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.

Trajectory Tracking Control of Mobile Manipulator Based on Improved Sliding Mode Control Algorithm

“…Due to the nonlinear, strongly coupled, and uncertain characteristics of manipulators, the precise control of manipulators has been a challenging and focal point in the field of control [19]. Some recent studies have used the model-based NN-based SMC approach in robot control [20][21][22][23]. Duan et al [24] proposed a neural network terminal SMC method that combines a fast non-singular terminal sliding mode control, radial basis function neural network, and improved sliding mode particle swarm optimization, which effectively improves the trajectory tracking accuracy of the manipulator under the influence of uncertain factors.…”

Non-Fragile Prescribed Performance Control of Robotic System without Function Approximation

“…In order to ensure the ideal transient performance of the control system, several control strategies based on prescribed performance control have been proposed [4][5][6][7][8].…”

“…This approach ensures both transient and steady-state performance of the system. In reference [7], the fixed-time sliding mode control is combined with PPC, and a radial basis neural network is employed to address the lumped uncertainty of the system. A method for controlling the performance of a robot system based on a fixed-time neural network is proposed.…”

Self-Evolving Chebyshev Radial Basis Function Neural Complementary Sliding Mode Control

“…The existing research has proven that the unified model NN based on Chebyshev polynomials not only has function approximation ability but also has a faster learning speed than the traditional feedforward or recursive NNs [31,32]. The parameter learning methods of NNs and gradient descent and genetic algorithms are investigated in [33,34].…”