Adaptive fast terminal sliding mode control of robotic manipulators based on dynamics feedforward

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.

Considering the improvement of transient response when tracking the trajectory of the robotic manipulator, a novel prescribed performance non-singular fast terminal sliding mode (PPNFTSM) controller is designed. The method performs the controller design by introducing performance functions with constraint effects, and, at the same time, transforms the trajectory tracking deviation using the hyperbolic tangent function, and a new error performance index function is designed accordingly to solve the dilemma that the prescribed performance control (PPC) depends on the first constrained value of the system; the error obtained from the transformation is then combined with the non-singular fast terminal sliding mode (NFTSM) for controller design. The proof of the stability is established based on Lyapunov functions. The proposed method does not require an initial tracking condition. This is verified by simulation and ensures that the tracking deviation approaches a delimited region near the equilibrium point with a prescribed transient performance and strong robust performance.

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

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.

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.

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.

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.

Seismic simulators can accurately reproduce multi-dimensional seismic wave motions. However, its control system faces challenges such as strong nonlinearity, intense coupling, and unknown external disturbances, making precise control compensation difficult to achieve. This paper presents a hybrid control strategy based on a nonlinear observer and fixed-time nonsingular fast terminal sliding mode control. First, the dynamics of a 6-UCU Stewart-platform-based parallel seismic simulator are modeled using the virtual work principle. Next, by integrating fixed-time theory with a nonsingular fast terminal sliding mode surface, rapid convergence of the tracking error within a fixed time is ensured, enhancing the system’s real-time performance while effectively avoiding singularities. To further improve the response speed, a double-exponential sliding mode reaching law is employed. A nonlinear observer is utilized for feedforward disturbance compensation and high-frequency chatter suppression. Finally, MATLAB/ADAMS co-simulation and experimental validation demonstrate that the proposed controller outperforms PID and sliding mode controllers (SMC). Results indicate a 78% reduction in oscillation energy density and achieve steady-state accuracy within ±0.02 mm, validating the efficacy of the proposed approach for high-precision seismic simulation.

Diseases such as cerebral palsy can lead to lower limb dysfunction in children. Lower limb rehabilitation exoskeletons have been clinically validated as effective interventions for gait rehabilitation of children. This study proposes a novel lower-limb gait rehabilitation exoskeleton design and its corresponding control method for pediatric applications. A dynamic model was established, and a nonsingular fast terminal sliding mode control (NFTSMC) strategy was developed to achieve precise trajectory tracking. The curve fitting was performed on a publicly available children’s gait dataset to generate reference hip and knee joint trajectories. The Lagrange method was subsequently employed to derive the dynamic model of the lower-limb exoskeleton. Control simulations were conducted using the proposed NFTSMC algorithm. Comparative analysis with traditional sliding mode control (SMC) demonstrated that NFTSMC reduced root mean square error (RMSE) by 75% (hip) and 67.4% (knee), while integral of time-weighted absolute error (ITAE) decreased by 77.3% and 92.3%, respectively. These results confirm that NFTSMC significantly enhances joint trajectory tracking accuracy, system response speed, and tracking precision.

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.

Adaptive disturbance observer-based dual-loop integral-type fast terminal sliding mode control for micro spacecraft and its gimbal tracking device

A novel adaptive non-singular fast terminal sliding mode control (NFTSMC) scheme is developed for a highly nonlinear two-link robotic manipulator (TLRM) system subject to system uncertainties and unknown disturbances. First, to compensate for the system uncertainties, neural network (NN) is employed to approximate the unknown nonlinear dynamic function. Subsequently, to address the challenges of disturbance compensation and unmeasured joint angular velocity, a nonlinear NN-based extended state observer (NN-based ESO) is introduced. The NN-based ESO facilitates accurate disturbance estimation and compensation, while also enabling simultaneous estimation of the joint angular velocity. Through the integration of these techniques, the closed-loop system’s stability is proven using the direct Lyapunov method, demonstrating remarkable tracking performance within finite time. Simulation results validate the effectiveness of the NFTSMC with the NN-based ESO, showcasing superior performance compared to alternative control strategies.

For high‐performance trajectory tracking at the nanometer scales, this paper presents a new fast terminal sliding mode controller, which combines a recursive integer‐order non‐singular high‐order sliding manifold and a fractional‐order fast fixed‐time reaching law to ensure globally fast convergence, and adopts a time‐delay‐estimation (TDE) based disturbance estimator deeming the designed controller robust to parameter uncertainty. Stability of the designed controller is verified through the Lyapunov framework, where the full analyses of convergence region and settling time are also presented. The tracking performance is experimentally verified on a piezo‐stack driven nano‐positioning platform. To showcase the performance improvements, measured closed‐loop performance of the proposed controller is contrasted with those obtained using three benchmark control approaches namely the basic Proportional‐Integral‐Derivative (PID), the popular Positive Position Feedback with Integral action (PPF+I), and the traditional linear sliding mode controller (LSMC).

The paper investigates a modified adaptive super-twisting sliding mode control (ASTSMC) for robotic manipulators with input saturation. To avoid singular perturbation while increasing the convergence rate, a modified sliding mode surface (SMS) is developed in this method. Using the proposed SMS, an ASTSMC is developed for robot manipulators, which not only achieves strong robustness but also ensures finite-time convergence. The boundary of lumped uncertainties cannot be easily obtained. A modified adaptive law is developed such that the boundaries of time-varying disturbance and its derivative are not required. Considering input saturation in practical cases, an ASTSMC with saturation compensation is proposed to reduce the effect of input saturation on tracking performances of robot manipulators. The finite-time convergence of the proposed scheme is analyzed. Through comparative simulations against two other sliding mode control schemes, the proposed method has been validated to possess strong adaptability, effectively adjusting control gains; simultaneously, it demonstrates robustness against disturbances and uncertainties.

This brief is devoted to the predesigned motion trajectory-based finite time dynamic positioning (DP) control for a marine surface vehicle (MSV) with unknown external disturbances. Firstly, a preset motion trajectory is presented through establishing the relationship function among position tracking errors and heading tracking error, facilitating the MSV to arrive in the equilibrium point along the pre-designed trajectory. Furthermore, a novel nonsingular and fast terminal sliding mode control (NTSMC) approach is investigated, which ensures faster convergence rate and better stability performance of the close-loop system than the conventional backstepping control approach. What’s more, by incorporating the adaptive technique with the NTSMC approach, an adaptive nonsingular and fast terminal sliding mode control (ANTSMC) strategy is addressed. Compared to the NTSMC approach, it strengthens robustness to disturbances and guarantees system states to converge to a closer neighborhood of the equilibrium point. Finally, simulation results illustrate the remarkable effectiveness of proposed control schemes.