Prescribed‐Time Prescribed Performance Leader Follower Formation Control for Wheeled Mobile Robots With Any Bounded Initial Value

ABSTRACT This paper investigates prescribed‐time prescribed performance control with any bounded initial values for wheeled mobile robot formation systems with uncertain dynamic models and visibility constraints. Visual information is provided by the fixed onboard camera. However, due to limitations in picture quality and frame size, there are constraints on both tracking distance and angle. In addition, constraints caused by collisions are also under consideration. Both barrier Lyapunov functions and performance functions are proposed to overcome these constraints. In contrast to existing prescribed performance control (PPC) methods, which necessitate the initial values of the tracking errors to fall within the prescribed performance functions, an error transformation method is introduced to ensure that the tracking errors can converge to the preset boundaries within a predefined time, regardless of the bounded initial values. Then, utilizing the backstepping procedure and neural network (NN) approximation, a practical prescribed‐time controller (PPTC) is formulated to guarantee the formation tracking errors can converge into a small neighborhood of the origin in the prescribed time while meeting the performance constraints. The NN approximation also achieves model uncertainty approximation in robot systems within the prescribed time. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.