This paper presents a novel five degrees of freedom (DOF) two-wheeled robotic machine (TWRM) that delivers solutions for both industrial and service robotic applications by enlarging the vehicle’s workspace and increasing its flexibility. Designing a two-wheeled robot with five degrees of freedom creates a high challenge for the control, therefore the modelling and design of such robot should be precise with a uniform distribution of mass over the robot and the actuators. By employing the Lagrangian modelling approach, the TWRM’s mathematical model is derived and simulated in Matlab/Simulink®. For stabilizing the system’s highly nonlinear model, two control approaches were developed and implemented: proportional-integral-derivative (PID) and fuzzy logic control (FLC) strategies. Considering multiple scenarios with different initial conditions, the proposed control strategies’ performance has been assessed.