This paper presents an assistive robotic system, for which the user can interact with a mobile robot using a haptic interface, for senior and disabled people. The system consists of a nonholonomic PeopleBot mobile robot and a Phantom Omni haptic interface. Several technical problems related to the system are addressed and solved. Specifically, the backstepping technique is used, and a new tracking algorithm is developed for the robot to follow the user on a 2-D space. An adaptive fuzzy logic-based windowing method is proposed to solve the velocity estimation problem in the controller. A simple haptic rendering algorithm is designed to generate the haptic feedback based on the position error. Experiments show that the user can guide the movement of the robot quite easily and smoothly using the haptic interface.