Trajectory tracking is one of the main control problems in the context of Wheeled Mobile Robots (WMRs). Besides, control of underactuated systems possesses a particular complexity and importance; so it has been focused by many researchers in recent years. In this paper, these two important control subjects are discussed regarding a Tractor-Trailer Wheeled Mobile Robot (TTWMR); which includes a differential drive wheeled mobile robot towing a passive spherical wheeled trailer. The use of spherical wheels instead of standard wheels in trailer makes the robot highly underactuated with severe nonlinearities. Spherical wheels are used for the trailer to increase robots’ maneuverability. In fact, standard wheels create nonholonomic constraints by means of pure rolling and nonslip conditions, and reduce robot maneuverability. In this paper, after introducing the robot, kinematics and kinetics models are obtained, and combined as the dynamics model. Then, based on physical intuition a new controller is developed for the robot, named as Lyapaunov-PID control algorithm. Then, singularity avoidance of the proposed algorithm is discussed and the stability of the algorithm is discussed. Simulation results reveal the suitable performance of the proposed algorithm. Finally, experimental implementation results are presented which verify the simulation results.