive forces on the wheels. The paper describes the dynamic model, the suggested control laws to achieve the passive behavior, and proof of concept experiments on a mobile robot at the University of Delaware. From a starting position, the assistive device guides the user to the goal in two phases. In the first phase, the user is guided to reach a goal position while pushing the robot through a handle attached to it. At the end of this first phase, the robot may not have the desired orientation. In the second phase, it is assumed that the user does not apply any further pushing force while the robot corrects the heading angle. A control algorithm is suggested for each phase. In the second phase, the desired heading angle is achieved at the cost of deviations from the final position. This excursion from the goal position is minimized by the controller. This control scheme is first verified in computer simulation. Then, it is implemented on a laboratory system that simulates a person pushing the robot, and the experimental results are presented.