Fixed-time Trajectory Tracking Control Research Articles

Fixed-time trajectory tracking control of a quadrotor UAV under time-varying wind disturbances: theory and experimental validation

This paper adopts a fixed-time method to study the trajectory tracking issue of a quadrotor unmanned aerial vehicle (UAV) under time-varying wind disturbances. Firstly, in order to address the impact of time-varying wind disturbances on UAV, a fixed-time disturbance observer is constructed to accurately estimate wind disturbances. Secondly, to improve control accuracy and convergence rate, a robust fixed-time controller is designed for the position and attitude system by combining the sliding mode control theory with fixed-time techniques. Furthermore, it is rigorously analyzed that the tracking error of the observer and controller can converge to zero via Lyapunov criterion, and the convergence time is independent of the initial state. Finally, the effectiveness and robustness of the designed control strategy are verified by numerical simulations and actual flight experiments, providing an effective connection between control theory and practical applications.

Distributed Event-Triggered Control for Manipulator with Fixed-Time Disturbance Observer

This article studies an event-triggered fixed-time trajectory tracking control problem of an n-joint manipulator system. Firstly, a fixed-time disturbance observer is proposed to reconstruct the total disturbance composed of external disturbances and model uncertainties, using the estimation as feedforward compensation to enhance the system robustness. Subsequently, based on the backstepping framework, a fixed-time controller with an event-triggering mechanism is designed for the manipulator to ensure the convergence of tracking errors to zero within a fixed time. Additionally, two event-triggering conditions are devised to reduce the transmission time of control input and the computation time of control output. Simultaneously, Zeno behavior is excluded through theoretical proof, validating the fixed-time stability of the closed-loop system. Finally, simulation verification is conducted on a two-joint manipulator, with results confirming the effectiveness of the control strategy.

Disturbance Observer-Based Fixed-Time Tracking Control for a Tilt Trirotor Unmanned Aerial Vehicle

This paper proposed a new fixed-time trajectory tracking control strategy based on the disturbance observer (DOB) for a tilt trirotor unmanned aerial vehicle (TTUAV) which is subject to unknown external disturbances. To facilitate the TTUAV's trajectory tracking controller design, the dynamic model of the TTUAV is divided into two subsystems, the position subsystem (outer-loop) and the attitude subsystem (inner-loop). For the dynamics of the TTUAV's outer-loop, the unknown external disturbances consist of the unknown wind disturbances, the unknown aerodynamic frictions forces, the lateral force generated by the rear servo and the states coupling between the outer-loop and the inner-loop. Then, a nonlinear DOB is designed to estimate the unknown external disturbances, and a nonsingular terminal sliding-mode controller (NTSMC) is further developed to drive the TTUAV's position tracking errors to zero in a fixed time. For the dynamics of the TTUAV's inner-loop, the unknown external disturbances are mainly introduced by the aerodynamic frictions torques. Then, a modified sliding mode controller is designed to reject the unknown external disturbances, and to ensure that the attitude tracking errors converge to zero exponentially. In addition, a composite stability analysis based on Lyapunov stability theory is provided to guarantee the fixed-time convergence of the closed-loop dynamics of the TTUAV. Finally, the results of the real-time experiments are presented to verify the effectiveness of the proposed control strategy.

Fixed-Time Trajectory Tracking Control of Fully Actuated Unmanned Surface Vessels with Error Constraints

This paper proposes a fixed-time prescribed performance control technique to address the challenge of precise trajectory tracking control for unmanned surface vessels (USVs) in the presence of external time-varying disturbances and input saturation. To begin with, a fixed-time disturbance observer is created to handle the time-varying external interference. The observer can accurately estimate and compensate for the disturbance in a fixed time, which effectively improves the robustness of the system. Furthermore, to guarantee both the transient and steady-state response of the system, we employed a specific control technology that ensures the trajectory tracking error remains within a preset bounded range. Then, combined with the fixed-time disturbance observer, the command filter, the prescribed performance control technology, and the fixed-time stability theory, a fixed-time trajectory tracking control law is designed to make the trajectory tracking error of the system converge in a fixed time. Finally, an experiment was designed to validate the suggested control scheme. The results show that under the same conditions, compared with the nonlinear controller and the finite-time controller, the absolute error tracking index of this paper is the lowest, which means that the presented control scheme has higher accuracy.

Reinforcement Learning-Based Fixed-Time Trajectory Tracking Control for Uncertain Robotic Manipulators With Input Saturation.

A fixed-time trajectory tracking control method for uncertain robotic manipulators with input saturation based on reinforcement learning (RL) is studied. The designed RL control algorithm is implemented by a radial basis function (RBF) neural network (NN), in which the actor NN is used to generate the control strategy and the critic NN is used to evaluate the execution cost. A new nonsingular fast terminal sliding mode technique is used to ensure the convergence of tracking error in fixed time, and the upper bound of convergence time is estimated. To solve the saturation problem of an actuator, a nonlinear antiwindup compensator is designed to compensate for the saturation effect of the joint torque actuator in real time. Finally, the stability of the closed-loop system based on the Lyapunov candidate is analyzed, and the timing convergence of the closed-loop system is proven. Simulation and experimental results show the effectiveness and superiority of the proposed control law.

Robust fixed-time trajectory tracking control of the dynamic positioning ship with actuator saturation

This paper addresses the fixed-time trajectory tracking control and setpoint regulation problems for dynamic positioning (DP) ships subject to unknown time-varying disturbances, system uncertainties, and actuator saturation. To meet the resistance of the low-frequency disturbances and system uncertainties, a continuous fixed-time disturbance observer (FTDO) based on integral sliding mode and fixed-time control is constructed. A nonlinear auxiliary dynamic system is introduced to mitigate the inconsistency between command forces and actual control forces, in which the feedback of the bias Δτ guarantees the input constraints for the design of the proposed controller. The explosion-of-complexity problem inherent in traditional backstepping is addressed based on a nonlinear first-order filter. Furthermore, a robust fixed-time control law with constraints is developed to track the predefined trajectory and the desired setpoint. Theoretical analyses demonstrate the fixed-time stability of the closed-loop system via Lyapunov analysis. Numerical simulation results illustrate the effectiveness and robustness of the proposed control approach.

Fixed-Time Trajectory Tracking Control of Unmanned Surface Vessels with Prescribed Performance Constraints

This study proposes a fixed-time precision tracking control scheme for unmanned surface vessels with complex disturbances and unknown system dynamics. The control scheme is based on a nonsingular fast terminal sliding mode and includes an adaptive fixed-time integral sliding mode lumped disturbance observer to precisely observe and compensate for lumped unknowns. To ensure system performance under both transient and steady-state conditions, a prescribed performance function was utilized to enable the trajectory tracking error to converge to a predetermined range. The proposed control scheme, called prescribed performance fixed-time precision tracking (PPFTPT), was designed to achieve precision tracking of a predetermined trajectory within a fixed time. The stability of the closed-loop system was analyzed using the Lyapunov stability theory. Simulation results using the Cybership II model confirmed the feasibility and superiority of the proposed PPFTPT scheme.

Unknown Input Observer-Based Fixed-Time Trajectory Tracking Control for QUAV with Actuator Saturation and Faults

The trajectory tracking control problem of a quadrotor unmanned aerial vehicle (QUAV) subject to external disturbances, inertia uncertainties, actuator faults, and input saturation is addressed in this paper. In contrast with previous works, input saturation herein refers to rotor speed saturation rather than thrust and torque saturation. First, the control system is decoupled into translational and rotational subsystems. Then, for both subsystems, two novel fixed-time unknown input observers (UIO) based on disturbance filtering are developed to estimate the lumped disturbance rapidly and precisely without awareness of the boundary of disturbances. Furthermore, fixed-time tracking controllers for translational and rotational subsystems are proposed based on the estimation values provided by UIO to stabilize tracking errors into a small region in fixed time regardless of the initial values. The theoretical analysis based on the Lyapunov method is presented to demonstrate the stability. Finally, the simulation results show that the proposed control method is effective. The comparison simulation is carried out to validate superiority of the proposed observer and its advantage can be summed up as: (1) the upper bound of the disturbance or its derivative is not needed; (2) the estimation results are smoother and the observation precision is higher due to the absence of sign function; (3) the mutant disturbance can be also estimated quickly and precisely.

Adaptive Neural Network-Based Fixed-Time Control for Trajectory Tracking of Robotic Systems

This brief investigates the problem of fixed-time trajectory tracking control of uncertain robotic systems. Firstly, an adaptive radial basis function neural network is designed to estimate the model uncertainties and viscous frictions in robotic systems. Secondly, a segmented terminal sliding mode control (TSMC) variable is adopted to alleviate the singularity problem. To improve the tracking performance, a new second-order fixed-time reaching law is designed. Then, in order to make the tracking errors converge to a small neighborhood of the origin in a fixed-time independent of the initial state, a novel fixed-time non-singular TSMC based on the adaptive neural network is proposed. Finally, the experimental results demonstrate the effectiveness and advantage of the proposed control method.

Fuzzy Adaptive Output-Feedback Constrained Trajectory Tracking Control for HFVs With Fixed-Time Convergence

This article proposes an output-feedback fixed-time trajectory tracking control methodology for hypersonic flight vehicles subject to asymmetric output constraints. In contrast to the state of the art, the most distinguishing feature of our control design lies in avoiding using conventional recursive design methods (e.g., backstepping technique, dynamic surface control, etc.) and in not relying on full-state availability. In the velocity control loop, an asymmetric integral barrier Lyapunov function is adopted to confine velocity variable within a well-defined compact set all the time. In the altitude control loop, after utilizing its cascaded property and proposing a novel scaling function, the original constrained system is transformed to an unconstrained one, which facilitates the control design and stability analysis. Moreover, the proposed control algorithm only involves one fuzzy logic approximator as well as one fixed-time differentiator in the transformed system and guarantees that the tracking errors of velocity and altitude converge into the user-defined residual sets within fixed time. Several comparative simulations have been conducted to highlight the superiorities of the developed method.

Robust fixed-time tracking control for underactuated AUVs based on fixed-time disturbance observer

This paper investigates the fixed-time trajectory tracking control problem of underactuated autonomous underwater vehicles (AUVs) subject to external disturbances. The backstepping control technique and fixed-time control method are integrated to guarantee that the trajectory of the AUV converges to the reference trajectory within a fixed-time. A continuous fixed-time disturbance observer is developed to estimate the unknown external disturbances. A nonlinear first-order filter is applied to avoid the adverse effect of “explosion of complexity” inherent in the conventional backstepping. Theoretical analyses demonstrate that under the fixed-time backstepping controller, the tracking errors of the AUV will converge towards a residual set in fixed time. Simulation results illustrate the effectiveness and superiority of the proposed control method.

Adaptive faster fixed-time trajectory tracking control for manipulator

Adaptive faster fixed-time trajectory tracking control for manipulator

Global fixed-time trajectory tracking control of underactuated USV based on fixed-time extended state observer

This paper studies the trajectory tracking problem of unmanned surface vehicle subject to unmeasurable velocities and unknown disturbances. By combining a fixed-time extended state observer (FESO) and a fixed-time differentiator, a fixed-time sliding mode control (FTSMC) law is proposed, in which a saturation function is adopted to make the terminal sliding mode surface leave the singularity area. The value of this paper can be described: first, this paper designs a novel guidance law that can converge in a fixed time to reduce the convergence time of the error. Then, unmeasurable velocities and lumped disturbances are estimated by applying a FESO. Meanwhile, a fixed-time differentiator is used to obtain real-time differential signals, thus reducing the difficulty of controller design. Subsequently, a novel auxiliary dynamic system is designed to address actuator saturation. According to Lyapunov’s theory, the entire closed-loop control system has uniformly global fixed-time stability (UGFTS). The superiority of the designed controller is demonstrated through numerical simulations.

Adaptive Disturbance-Observer-Based Continuous Sliding Mode Control for Small Autonomous Underwater Vehicles in the Trans-Atlantic Geotraverse Hydrothermal Field with Trajectory Modeling Based on the Path

Considering intense hydrothermal activities and rugged topography in a near-bottom environment of the trans-Atlantic geotraverse (TAG) hydrothermal mound, a small autonomous underwater vehicle (S-AUV) will suffer from time-varying disturbances, model uncertainties, actuator faults, and input saturations. To handle these issues, a fault-tolerant adaptive robust sliding mode control method is presented in this paper. Firstly, unknown disturbances, model uncertainties, and actuator faults of the S-AUV are synthesized into a lumped uncertain vector. Without requiring the upper bound and gradient of the uncertainties, a continuous adaptive finite-time extended state observer is designed to estimate the lumped uncertain vector. Then, an auxiliary dynamic system composed of continuous functions is introduced to deal with input saturations, thereby contributing to achieving fixed-time trajectory tracking control of S-AUVs. Based on a designed continuous fixed-time nonsingular fast sliding mode surface, the proposed continuous adaptive controller is chattering free. Simulated topography is built according to topographic data of the TAG mound, and a smooth trajectory model is constructed by cubic spline interpolation. Comprehensive simulations performed on an actual S-AUV model are given to validate the effectiveness and superiority of the presented algorithm.

Disturbance observer-based robust fixed-time integrated trajectory tracking control for space manipulator

AbstractThis article investigates the fixed-time trajectory tracking control of a free-flying rigid space manipulator perturbed by model uncertainties and external disturbances. A novel robust fixed-time integrated controller is developed by integrating a nominal fixed-time proportional–differential-like controller with a fixed-time disturbance observer. It is strictly proved that the proposed controller can ensure the position and velocity tracking errors regulate to zero in fixed time even subject to lumped disturbance. Benefiting from the feedforward compensation, the proposed controller has the strong robustness and excellent disturbance attenuation capability. The effectiveness and advantages of the proposed control approach are validated through simulations and comparisons.

Fixed-time trajectory tracking control for nonholonomic mobile robot based on visual servoing

This paper aims to discuss fixed-time tracking control problem for a nonholonomic wheeled mobile robot based on visual servoing. At first, by making use of the pinhole camera model, the robot system model with uncalibrated camera parameters is given. Then, the tracking error system between the mobile robot and desired trajectory is proposed. Thirdly, on the basis of fixed-time control theory and Lyapunov stability analysis, fixed-time tracking control laws are proposed for the mobile robot such that the robot can track the reference trajectory in a fixed time. It is well known that the convergence time for the finite-time control systems is usually dependent on the initial state of the system. However, the settling time obtained by the fixed-time control is independent of the system initial conditions and only determined by the controller parameters, which is more in line with practical application. Simulation results are given at the end.

Practical fixed-time trajectory tracking control of constrained wheeled mobile robots with kinematic disturbances

This paper addresses the problem of practical fixed-time trajectory tracking for wheeled mobile robots (WMRs) subject to kinematic disturbances and input saturation. Firstly, considering the under-actuated characteristics of the WMR systems, the WMR model under kinematic disturbances is transformed into a two-input two-output interference system by using a set of output equations. Then, the tracking error state equation with lumped disturbances in the acceleration-level pseudo-dynamic control (ALPDC) structure is established. The lumped disturbances are estimated by a designed fixed-time extended state observer (FESO) without requiring the differentiability of the first-time derivatives of the kinematic disturbances. Meanwhile, a practical fixed-time output feedback control law is developed for trajectory tracking. By resorting to the Lyapunov stability theorem, the fixed-time stability analysis of the closed-loop WMR system in the presence of input saturation is conducted. Finally, simulation results are presented to show the effectiveness of the proposed approach.

Neural network-based fixed-time sliding mode control for a class of nonlinear Euler-Lagrange systems

In this paper, the problem of robust fixed-time trajectory tracking control for a class of nonlinear Euler-Lagrange (EL) systems with exogenous disturbances and uncertain dynamics is addressed. A neural network (NN)-based adaptive estimation algorithm is employed to approximate the continuous uncertain dynamics, so that the dynamics of the EL system can be rebuild based on the estimations. In order to guarantee the EL system following the desired trajectory within a fixed-time, an adaptive fixed-time sliding mode control law is proposed to remedy the negative influence of uncertain dynamics and exogenous disturbances. Lyapunov stability theory is utilized to prove the stability and fixed-time convergence of the EL system. The efficiency of the developed NN-based adaptive fixed-time control strategy is substantiated with simulation results.

Extended state observer-based fixed-time trajectory tracking control of autonomous surface vessels with uncertainties and output constraints

A fixed-time trajectory tracking control of autonomous surface vessels (ASVs) subject to unmeasured speed is studied in this work. By using the homogeneity-based Lyapunov method, the unknown system states, including the unmeasured speed and lumped disturbances, are estimated by using a novel extended state observer (ESO) within fixed time. Subsequently, using the estimated states, the task of fixed-time tracking is completed with the aid of a newly proposed output-constrained power integrator method, which makes the vessel position and heading strictly within the predefined output constraints, and the tracking errors can be reduced to a range of zero under the continuous control action. The practical fixed-time stability (FTS) of the closed-loop system is analyzed in the sense of Lyapunov, while the output constraints can be well maintained during maneuvering. Finally, the ascendancy of the designed scheme is exhibited by simulation comparisons.

Robust fixed-time trajectory tracking control of marine surface vessel with feedforward disturbance compensation

This paper proposes a novel robust fixed-time control approach for the trajectory tracking control of a fully actuated marine surface vessel (MSV) subject to system uncertainties and external disturbances. First, a nominal fixed-time controller is originally designed based on the bi-limit homogeneous method. The nominal fixed-time controller can guarantee the position and velocity tracking errors converge to zero in fixed time in the absence of lumped disturbance. Then, a new type of fixed-time disturbance observer is introduced to estimate the lumped disturbance in fixed time. Finally, a robust fixed-time controller is developed by integrating the nominal fixed-time controller with the fixed-time disturbance observer. The robust fixed-time controller can guarantee the position and velocity tracking errors converge to zero in fixed time even in the presence of lumped disturbance. Benefiting from the feedforward disturbance compensation, the robust fixed-time controller has the strong robustness and excellent disturbance attenuation capability. Numerical simulations and comparisons demonstrate the effectiveness and advantages of the proposed control approach.