A combined backstepping and fractional-order PID controller to trajectory tracking of mobile robots

Trajectory tracking is a critical problem in the field of mobile robotics. In this paper, a control scheme combined with backstepping and fractional-order PID is developed for the trajectory tracking of the differential-drive mobile robot. The kinematic and dynamic models of the mobile robot are described in detail for the trajectory tracking controller design. Then, based on the model of the mobile robot, the design of the trajectory tracking control system is addressed by combining backstepping with fractional-order PID. Moreover, to obtain an optimal control system, an improved beetle swarm optimization algorithm is presented to tune the parameters of the kinematic and dynamic controllers simultaneously. Finally, several simulations are implemented to the trajectory tracking of mobile robots in the cases with and without skidding and sliding, and the results can confirm the effectiveness and superiority of the combined control scheme. Abbreviations: FOPID: fractional-order PID; FOPD: fractional-order PD; DDMR:differential-drive mobile robot; BAS: beetle antennae search; BA: beetle antennae; PSO:particle swarm optimization; BSO: beetle swarm optimization.