This research work introduces a new approach to control the trajectory tracking of differentially driven mobile robots (DDMR), enabling precise and accurate motion in diverse applications. The proposed control design combines kinematic constraints and linear feedback control to achieve effective trajectory tracking. By considering the inherent holonomic kinematic constraints of the DDMR, the dynamics of the robot are accurately represented. The control problem is formulated as an optimization task to minimize position errors, and a linear feedback control law is devised to regulate the velocity of the robot and steering commands. This control design ensures trajectory tracking while satisfying the kinematic constraints, resulting in improved performance and maneuverability. The effectiveness and robustness of the proposed approach are demonstrated through simulations conducted in a MATLAB environment using a simulated MBOT-type robot. The results show accurate tracking of desired trajectories, with a average maximum mean squared error (MSE) of 1.68x10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup> and an average integral of absolute error (IAE) of 4.25x10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> . Overall, this methodology makes a valuable contribution to the field of DDMR control, opening doors for enhanced trajectory tracking capabilities in real-world applications.