**Abstract**

The design strategy of an adaptive Proportional-Integral-Derivative (PID)-like fuzzy controller for an anti-slip Quarter-Car robotic system is proposed. The proposed control system is constructed by two loops, an external one for lineal speed control and an internal loop for current control. A motion profile is used to follow a trajectory. The slip is computed, such as the difference between the linear velocity given by an S-curve velocity profile and the longitudinal speed calculated according to the rotational speed of the Quarter-Car tire. This difference is the input of the external control loop. Whether the slip is significant, the slave controller must do that both velocities go at the same speed controlling the current of the direct current (DC) motor. On the other hand, the mathematical model of a tire coupled to the DC-motor model is presented to simulate the system and controller response. To test the robustness of the system, different scenarios are presented where the slip coefficient varies depending on the work surface. Three surfaces were selected to test the performance of the controller, dry, wet, and icy surfaces, while the system had a trajectory.

**Keywords:** fuzzy control, slip-control, traction controller, trajectory planning, quarter-car robot
