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A design of an optimal backstepping fractional order proportional integral derivative (FOPID) controller for handling the trajectory tracking problem of wheeled mobile robots (WMR) is examined in this study. Tuning parameters is a challenging task, to overcome this issue a hybrid meta-heuristic optimization algorithm has been utilized. This evolutionary technique is known as the hybrid whale grey wolf optimizer (HWGO), which benefits from the performances of the two traditional algorithms, the whale optimizer algorithm (WOA) and the grey wolf optimizer (GWO), to obtain the most suitable solution. The efficiency of the HWGO algorithm is compared against those of the original algorithms WOA, GWO, the particle swarm optimizer (PSO), and the hybrid particle swarm grey wolf optimizer (HPSOGWO). The simulation results in MATLAB–Simulink environment revealed the highest efficiency of the suggested HWGO technique compared to the other methods in terms of settling and rise time, overshoot, as well as steady-state error. Finally, a star trajectory is made to illustrate the capability of the mentioned controller. [ABSTRACT FROM AUTHOR]