RBFNN-based nonsingular fast terminal sliding mode control for robotic manipulators including actuator dynamics

For accurate trajectory tracking of robotic manipulators with actuators, a novel nonsingular fast terminal sliding mode control (NFTSMC) strategy based on radial basis function neural network (RBFNN) is put forward and investigated in this paper. Because of the existence of nonsingular fast terminal sliding mode (NFTSM) manifold, the controller possesses high precision and fast convergence. Considering that it is difficult to obtain accurate model parameters owing to modeling errors or external disturbances, RBFNN is used to approximate the nonlinear uncertainties due to its simple structure and great generalization ability. A new adaptive law is designed to adjust RBFNN. In order to compensate the estimation errors and suppress other unstable factors, a robust term is introduced. A new adaptive law is developed to flexibly adjust the robust term. Then, Lyapunov theory is applied to prove the system stability and finite-time convergence. Finally, a small-sized industrial robotic manipulator Epson LS3-401S with its first two joints is taken as the simulation plant, and several simulations between the proposed controller and the other two controllers are performed. External disturbances and other two conditions are considered to simulate the real environment, and the corresponding results verify the effectiveness and superiority of the proposed controller.

This paper presents a novel adaptive fast-terminal neuro-sliding mode control (AFTN-SMC) for a two-link robot manipulator with unknown dynamics and external disturbances. The proposed controller is chattering-free and adaptive to the time-varying system uncertainties. Furthermore, the radial base function neural network (RBFNN) is employed to approximate the unknown state dynamics. The simulations have been completed in MATLAB, which illustrates the successful implementation of the proposed controller. The results showcased the effectiveness of the AFTN-SMC in achieving accurate tracking and stability, even in the presence of uncertainties and parameter variations. The incorporation of the RBFNN in the controller proved to be a valuable tool for approximating the unknown dynamics, enabling accurate estimation and control of the manipulator’s behavior. The research presented in this paper contributes to the advancement in control techniques for robot manipulators in diverse industrial and automation applications.

A manipulator often cannot converge rapidly within finite time and has low tracking accuracy owing to factors such as manipulator model errors and external disturbances. To address these problems, this paper proposes a time-varying non-singular fast terminal sliding mode control scheme based on an improved variable power–power reaching law. First, three radial basis function neural networks (RBFNNs) are employed to approximate the dynamic parameters of the manipulator model and thus realize model-free control. Second, to achieve faster finite-time convergence of the system state, a time-varying non-singular fast terminal sliding-mode (NFTSM) surface is designed according to the system state change. In addition, an improved variable power–power reaching law is adopted to avoid chatter and eliminate approximation errors. Finally, comparative simulation experiments are conducted using a 2-DOF manipulator as the research object. The results show that the proposed control scheme facilitates fast convergence, high-precision trajectory tracking, and effective suppression of system chatter under complex uncertainties, thereby confirming its utility and superiority.

In this paper, a radial basis function (RBF) neural network based sliding mode control is presented. Taking CW equation as dynamics model, the parameter perturbation and external disturbance has been considered. The controller consists of two parts, one is the feed-forward control, and the other is feedback sliding mode control using RBF neural network. Based on Lyapunov stability theory, the adaptive law of neural network has been obtained. Simulation results suggest that the control scheme can initialize the formation and maintain the relative motion according to the desired trajectory. The inherent chattering of sliding mode control has been weaken and the accuracy of trajectory tracking has greatly improved with the use of RBF neural network.

To improve the trajectory tracking accuracy of robotic manipulators, an adaptive fast terminal sliding mode control of the robotic arm based on the dynamics feedforward compensation is proposed. The controller consists of two parts: one is a feedforward compensation controller based on the dynamics model for reducing the upper bound value of the uncertainty term, and the other is an adaptive fast terminal sliding mode controller designed based on the Lyapunov method for eliminating the effect of the upper bound of the uncertainty term on the tracking performance, and also for reducing the chattering. The experimental comparison results show that the root mean square error and maximum error of trajectory tracking of our proposed controller are smaller under the working conditions with and without end-effector loads, which can significantly improve the trajectory tracking accuracy of robotic manipulators.

This paper investigates trajectory tracking control of a dielectric electro-active polymers (DEAP) actuator with hysteresis nonlinearity by using second-order adaptive discrete-time fast terminal sliding mode control (2-ADFTSMC) scheme. Taking into account that the hysteresis behaviour is asymmetric rate-dependent, a Hammerstein model is established to represent the DEAP actuator. Then, based on a novel 2-ADFTSM function and a terminal-sliding-mode-type switching control law, a 2-ADFTSMC scheme is proposed to improve the trajectory tracking performance. Furthermore, the stability of the closed-loop system is proved. Compared with discrete-time sliding mode control (DSMC) and discrete-time fast terminal sliding mode control (DFTSMC) schemes, the proposed control scheme can provide higher tracking accuracy, faster convergence speed, and stronger robustness in presence of model uncertainties and external disturbances. The effectiveness and practicality of the proposed control scheme are validated through the experiments on the DEAP actuator.

This paper develops a novel non-singular terminal sliding mode control scheme for trajectory tracking of robot manipulators in the presence of external disturbances and uncertainties. Firstly, with the introduction of two nonlinear terms, a newly terminal sliding surface is designed. Then utilizing this sliding surface, a novel non-singular terminal sliding mode controller is proposed to eliminate the reaching interval, singularity issue and subsequently with this controller, the finite time error convergence is also assured. In the proposed controller, radial basis function neural network is employed to approximate highly uncertain nonlinear dynamics of robot manipulators using update laws derived with Lyapunov approach. Meanwhile, the effects of approximation errors are attenuated with $$H_\infty $$ performance criterion by introducing a robust term into the controller. As a result of proposed approach, asymptotic convergence of tracking errors is achieved within finite time and the approximation errors are attenuated to desired levels. The numerical simulation result shows the effectiveness of proposed controller for the case of microbot type robot manipulator.

In this paper, radial basis function network (RBFN) with sliding-mode controller (SMC) is designed to the joint position control of two-link robot manipulators for periodic motion and predefined trajectory tracking control. Radial basis function uses curve fitting mode to obtain the nonlinear mapping. The unavoidable learning procedure degrades its transient performance in the existence of disturbance. Sliding-mode control is effective in overcoming uncertainties and has a fast transient response, while the control effort is discontinuous and creates chattering. For this defect, a saturation function is utilized to improve it. The back-propagation (BP) algorithm and Lyapunov stability theorem are used to decide a suitable update law and sliding-mode switch gain, respectively. Thus, the satisfied performance will be obtained, which better than the controller with single RBFN controller, sliding mode controller. The simulated results of a two-link robotic manipulator for the joint frictions, changing link masses and adding external disturbances are provided to show that the effectiveness of the proposed control scheme.

This paper reports our study of an adaptive finite‐time neural network control scheme for redundant parallel manipulators. The proposed controller is based on fully tuned radial basis function neural networks (RBFNs), nonsingular fast terminal sliding mode control (NFTSMC), and nonlinearities in output feedback. RBFNs with a fully online update on the output weights and both the centers and variances of Gaussian functions are used to estimate system uncertainties and disturbances. The proposed approach possesses several advantages over other existing approaches like robustness, rapid response, nonsingularity, higher precision, finite‐time convergence, and better tracking control performance. The stability of the parallel manipulators is ensured by the Lyapunov theory. Finally, simulation results validate the effectiveness of the proposed methodology.

This paper presents a Radial Basis Function neural network based higher-order Sliding Mode Control for robust control of a dynamical system. A conventional sliding mode controller is suffering from a chattering problem, and the Super Twisting Algorithm is a special kind of higher-order Sliding Mode Control that has the capability of minimizing the chattering problem. There are also unknown model parameters and external disturbances that exert a negative influence on the control performance. To address the issues of model uncertainties and chattering, a Radial Basis Function (RBF) neural network based Super Twisting Algorithm is designed. The RBF neural network evaluates the model parameters and uncertainties, while the Super Twisting approach mitigates chattering, hence improving the controller’s overall performance. Lyapunov stability based adaptive laws are derived for online updating of the parameters of the neural network. The proposed control algorithm was tested on a 2-degree-of-freedom serial flexible joint robotic arm to investigate its efficacy. The controller has a lower control chattering amplitude, lower control energy consumption, and a good tracking response, when compared to the RBF based conventional Sliding Mode controller and simple STA controller, as shown by the results.

This paper presents a direct robust adaptive tracking control strategy for the Iongitudinal motion of electric vehicles (EVs) subject to parametric uncertainties, nonlinear dynamics, and external disturbances. The vehicle longitudinal dynamics are formulated as a second-order nonlinear system with unknown nonlinearities. Unlike conventional indirect adaptive approaches that first identify unknown system dynamics, a radial basis function neural network (RBFNN) is employed to directly approximate the ideal feedback control law derived from sliding mode theory and Lyapunov synthesis. A robust adaptive law incorporating -modification is designed for online neural network weight update, enhancing robustness against approximation errors and bounded disturbances without requiring prior knowledge of their bounds. Lyapunov-based stability analysis rigorously demonstrates that all closed-loop signals are uniformly ultimately bounded (UUB), with tracking error converging to a tunable residual set around zero. The controller achieves model-independent operation, requiring no exact knowledge of vehicle nonlinear dynamics. Comprehensive simulations under step commands, and multi-frequency trajectories, together with parametric variations and road grade disturbances, validate the effectiveness of the proposed scheme in achieving accurate velocity tracking and superior robustness compared to conventional PID and sliding mode control. The main source code of this paper, including all simulation scripts and neural network modules, can support information found in S1 Pdf file.

This paper presents a robust proportional derivative adaptive nonsingular finite-time synergetic tracking control (PDAFS) for a parallel Delta robot system. First, a finite-time synergetic controller combined with a proportional derivative (PD) control is constructed based on an object-oriented model to fulfill the robust tracking control of the robot. Then, an adaptive radial basis function approximation neural network (RBF) is designed to compensate for the effects of uncertainty parameters and external disturbances. Second, a second-order sliding mode (SOSM) differentiator is implemented to reduce the chattering noises due to the low-resolution encoders. Third, the stability theorems of the proposed control scheme are provided, where the Lyapunov stability theory is used to prove the theorems. Then, simulations of the helix trajectory tracking and the pick-and-place task are demonstrated on the Delta robot to validate the advantages of the proposed control scheme. Based on the advances, an implementing control system of the proposed controller is performed to improve the Delta robot’s performance in the experiments.

Considering a class of quadrotor with variable mass of load and external disturbance, a novel control strategy based on adaptive non‐singular fast terminal sliding mode control is proposed to control in this article. Like external disturbances, internal disturbance caused by mass change will further affect the stability of the system and reduce the reliability of the system. Firstly, the dynamic modeling of a quadrotor with variable mass is carried out based on Euler Newton formulation. Then, a non‐singular fast terminal sliding mode controller based on adaptive integral backstepping is designed to overcome some external and internal disturbances. Meanwhile, an adaptive mass estimation algorithm is developed for real‐time mass estimation. Finally, through several groups of compared simulation results shows that the proposed method owns superior tracking performance for the quadrotor in both of mass change and external disturbance conditions.

In this paper, two novel adaptive finite-time control schemes are proposed for position tracking of nonlinear teleoperation system, which dynamic uncertainties, actuator saturation, and time-varying communication delays are considered. First, a novel auxiliary variable is designed to provide more stable performance. The radial basis function (RBF) neural network is introduced to estimate dynamic uncertainties. Second, two adaptive finite-time control schemes are investigated. In control scheme I, the RBF neural network and the gain switching strategy are applied to compensate the actuator saturation. In control scheme II, an auxiliary compensation filter and the compensation adaptive update laws, which contain the finite-time structure, are developed for dealing with saturation. Third, the finite-time adaptive controller is designed in each of these two control schemes. Based on the multiple Lyapunov function method, the closed-loop teleoperation system with these two control methods is proved to be bounded and finite-time stability. Finally, the simulation experiments are performed and the comparisons with other control methods are shown. The effectiveness of the proposed control schemes is demonstrated.

This paper proposes a non-singular fast terminal sliding mode control strategy based on the self-organizing radial basis function neural network (RBFNN) approximation for the train key network system to realize the safe and reliable operation of the train. In order to improve the RBFNN approximation performance and speed, an improved multi-strategy particle swarm optimization (IMPSO) algorithm, which utilizes multi-strategy evolution ways with a nonlinear deceasing inertia weight to improve the global optimizing performance of particle swarm, is proposed to optimize the structure and parameters for better mapping the highly nonlinear characteristics of train traction braking. In addition, the IMPSO is also introduced into a non-singular fast terminal sliding mode (NFTSM) controller to obtain the most appropriate tuning parameters of the controller and suppresses the chattering phenomenon from sliding mode controller. The stability characteristic of the system under the proposed NFTSM controller is studied based on the Lyapunov theory. Further combined with effective delay prediction and delay compensation methods, the NFTSM high-precision control of the train key nonlinear network system is implemented. The simulation results show that the proposed method has more efficient and robust tracking performance and real-time performance compared with other control methods, which can provide effective means for realizing the symmetrical bus control by automatic train operation (ATO) at both ends of the train, with the safe operation of the train under every complex motion condition.