Observer-based proportional integral derivative control for trajectory tracking of wheeled mobile robots with kinematic disturbances

This manuscript presents a novel observer-based proportional integral derivative (PID) control methodology for trajectory tracking control of wheeled mobile robots (WMR) disturbed by kinematic disturbances. The new proposal employs the kinematic model of the WMR robot together with a reference system to generate a transformed set of two decoupled and disturbed second-order systems. The control design stage consists in dividing the control signal into two parts. The first one uses an observer to compensate for the effect of the kinematic disturbances, which makes all the disturbances affecting the closed-loop system converge to zero uniformly and asymptotically. Then, the second control part consists of a PID controller designed to achieve asymptotic convergence of the tracking error. We provide a synthesis procedure through rigorous Lyapunov-based analysis, demonstrating that the new control scheme achieves the trajectory tracking control objective. Also, we include a set of numerical simulations to assess the performance of the new controller. Here, we compare our novel methodology against a feedback controller and a finite-time controller. The numerical simulations demonstrate that the proposed control scheme achieves the trajectory tracking objective despite kinematic disturbances and outperforms the other control methodologies with the lowest overshoots and tracking errors.