The wheeled mobile robot with differential thrust consists of two independent active wheels and a passive spherical wheel. Assuming its net rolling and non-uncertainty, this robot is a nonlinear system bound to non-holonomic constraints. This system also falls into the category of systems with a lack of operators. Tracing time travel paths is one of the most difficult issues in the field of wheeled robots that we will address in this article. In this regard, first the kinematic model of the system with the presence of uncertainty on the control inputs is expressed in which the linear velocity and angular velocity of the robot are considered system inputs. After determining the desired reference paths, using the linearization of the designed feedback controller ensures the stability of all system state variables globally. The controller is then designed with adaptive rules to solve the problem of tracking time paths based on input-output control in the presence of uncertainties. The stability of this controller is also proven globally. Finally, the performance of the designed controllers to compensate for the uncertainties will be compared by comparing the results.