Trajectory tracking is one of the main control problems in the context of Wheeled Mobile Robots (WMRs). Control of underactuated systems has been focused by many researchers during past few years. In this paper, tracking control of a Tractor–Trailer Wheeled Mobile Robot (TTWMR) has been discussed. TTWMR includes a differential drive WMR towing a passive spherical wheeled trailer. Spherical wheels in contrast with standard wheels make the robot highly underactuated with severe non-linearities. Underactuation is due to the use of spherical wheeled trailer to increase robots' maneuverability and degrees of freedom. In fact, standard wheels are subjected to non-holonomic constraints due to pure rolling and non-slip conditions, which reduce robot maneuverability. In this paper, after introducing the robot, kinematics and kinetics models are obtained. Then, based on a physical intuition, a novel control algorithm is developed for the robot, i.e. Lyapunov-PID control algorithm. Subsequently, singularity avoidance of the proposed algorithm is discussed and the stability of the algorithm is analyzed. Finally, simulation and experimental results are presented which reveal the effectiveness of the proposed algorithm.

The inverse problem of the Mei symmetry for nonholonomic systems with variable mass is studied. Firstly, the authors discuss the Mei symmetry of the holonomic system opposite to a nonholonomic system. Secondly, weak and strong Mei symmetries of a nonholonomic system are concluded through restriction equations and additional restriction equations. Thirdly, the relevant conserved quantity is deduced by means of the structure equation for the gauge function. Fourthly, the inverse problem of the Mei symmetry is obtained by the Noether symmetry. Finally, the paper offers an example to illustrate the application of the research result.