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This study discusses the tracking trajectory issue of the exoskeleton under the bounded disturbance and designs an useful tracking trajectory control method to solve it. By using the proposed control method, the tracking error can be successfully convergence to the assigned boundary. Meanwhile, the chattering effect caused by the actuators is already reduced, and the tracking performance of the pneumatic artificial muscles (PAMs) elbow exoskeleton is improved effectively.

A prescribed performance sliding mode control method was developed in this study to fulfill the joint position tracking trajectory task on the elbow exoskeleton driven by two PAMs. In terms of the control structure, a dynamic model was built by conforming to the adaptive law to compensate for the time variety and uncertainty exhibited by the system. Subsequently, a super-twisting algorithm-based second-order sliding mode control method was subjected to the exoskeleton under the boundedness of external disturbance. Moreover, the prescribed performance control method exhibits a smooth prescribed function with an error transformation function to ensure the tracking error can be finally convergent to the pre-designed requirement.

From the theoretical perspective, the stability of the control method was verified through Lyapunov synthesis. On that basis, the tracking performance of the proposed control method was confirmed through the simulation and the manikin model experiment.

As revealed by the results of this study, the proposed control method sufficiently applies to the PAMs elbow exoskeleton for tracking trajectory, which means it has potential application in the actual robot-assisted passive rehabilitation tasks.

With the increasing demands of industrial applications, it is imperative for robots to accomplish good contact-interaction with dynamic environments. Hence, the purpose of this research is to propose an adaptive fractional-order admittance control scheme to realize a robot–environment contact with high accuracy, small overshoot and fast response.

Fractional calculus is introduced to reconstruct the classical admittance model in this control scheme, which can more accurately describe the complex physical relationship between position and force in the interaction process of the robot–environment. In this control scheme, the pre-PID controller and fuzzy controller are adopted to improve the system force tracking performance in highly dynamic unknown environments, and the fuzzy controller is used to improve the trajectory, transient and steady-state response by adjusting the pre-PID integration gain online. Furthermore, the stability and robustness of this control algorithm are theoretically and experimentally demonstrated.

The excellent force tracking performance of the proposed control algorithm is verified by constructing highly dynamic unstructured environments through simulations and experiments. In simulations and experiments, the proposed control algorithm shows satisfactory force tracking performance with the advantages of fast response speed, little overshoot and strong robustness.

The control scheme is practical and simple in the actual industrial and medical scenarios, which requires accurate force control by the robot.

A new fractional-order admittance controller is proposed and verified by experiments in this research, which achieves excellent force tracking performance in dynamic unknown environments.

An active disturbance rejection controller (ADRC) based on model compensation is proposed in this paper. The method should first be taken a nominal model of the robot to compensate. Subsequently, the uncertain external disturbance is estimated and compensated is used an expansion state observer (ESO) in real time, which can reduce the estimating range of observation for ESO. The purpose of this paper is to suggest a novel method to improve the system tracking performance, as well as the dynamic and static performance index.

A welding robot is a complicated system with uncertainty, time-varying, strong coupling and a nonlinear system; it is more complex as if it is used in an underwater environment, and it is difficult to establish an accurate dynamic model for an underwater welding robot. Aiming at the tracking control of an underwater welding robot, it is difficult to achieve the control performance requirements by the conventional proportional integral derivative method to realize automatic tracking of the seam.

The simulation experiment is carried out by MATLAB/Simulink, and the application experiment is recorded. The experimental results show that the control method is correct and effective, and the system’s tracking performance is stable, and the robustness and tracking accuracy of the system are also improved.

The seam gets plumper and smoother, with better continuity and no undercut phenomenon.

The study aims to equip robots with the ability to precisely maintain interaction forces, which is crucial for tasks such as polishing in highly dynamic environments with unknown and varying stiffness and geometry, including those found in airplane wings or thin, soft materials. The purpose of this study is to develop a novel adaptive force-tracking admittance control scheme aimed at achieving a faster response rate with higher tracking accuracy for robot force control.

In the proposed method, the traditional admittance model is improved by introducing a pre-proportional-derivative controller to accelerate parameter convergence. Subsequently, the authors design an adaptive law based on fuzzy logic systems (FLS) to compensate for uncertainties in the unknown environment. Stability conditions are established for the proposed method through Lyapunov analysis, which ensures the force tracking accuracy and the stability of the coupled system consisting of the robot and the interaction environment. Furthermore, the effectiveness and robustness of the proposed control algorithm are demonstrated by simulation and experiment.

A variety of unstructured simulations and experimental scenarios are designed to validate the effectiveness of the proposed algorithm in force control. The outcomes demonstrate that this control strategy excels in providing fast response, precise tracking accuracy and robust performance.

In real-world applications spanning industrial, service and medical fields where accurate force control by robots is essential, the proposed method stands out as both practical and straightforward, delivering consistently satisfactory performance across various scenarios.

This research introduces a novel adaptive force-tracking admittance controller based on FLS and validated through both simulations and experiments. The proposed controller demonstrates exceptional performance in force control within environments characterized by unknown and varying.

This research aims to present a novel cooperative control architecture designed specifically for roads with variations in height and curvature. The primary objective is to enhance the longitudinal and lateral tracking accuracy of the vehicle.

In addressing the challenges posed by time-varying road information and vehicle dynamics parameters, a combination of model predictive control (MPC) and active disturbance rejection control (ADRC) is employed in this study. A coupled controller based on the authors’ model was developed by utilizing the capabilities of MPC and ADRC. Emphasis is placed on the ramifications of road undulations and changes in curvature concerning control effectiveness. Recognizing these factors as disturbances, measures are taken to offset their influences within the system. Load transfer due to variations in road parameters has been considered and integrated into the design of the authors’ synergistic architecture.

The framework's efficacy is validated through hardware-in-the-loop simulation. Experimental results show that the integrated controller is more robust than conventional MPC and PID controllers. Consequently, the integrated controller improves the vehicle's driving stability and safety.

The proposed coupled control strategy notably enhances vehicle stability and reduces slip concerns. A tailored model is introduced integrating a control strategy based on MPC and ADRC which takes into account vertical and longitudinal force variations and allowing it to effectively cope with complex scenarios and multifaceted constraints problems.

The purpose of this paper is to design a new trajectory error compensation method to improve the trajectory tracking performance and compliance of the knee exoskeleton in human–exoskeleton interaction motion.

A trajectory error compensation method based on admittance-extended Kalman filter (AEKF) error fusion for human–exoskeleton interaction control. The admittance controller is used to calculate the trajectory error adjustment through the feedback human–exoskeleton interaction force, and the actual trajectory error is obtained through the encoder feedback of exoskeleton and the designed trajectory. By using the fusion and prediction characteristics of EKF, the calculated trajectory error adjustment and the actual error are fused to obtain a new trajectory error compensation, which is feedback to the knee exoskeleton controller. This method is designed to be capable of improving the trajectory tracking performance of the knee exoskeleton and enhancing the compliance of knee exoskeleton interaction.

Six volunteers conducted comparative experiments on four different motion frequencies. The experimental results show that this method can effectively improve the trajectory tracking performance and compliance of the knee exoskeleton in human–exoskeleton interaction.

The AEKF method first uses the data fusion idea to fuse the estimated error with measurement errors, obtaining more accurate trajectory error compensation for the knee exoskeleton motion control. This work provides great benefits for the trajectory tracking performance and compliance of lower limb exoskeletons in human–exoskeleton interaction movements.

This paper aims to study a neural network-based fault-tolerant controller to improve the tracking control performance of an unmanned autonomous helicopter with system uncertainty, external disturbances and sensor faults, using the prescribed performance method.

To ensure that the tracking error satisfies the prescribed performance, the authors adopt an error transformation function method. A control scheme based on the neural network and high-order disturbance observer is designed to guarantee the boundedness of the closed-loop system. A simulation is performed to prove the validity of the control scheme.

The developed adaptive fault-tolerant control method makes the system with sensor fault realize tracking control. The error transformation function method can effectively handle the prescribed performance requirements. Sensor fault can be regarded as a type of system uncertainty. The uncertainty can be approximated accurately using neural networks. A high-order disturbance observer can effectively suppress compound disturbances.

The tracking performance requirements of unmanned autonomous helicopter system are considered in the design of sensor fault-tolerant control. The inequality constraint that the output tracking error must satisfy is transformed into an unconstrained problem by introducing an error transformation function. The fault state of the velocity sensor is considered as the system uncertainty, and a neural network is used to approach the total uncertainty. Neural network estimation errors and external disturbances are treated as compound disturbances, and a high-order disturbance observer is constructed to compensate for them.

A distinctive feature of tilt-rotor UAVs is that they can be fully actuated, whereas in fixed-angle rotor UAVs (e.g. common-type quadrotors, octorotors, etc.), the associated dynamic model is characterized by underactuation. Because of the existence of more control inputs, in tilt-rotor UAVs, there is more flexibility in the solution of the associated nonlinear control problem. On the other side, the dynamic model of the tilt-rotor UAVs remains nonlinear and multivariable and this imposes difficulty in the drone's controller design. This paper aims to achieve simultaneously precise tracking of trajectories and minimization of energy dissipation by the UAV's rotors. To this end elaborated control methods have to be developed.

A solution of the nonlinear control problem of tilt-rotor UAVs is attempted using a novel nonlinear optimal control method. This method is characterized by computational simplicity, clear implementation stages and proven global stability properties. At the first stage, approximate linearization is performed on the dynamic model of the tilt-rotor UAV with the use of first-order Taylor series expansion and through the computation of the system's Jacobian matrices. This linearization process is carried out at each sampling instance, around a temporary operating point which is defined by the present value of the tilt-rotor UAV's state vector and by the last sampled value of the control inputs vector. At the second stage, an H-infinity stabilizing controller is designed for the approximately linearized model of the tilt-rotor UAV. To find the feedback gains of the controller, an algebraic Riccati equation is repetitively solved, at each time-step of the control method. Lyapunov stability analysis is used to prove the global stability properties of the control scheme. Moreover, the H-infinity Kalman filter is used as a robust observer so as to enable state estimation-based control. The paper's nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs. Finally, the nonlinear optimal control approach for UAVs with tilting rotors is compared against flatness-based control in successive loops, with the latter method to be also exhibiting satisfactory performance.

So far, nonlinear model predictive control (NMPC) methods have been of questionable performance in treating the nonlinear optimal control problem for tilt-rotor UAVs because NMPC's convergence to optimum depends often on the empirical selection of parameters while also lacking a global stability proof. In the present paper, a novel nonlinear optimal control method is proposed for solving the nonlinear optimal control problem of tilt rotor UAVs. Firstly, by following the assumption of small tilting angles, the state-space model of the UAV is formulated and conditions of differential flatness are given about it. Next, to implement the nonlinear optimal control method, the dynamic model of the tilt-rotor UAV undergoes approximate linearization at each sampling instance around a temporary operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. The linearization process is based on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. The modelling error, which is due to the truncation of higher-order terms from the Taylor series, is considered to be a perturbation that is asymptotically compensated by the robustness of the control scheme. For the linearized model of the UAV, an H-infinity stabilizing feedback controller is designed. To select the feedback gains of the H-infinity controller, an algebraic Riccati equation has to be repetitively solved at each time-step of the control method. The stability properties of the control scheme are analysed with the Lyapunov method.

There are no research limitations in the nonlinear optimal control method for tilt-rotor UAVs. The proposed nonlinear optimal control method achieves fast and accurate tracking of setpoints by all state variables of the tilt-rotor UAV under moderate variations of the control inputs. Compared to past approaches for treating the nonlinear optimal (H-infinity) control problem, the paper's approach is applicable also to dynamical systems which have a non-constant control inputs gain matrix. Furthermore, it uses a new Riccati equation to compute the controller's gains and follows a novel Lyapunov analysis to prove global stability for the control loop.

There are no practical implications in the application of the nonlinear optimal control method for tilt-rotor UAVs. On the contrary, the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state-dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems which can be transformed to the linear parameter varying (LPV) form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions. The stability properties of the Galerkin series expansion-based optimal control approaches are still unproven.

The proposed nonlinear optimal control method is suitable for using in various types of robots, including robotic manipulators and autonomous vehicles. By treating nonlinear control problems for complicated robotic systems, the proposed nonlinear optimal control method can have a positive impact towards economic development. So far the method has been used successfully in (1) industrial robotics: robotic manipulators and networked robotic systems. One can note applications to fully actuated robotic manipulators, redundant manipulators, underactuated manipulators, cranes and load handling systems, time-delayed robotic systems, closed kinematic chain manipulators, flexible-link manipulators and micromanipulators and (2) transportation systems: autonomous vehicles and mobile robots. Besides, one can note applications to two-wheel and unicycle-type vehicles, four-wheel drive vehicles, four-wheel steering vehicles, articulated vehicles, truck and trailer systems, unmanned aerial vehicles, unmanned surface vessels, autonomous underwater vessels and underactuated vessels.

The proposed nonlinear optimal control method is a novel and genuine result and is used for the first time in the dynamic model of tilt-rotor UAVs. The nonlinear optimal control approach exhibits advantages against other control schemes one could have considered for the tilt-rotor UAV dynamics. For instance, (1) compared to the global linearization-based control schemes (such as Lie algebra-based control or flatness-based control), it does not require complicated changes of state variables (diffeomorphisms) and transformation of the system's state-space description. Consequently, it also avoids inverse transformations which may come against singularity problems, (2) compared to NMPC, the proposed nonlinear optimal control method is of proven global stability and the convergence of its iterative search for an optimum does not depend on initialization and controller's parametrization, (3) compared to sliding-mode control and backstepping control the application of the nonlinear optimal control method is not constrained into dynamical systems of a specific state-space form. It is known that unless the controlled system is found in the input–output linearized form, the definition of the associated sliding surfaces is an empirical procedure. Besides, unless the controlled system is found in the backstepping integral (triangular) form, the application of backstepping control is not possible, (4) compared to PID control, the nonlinear optimal control method is of proven global stability and its performance is not dependent on heuristics-based selection of parameters of the controller and (5) compared to multiple-model-based optimal control, the nonlinear optimal control method requires the computation of only one linearization point and the solution of only one Riccati equation.

Quadrotors have been applied in various fields. However, because the quadrotor is subject to multiple disturbances, consisting of external disturbances, actuator faults and parameter uncertainties, it is difficult to control the unmanned aerial vehicle (UAV) to achieve high-precision tracking performance. This paper aims to design a safety controller that uses observer and neural network method to improve the tracking performance of UAV under multiple disturbances. The experiments prove that this method is effective.

First, to actively estimate and compensate the synthetic uncertainties of the system, a finite-time extended state observer is investigated, and the disturbances are transformed into the extended state of the system for estimation. Second, an adaptive neural network controller that does not accurately require the dynamic model knowledge is designed based on the estimated value, where the weights of the neural network can be dynamically adjusted by the adaptive law. Furthermore, the finite-time bounded convergence of the proposed observer and the stability of the system are proved through homogeneous theory and Lyapunov method.

The figure-“8” climbing flight simulation and real flight experiments illustrate that the proposed safety control strategy has good tracking performance.

This paper proposes the safety control structure of the UAV, which combines the extended state observer with the neural network method. Numerical simulation results and actual flight experiments demonstrate the effectiveness of the proposed control strategy.

To improve the position tracking efficiency of the upper-limb rehabilitation robot for stroke hemiplegia patients, the optimization Learning rate of the membership function based on the fuzzy impedance controller of the rehabilitation robot is propose.

First, the impaired limb’s damping and stiffness parameters for evaluating its physical recovery condition are online estimated by using weighted least squares method based on recursive algorithm. Second, the fuzzy impedance control with the rule has been designed with the optimal impedance parameters. Finally, the membership function learning rate online optimization strategy based on Takagi-Sugeno (TS) fuzzy impedance model was proposed to improve the position tracking speed of fuzzy impedance control.

This method provides a solution for improving the membership function learning rate of the fuzzy impedance controller of the upper limb rehabilitation robot. Compared with traditional TS fuzzy impedance controller in position control, the improved TS fuzzy impedance controller has reduced the overshoot stability time by 0.025 s, and the position error caused by simulating the thrust interference of the impaired limb has been reduced by 8.4%. This fact is verified by simulation and test.

The TS fuzzy impedance controller based on membership function online optimization learning strategy can effectively optimize control parameters and improve the position tracking speed of upper limb rehabilitation robots. This controller improves the auxiliary rehabilitation efficiency of the upper limb rehabilitation robot and ensures the stability of auxiliary rehabilitation training.