A novel fixed-time prescribed performance sliding mode control for uncertain wheeled mobile robots

Area of Science:

• Robotics
• Control Systems Engineering
• Applied Mathematics

Background:

• Wheeled mobile robots (WMRs) face challenges in trajectory tracking due to wheel slipping, skidding (WSS), and external disturbances.
• Existing control methods often struggle to guarantee rapid convergence and robustness simultaneously.

Purpose of the Study:

• To develop a novel fixed-time prescribed performance sliding mode control (FPP-NFTSMC) method for WMRs.
• To address trajectory tracking errors caused by WSS and external disturbances.
• To ensure fixed-time convergence of tracking errors within predefined performance bounds.

Main Methods:

• Introduction of a new prescribed performance sliding surface combining a prescribed performance function (PPF) and a non-singular fast terminal sliding function (NFTSF).
• Development of the FPP-NFTSMC algorithm based on the proposed sliding surface.
• Integration of a uniform second-order sliding mode (USOSM) algorithm to mitigate chattering and ensure a continuous control signal.
• Analysis of fixed-time stability using Lyapunov stability theory.

Main Results:

• The proposed FPP-NFTSMC method guarantees tracking errors converge to zero within a fixed time.
• The control strategy ensures that error states remain within predefined performance limits.
• The integrated USOSM algorithm effectively reduces the chattering effect, providing a smoother control signal.
• Simulations demonstrate the method's effectiveness in tracking straight-line and U-shaped trajectories under disturbances.

Conclusions:

• The FPP-NFTSMC method offers a robust solution for high-precision trajectory tracking in WMRs.
• The approach successfully addresses WSS and external disturbances while ensuring fixed-time convergence and bounded errors.
• The combination of PPF, NFTSMC, and USOSM provides superior performance compared to conventional methods.