This work presents a modeling and control of a mobile differential robot. The main objective was to implement a Proportional Integral controller tuned by the Direct Synthesis method, use a velocity trajectory controller and perform predetermined paths. For this, the coefficients of the motors were determined and validated and it was also made the verification of speeds sensors and electrical sensors of the motors. The secondary objective was to use a controller based on robot dynamics, using the adaptive nonlinear model based on reference velocity equations and the dynamic model based on Newton Euler equations is also presented, but its practical implementation was not feasible with the pole allocation linear controller due to the high voltage values delivered by the controller. To determine the parameters of the dynamic models, system identification tests were performed and then the least squares algorithm was used. Genetic algorithms were used to determine the gains of reference speed controllers and several simulations were performed to understand the robot's behavior during the execution of paths. In this dissertation, tests for monitoring the robot's position and speed in a linear path and in a circle are presented, where there is a comparison between the monitoring of the robot and the LIDAR sensor using a PI controller and a trajectory control.Tests are also presented with dynamic velocity controllers moving in a straight line, an attempt to execute a circular path and the realization of the square path, in addition to the simulations presented. Some aspects that hindered the implementation of the dynamic controller were noted, such as the deviation in linear tracking, noise in the velocities and the large error in the angular velocity tracking. The work presented the initial stages of modeling and implantation of a robotic system in which, for low speed conditions, there is a satisfactory behavior in the execution of the paths. In the tests with dynamic speed controllers, it was evident that noise in the system may have caused the non-desired implementation, in addition to possible physical constructive interference of the robotic system.