Parallel parking of a car-like mobile robot based on the P-domain path tracking controllers

This study presents high-precision path tracking controllers to follow a parking path in which change in the movement direction is required along it. Compared with other existing path tracking controllers, the automatic control of the movement direction and the necessity of zero velocity at the switching and end points of the parking manoeuvre are considered in the controller design. To this aim, two time-domain functions are proposed depending on the movement direction. Then, two function-domain tracking controllers based on feedback linearisation control and sliding mode control (SMC) structures are designed. The stability of the tracking controllers is analysed and guaranteed. Unlike the conventional SMC, the control signals of the function-domain SMC are very smooth. Moreover, designing the tracking controller in the function-domain can be a solution to modify the tracking controllers that have problem in the control law for the steering angle at zero speed. In the proposed controllers, the steering angle and the driving velocity are fully controlled by the controllers, and the robot automatically stops at the critical points independent of the position estimation and velocity tracking errors. Simulation results demonstrate the effectiveness of the proposed controllers to steer the robot along the reference path.