The problem of controlling a differential drive mobile robot carrying different objects with different and known mass and inertia is investigated. The design objective is noninteracting control of robot’s velocity and orientation angle, while ensuring stability, asymptotic command following, and model following for all object loads. In order to satisfy this objective, a common dual-layer PI-PID controller is proposed. The inner layer control consists of two PI controllers dedicated to regulating the angular velocities of the active wheels. For the outer layer, a multivariable PID controller is designed based on the inner closed-loop system. The parameters of both control layers are optimized using a metaheuristic algorithm that minimizes specific cost functions, representing the deviation of the linear closed-loop systems (corresponding to different loads) from an ideal model. The effectiveness of the proposed control scheme is demonstrated through simulations of the application of the control scheme to the original nonlinear system models.