Improving the path tracking performance of two-wheel differential mobile robots is very important, especially in problems that consider dynamic nonlinearities and motor torque constraints. This paper proposes a hybrid controller that combines backstepping control (BSC) with fractional order PID controller (FOPID). The parameters of BSC after being proven globally stable by Lyapunov will be determined by the hedge algebra method. The parameters of the FOPID controller are optimized using an improved metaheuristic algorithm, which is a combination of the wolf optimizer (GWO) algorithm with the slime molding algorithm. This is intended to improve trajectory tracking accuracy. In this work, the optimization process for FOPID is based on a cost function consisting of Integral absolute error and integral squared error, which helps to reduce the position and velocity errors. The controller performance is validated through MATLAB-Simulink with various trajectory scenarios and compared with conventional optimization methods such as standard PSO and GWO. Simulation results show superior trajectory tracking, error reduction and improved control performance.
Dinh et al. (Sat,) studied this question.