The sliding mode control approach design for nonholonomic mobile robots based on non‐negative piecewise predefined‐time control law

Abstract

In this paper, a novel trajectory tracking control method of nonholonomic mobile robots based on the non-negative piecewise predefined-time theorem is proposed. The idea of cascade control is used to divide the posture error system of the mobile robot into two subsystems. Firstly, for the first-order subsystem, an active predefined-time controller is designed to realize that the angle error system converges and stabilizes to zero within a given time, which is preset in advance. Secondly, a novel predefined-time sliding mode controller is designed for the second-order subsystem, which adds a constant to compensate for the influence of singularity. Moreover, compared with the existing fixed-time control algorithm, the control scheme proposed in this paper provides a more accurate upper bound of the settling time estimation. For convenience, the complex expression of the settling time estimation is transformed into an adjustable parameter. Furthermore, the stability of the two developed controllers is analyzed and some conditions for selecting parameters are given. Finally, the simulation results show the feasibility and correctness of the proposed control algorithm.