Adaptive fractional‐order non‐singular fast terminal sliding mode control for robot manipulators

A Global Fast Terminal Sliding Mode Controller (GFTSMC) is proposed for n-link robotic manipulators by employing the Fast Terminal Sliding Mode (FTSM) control concept in both the reaching phase and the sliding phase. Under the control, the system states will reach FTSM in desired finite time and then converge to the origin along the FTSM in specified finite time, resulting in a reduced steady tracking error in comparison with the conventional sliding mode controller. The proposed controller is continuous and therefore chattering-free. An example is presented to demonstrate its effectiveness.

The paper presents a method of synthesizing the Variable Structure Controller (VSC) based on the Fast Terminal Sliding Mode (FTSM) control for an optoelectronic observatory to eliminate the effects of the vibration and the change of vehicle’s direction. An improved fast terminal sliding surface and a fuzzy saturation function have been proposed to develop the improved fast terminal sliding mode variable structure controller (IFTSM-VSC). Based on the theory of Lyapunov stability, the article has proved that the IFTSM-VSC controller ensures the Line of Sight (LOS) stabilization of the observation devices and ensures the tracking errors converge to zero in finite time. The simulation uses data about the vibration and navigation of the vehicle recorded on some streets and roads. Simulation results in Matlab/Simulink show the effectiveness of the IFTSM-VSC controller.

This article proposed a variable gain fast terminal sliding mode controller with an estimator of the uncertainty model for a piezo positioning stage system. The designed terminal sliding mode control has some advantages over the linear sliding mode control such as fast convergence and chattering reduction while maintains its robustness to the uncertainties. Next, an indirect technique is developed to enable the elimination of the singularity problem corresponding to initial terminal sliding mode control. In addition, a cerebellar model articulation controller is carried out to estimate the nonlinear dynamics of the piezo positioning stage. To deal with unknown bounds of uncertainties and disturbances, the proposed scheme consists of using online tuning control gains that ensure the establishment of a real terminal sliding mode in a finite time. Moreover, a fuzzy logic scheme is presented to smooth out the discontinuity part of the control signal, hence improve the control performance. Stability analysis of closed loop system is provided using the Lyapunov function method. Experiment results are presented to evaluate the effectiveness of the designed control approach.

To eliminate the effect of the uncertain disturbances and improve the control accuracy of spacecraft Attitude Control System, a nonlinear control algorithm named nonsingular terminal sliding-mode feedback controller is proposed in this work, which is mainly made up of nonsingular terminal sliding-mode controller and sliding-mode feedback controller. In the first place, nonsingular terminal sliding-mode controller is designed, which guarantees global asymptotic convergence of the attitude in the presence of the uncertain perturbations from the space. Despite that, it is the influence of the uncertain disturbances that hinder the control accuracy. Then, in order to promote the control accuracy, the sliding-mode feedback controller based on the principle of minimum sliding-mode error is proposed, which is used to compensate the control errors of the nonsingular terminal sliding-mode controller caused by the uncertainties. Hence, the determination principle of the weighting matrix in sliding-mode feedback controller is discussed, and the algorithm structure of the sliding-mode feedback controller is also analyzed, which provides the theoretical basis for the sliding-mode feedback controller. By contrast, an adaptive fuzzy algorithm is designed and introduced into the nonsingular terminal sliding-mode controller to improve the control accuracy, which named the nonsingular terminal fuzzy sliding-mode controller. Last but not the least, several numerical examples are presented to demonstrate the efficacy of the proposed nonsingular terminal sliding-mode feedback controller. Simulation results confirm that the control accuracy of the nonsingular terminal sliding-mode feedback controller is higher than the nonsingular terminal sliding-mode controller and the same as nonsingular terminal fuzzy sliding-mode controller. Not only is the calculation of the nonsingular terminal fuzzy sliding-mode feedback controller smaller than nonsingular terminal fuzzy sliding-mode controller, the adjusted parameters are also fewer than nonsingular terminal fuzzy sliding-mode controller obviously. The numerical results clearly indicate that the proposed nonsingular terminal sliding-mode feedback controller based on the principle of minimum sliding-mode error can compensate control errors accurately and quickly; therefore, it can reduce the effect of the uncertainties from the space indirectly.

In order to solve the attitude synchronization control problem of an on-orbit servicing spacecraft autonomously docking to a tumbling satellite with the unknown bounded disturbances and system uncertainties, a fast terminal sliding mode control law is presented in this paper. The most important contribution of this paper is to design an attitude synchronization control law, which will be realized by the terminal sliding mode control method, for a servicing spacecraft autonomously docking to a freely tumbling satellite in space. First of all, the model of relative attitude dynamics is derived from the attitude dynamics of servicing spacecraft and tumbling satellite. Then, the relative attitude dynamic model is converted to the normal formation to apply the control method of fast terminal sliding mode. Furthermore, a fast terminal sliding mode control law for attitude synchronization is designed based on the normal formation of relative attitude dynamic model. During the design process of the control law, the measurement errors and parameter variations are also considered. Finally, several numerical simulations are conducted to verify the designed attitude synchronization control law, and the results verified the effectiveness of the designed control law. Moreover, it's robustness to the unknown bounded disturbances, system uncertainties and measurement errors has also been demonstrated.

This article proposes an adaptive nonsingular fast terminal sliding mode control scheme with piecewise fast multi-power reaching law for tracking control of underactuated autonomous underwater vehicles under model uncertainties, ocean disturbances, and measurement noise. This control approach enhances the robustness and guarantees faster convergence of state error to zero in finite time while reducing the chattering effect. Utilizing the benefit of adaption law prevents overestimating control parameters, and it eliminates the need for the upper bound value of disturbances. The overall stability of the system is analyzed using the Lyapunov criterion. The results of the proposed approach are compared with adaptive nonsingular terminal sliding mode control and adaptive sliding mode control. The performance of the proposed control approach is evaluated by using the performance indices root mean square error and chattering indicator. The simulation results confirm the efficiency of the proposed approach.

Adaptive nonsingular fast terminal sliding-mode control for the tracking problem of uncertain dynamical systems

This paper investigates the trajectory-tracking problem of an uncertain quadrotor in the presence of complex disturbances. A new fractional-order terminal sliding mode control method (FOTSMC) is designed for a quadrotor attitude, which can increase the control robustness against the external disturbances and modeling uncertainty, and decrease the chattering problem. A new fractional non-integer sliding mode control technique for a quadrotor position is designed to stabilize its state variables and attenuate wind disturbance and the effects of variation in the mass. The stability analysis is studied by the Lyapunov theory. Numerical simulation for complex flight trajectory under disturbances is given to illustrate the validity of the proposed methods.

In this paper, a nonsingular, essentially continuous and finite-time convergent impact angle constrained guidance law for intercepting stationary, constant speed, and maneuvering targets is developed using advanced terminal sliding mode control schemes and extended state observer. In order to achieve the specified intercept angle in finite time without singularity, the nonsingular fast terminal sliding mode control algorithm is employed to construct sliding surface. The fast terminal sliding mode control technique is used to establish the reaching law, so the system trajectory converges quickly from initial state to the switching surface in the whole reaching phase and the proposed guidance law is essentially continuous. Noticing the interception of a maneuvering target, the unknown target acceleration is estimated and compensated using extended state observer. Due to its inherent attribute of singularity-free, continuity, and faster convergence rate, no approximation is necessary in the implementation of the proposed guidance law, so better tracking accuracy of the desired intercept angle in a shorter time with a smoother guidance command can be guaranteed compared with conventional terminal sliding mode guidance law. A large number of numerical simulations are implemented to justify the effectiveness of the proposed guidance law.

This work proposes a non-singular fast terminal sliding mode control (NFTSMC) strategy based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm and a nonlinear disturbance observer (NDO) to address the issues of modeling errors, motion disturbances, and transmission friction in robotic manipulators. Firstly, a novel modular serial 5-DOF robotic manipulator configuration is designed, and its kinematic and dynamic models are established. Secondly, a nonlinear disturbance observer is employed to estimate the total disturbance of the system and apply feedforward compensation. Based on boundary layer technology, an improved NFTSMC method is proposed to accelerate the convergence of tracking errors, reduce chattering, and avoid singularity issues inherent in traditional terminal sliding mode control. The stability of the designed control system is proved using Lyapunov stability theory. Subsequently, a deep reinforcement learning (DRL) agent based on the TD3 algorithm is trained to adaptively adjust the control gains of the non-singular fast terminal sliding mode controller. The dynamic information of the robotic manipulator is used as the input to the TD3 agent, which searches for optimal controller parameters within a continuous action space. A composite reward function is designed to ensure the stable and efficient learning of the TD3 agent. Finally, the motion characteristics of three joints for the designed 5-DOF robotic manipulator are analyzed. The results show that compared to the non-singular fast terminal sliding mode control algorithm based on a nonlinear disturbance observer (NDONFT), the non-singular fast terminal sliding mode control algorithm integrating a nonlinear disturbance observer and the Twin Delayed Deep Deterministic Policy Gradient algorithm (TD3NDONFT) reduces the mean absolute error of position tracking for the three joints by 7.14%, 19.94%, and 6.14%, respectively, and reduces the mean absolute error of velocity tracking by 1.78%, 9.10%, and 2.11%, respectively. These results verify the effectiveness of the proposed algorithm in enhancing the trajectory tracking accuracy of the robotic manipulator under unknown time-varying disturbances and demonstrate its strong robustness against sudden disturbances.

A favorable option to supply unbalanced loads and provide the neutral wire is the four-leg inverter. Controllers with high robustness and dynamic response should be used to adjust the inverter load voltages for unknown, unbalanced, and nonlinear loads. Sliding mode controls (SMCs) have a simple structure, good robustness against model parameter uncertainties, and desirable transient response. However, chattering phenomena, variable switching frequency, and error convergence to the operating point on infinite time are the main weaknesses of the conventional SMC method. In this paper, to restrict the conversion time to a finite and controllable value, terminal sliding mode control (TSMC) and fast terminal sliding mode control (FTSMC) procedures are proposed to regulate the load voltages of the four-leg inverter. In these methods, a continuous control output is suggested to fix the switching frequency and reduce chattering phenomena significantly. Furthermore, the proposed methods are highly robust against model parameter uncertainties. Different simulation and experimental results on a 3-kW test bench under different loading conditions are done to validate the significant performance of the proposed methods.

Safe and efficient autonomous lane changing is a key step of connected automated vehicles (CAVs), which can greatly reduce the traffic accident rate and relieve the traffic pressure. Aiming at the requirements of the smoothness and efficiency of the lane-changing trajectory of CAVs, it is necessary to design the lane changing controller to integrate the sensing, decision-making, and control tasks in the driving process. Firstly, based on the vehicle dynamics model, this paper proposes a vehicle lane-changing control strategy based on NNTSMC method (neural network enhanced non-singular fast terminal sliding mode control). The designed lane-changing controller can well realize the designed path tracking, and both lateral position and yaw angle can well track the expected value. This method enables the vehicle to control the front wheel steering angle intelligently, and the lateral acceleration during steering changes in the small scope, which ensures the steering stability of the vehicle. In this study, an improved adaptive RBF neural network with bounded mapping is designed to estimate the upper bound of the total disturbance of the system, which effectively reduces the chattering phenomenon of the control force. The Lyapunov function constructed in this study proves that the designed controller can ensure the stability of the controlled system. Finally, a comparative experiment is performed by the MATLAB/Simulink-CarSim co-simulation. Compared with SMC and TSMC (non-singular fast terminal sliding mode control), the proposed method has a performance improvement of at least 58.0% and 34.1%, respectively. The effectiveness and superiority of the proposed control method were confirmed by the experiments on the co-simulation platform.

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.

Chapter 9 - Fast terminal sliding mode controller for high speed and complex maneuvering of unmanned aerial vehicles

Under the constraints of uncertain hydrodynamic parameters and external disturbances caused by wind, density, and temperature gradients, a trajectory tracking control issue is studied. To be specific, a finite-time controller is developed by using the non-singular fast terminal sliding mode control technique. The position tracking error tends to zero with faster convergence. Besides, we present a robust differentiator in order to estimate the unknown external disturbances and uncertainties. The boundedness of system states in settling time is discussed. Finally, simulation results show that the proposed control algorithm can achieve better performance in terms of rapid transient response, high steady-state accuracy, and controller quality, as compared with some existing sliding mode control laws.