Autonomous mobile robots are a major focus of research due to their applicability and interdisciplinarity. Depending on the type of locomotion, the system’s controller needs to handle not only trajectory tracking but also the way the system interacts with the ground. Mobile robots with differential drive wheels, in addition to having high nonlinearity, possess an inherent characteristic due to their geometry: their wheels can only rotate around fixed axes, without steering. As a result, longitudinal and lateral slip is inevitable, especially when the system is in motion under significant dynamic effects. Nonlinear Model Predictive Control (NMPC) is widely used in these cases, as it can handle systems with multiple constraints. This work presents mathematical models of a skid-steer mobile robot, derived from differential drive, including longitudinal slip, to which NMPC is applied for trajectory tracking, achieving trajectories similar to the reference. Given that the processing cost of such controllers can be very high for real-time use, a hierarchical control is developed, optimizing the longitudinal forces between the wheels and the ground to find reference slips for a given trajectory to be followed. Since in a real environment not all states can be measured, the control also needs to estimate the unmeasured states. Moving Horizon State Estimation (MHSE), derived from the fundamentals of NMPC, was used to perform the estimation, as it has the resources to keep the system within the constraints. With MHSE, the system’s slip can be calculated from the estimated states for the trajectories obtained with Model Predictive Control (MPC). Finally, a neural network was trained with the predicted and estimated states using MHSE to replace it so that the entire control could be used in real-time. As a result, computational time was reduced due to the replacement of MHSE.