A Finite-Time Non-Singular Fast Terminal Sliding Mode Control of Wheeled Mobile Robots With Prescribed Performance

Abstract

Wheeled mobile robots (WMRs) have become increasingly vital role in modern industries. This research proposes a novel finite-time prescribed performance sliding mode control (SMC) algorithm for the trajectory tracking of WMRs under effects of wheel slipping, wheel skidding, and external disturbances. The proposed approach consists of two key components. First, a novel sliding surface is proposed based on a prescribed performance function (PPF) and a non-singular fast terminal sliding function (NFTSF), referred to as PP-NFTSF. The proposed PP-NFTSF ensures that tracking errors converge to zero in finite time, while the PPF and a transformed error function ensure stability throughout the robot's operation by maintaining error states within predefined bounds. This framework ensures boundaries around zero, thus guaranteeing that the position tracking error will be zero when the transformed error reaches zero. Second, a novel finite-time non-singular fast terminal SMC (NFTSMC) law with prescribed performance tracking errors, referred to as FPP-NFTSMC, is proposed. This control law incorporates a second-order algorithm to generate a continuous control signal, effectively minimizing the chattering phenomenon of SMC. Overall, the proposed control method maintains all the advantages of PPF, NFTSMC, and the second-order algorithm, achieving high position tracking performance, decreasing the chattering phenomenon, obtaining finite-time convergence, guaranteeing tracking error within the boundary of the PPF, and robustness. To illustrate the stability and finite-time convergence of the WMR systems, a proof using the Lyapunov stability theory is performed. The effectiveness of the proposed control method is validated using two working scenarios: tracking straight and U-shaped trajectories for a 4-WMR.