Intelligence incorporated in many devices makes it easier to achieve self-balancing and autonomous driving in differential drive robot. Basically, differential drive robotic system describes an unstable, nonlinear system related to an inverted pendulum. The research attempts to harness the parameters obtained from a computer-aided design tool (Solid works) to model the system for complete stability control and dynamic motion of the system within a planned trajectory. A linearized dynamic equation is obtained for the overall system design of a mobile robot, and the linear quadratic regulator concept is adopted to obtain an optimum state feedback gain. The simulation results are obtained on MATLAB software interfaced with an Arduino board with deployable sensor technologies. Scenarios of disturbance would be simulated to ascertain the stability conditions of the system at static position or dynamic position. Signal analysis and computer vision techniques serve as leverage to make the design achievable. Localization and navigation referred to as tracking a planned trajectory or moving through paths filled with obstacles in a given space are also included.