In this thesis, a kinematic model for controlling an Omni-directional 3 DOF DDR with an external navigation point is presented. Two different dynamic models for investigating the resulting torque on the three active motors on the robot are also developed and validated. The focus of the thesis is on the design of kinematic and dynamic models in an ideal environment and the kinematic model in a high fidelity environment. The kinematic model uses inverse kinematics to translate the controlling motion reference from the external navigation point to the three active motors on the DDR. The thesis also includes a comparison of the two different dynamic models based on Kane's method and Newton's second law of motion, respectively. The models presented in this thesis could aid autonomous robots with attached payloads such as hospital beds move with the centre of geometry as a focal point and thereby perform movements. The results show that such a kinematic model for controlling the specific robot is shown to be feasible in an ideal environment. However, due to PID controllers for the active wheel motors not being exact enough, the model in the high fidelity environment does not perform correctly in all cases. Furthermore, the dynamic model results provide an understanding of the difference of torque dependant on the distance to the navigation point.