Fixed-Time RBFNN-Based Prescribed Performance Control for Robot Manipulators: Achieving Global Convergence and Control Performance Improvement

Abstract

This paper proposes a fixed-time neural network-based prescribed performance control method (FNN-PPCM) for robot manipulators. A fixed-time sliding mode controller (SMC) is designed with its strengths and weaknesses in mind. However, to address the limitations of the controller, the paper suggests alternative approaches for achieving the desired control objective. To maintain stability during a robot’s operation, it is crucial to keep error states within a set range. To form the unconstrained systems corresponding to the robot’s constrained systems, we apply modified prescribed performance functions (PPFs) and transformed errors set. PPFs help regulate steady-state errors within a performance range that has symmetric boundaries around zero, thereby ensuring that the tracking error is zero when the transformed error is zero. Additionally, we use a singularity-free sliding surface designed using transformed errors to determine the fixed-time convergence interval and maximum allowable control errors during steady-state operation. To address lumped uncertainties, we employ a radial basis function neural network (RBFNN) that approximates their value directly. By selecting the transformed errors as the input for the RBFNN, we can minimize these errors while bounding the tracking errors. This results in a more accurate and faster estimation, which is superior to using tracking errors as the input for the RBFNN. The design procedure of our approach is based on fixed-time SMC combined with PPC. The method integrates an RBFNN for precise uncertainty estimation, unconstrained dynamics, and a fixed-time convergence sliding surface based on the transformed error. By using this design, we can achieve fixed-time prescribed performance, effectively address chattering, and only require a partial dynamics model of the robot. We conducted numerical simulations on a 3-DOF robot manipulator to confirm the effectiveness and superiority of the FNN-PPCM.

Keywords

• fixed-time stability
• prescribed performance control
• radial basis function neural network
• robot manipulators