Several drive mechanisms for different robots are at hand in current days. Bicycle steering, Ackerman steering, differential drive are some principal drive mechanisms that are being deployed in robots these days. The differential drive needs the wheel rotations to be updated very frequently. But it is most commonly deployed on the robots with two wheels and casters, as discussed in this work. It also can be used to have an independent control for each of the wheels with independent control signals. This work deals with the modeling of the differential drive mechanism for a robot with two main drive wheels and two casters, which takes the angular orientation of the steering wheel as input. For simplicity, this work considers that casters have no influence on any aspect of the differential drive. An adaptive model, whose output depends on the real-time input from the gamers steering wheel and produces required output has been formulated. This work differs from the other differential drives in the context that the steering wheel and the robot wheels have no physical connection. The proposed model has been implemented in python and integrated with the Robot Operating System (ROS). The steering wheel, which is used to generate commands using, is attached to the controller at the control station and the ROS_Node thus created is used to read the values from the steering and generate commands for each of the left and right wheels. These commands are transferred to the controller on the mobile platform, which in turn generates control signals for actuators. This work also deals with the deployment of the proposed model using the Universal Robot Description Format (URDF) of the robot in the Gazebo simulation and evaluating it using the Nitho Drive Pro steering wheel. To prove that the differential drive mechanism can be used to control the robot efficiently in any type of terrain, a ROS python node is used to control and maneuver the robot.