Fixed-time output feedback trajectory tracking control of marine surface vessels subject to unknown external disturbances and uncertainties

Distributed observer-based prescribed-time affine formation control for underactuated unmanned surface vessels under DoS attack

This study addresses the control challenges of distributed prescribed-time maneuvers for underactuated unmanned surface vessels (USVs) operating in affine formation under adverse conditions, including ocean disturbances, unmodeled dynamics, and denial-of-service (DoS) attacks. The research develops a control scheme that enables USVs to perform complex maneuvers such as translation, shearing, rotation, and scaling, despite intermittent communication failures due to periodic DoS attacks. The approach integrates a distributed prescribed-time observer (DPTO) for each vessel to monitor local time-varying desired states, coupled with an adaptive prescribed-time local tracking control (APTLTC) strategy that drives the USV to track the desired states. The effectiveness and robustness of this control solution are validated through theoretical analysis and simulation, demonstrating significant resilience against network disruptions. This study contributes to safer maritime operations by providing a robust control framework for underactuated USVs under cyber-physical threats.

Barrier lyapunov function-based homogeneous fixed-time controller design for a double integrator system

This study proposes a controller design for the fixed-time stabilisation of a double integrator system (DIS), taking into account both output and state constraints. The controller combines Barrier Lyapunov Function (BLF)-based control method with homogeneous fixed-time controllers to provide faster convergence, eliminate the singularity of BLF-based fixed-time control algorithms, and guarantee precise convergence to the origin while maintaining the constraints. Three different cases including output constraint, output and state constraints, and fixed-time extended-state observer-based control for the disturbed DIS are studied. Several sets of simulations are carried out and comparisons are made with several finite-time and fixed-time controllers. In addition, the proposed control system is applied to the lateral control of an autonomous vehicle. Simulation results outline faster convergence, faster response, less sensitivity to sensor noise, more capability in disturbance rejection, and more accurate positioning compared to previous control systems.

Collision-free automatic berthing of maritime autonomous surface ships via safety-certified active disturbance rejection control

This paper addresses the automatic berthing of a maritime autonomous surface ship operating in a confined water environment subject to static obstacles, dynamic obstacles, thruster constraints, and space constraints due to shorelines. A safety-certified active disturbance rejection control (ADRC) method is proposed for achieving the automatic berthing task of an MASS in the presence of model uncertainties and ocean disturbances. An extended state observer (ESO) based on a second-order robust exact differentiator (RED) is employed to estimate an extended state vector consisting of internal model uncertainties and external ocean disturbances. With the aid of the RED-based ESO, a nominal ADRC law is designed to achieve the position and heading stabilization. To avoid collisions with static obstacles, dynamic obstacles, and shorelines, input-to-state safe high-order control barrier functions are used to guarantee safety. Optimized control signals are obtained based on a constrained quadratic programming (QP) problem within safety constraints. In order to translate the control signals into the individual thruster command, a constrained QP problem is further used to search for optimized commands in real time. It is proven that the closed-loop automatic berthing system is input-to-state stable. By using the proposed method, the MASS is able to reach the desired position and heading with collision avoidance. Simulation results verify the effectiveness of the proposed safety-certified ADRC method for automatic berthing.

Nonsingular fast terminal sliding mode tracking control for underwater glider with actuator physical constraints

An adaptive finite-time composite control (AFTCC) scheme is designed for the pitch angle trajectory tracking control of Underwater Glider (UG) with actuator physical constraints, uncertain dynamics and external disturbances. Firstly, a novel nonsingular fast terminal sliding mode control (NFTSMC) law is designed that can avoid singular problems, significantly reduce chattering, and achieve finite-time convergence of the system states. Secondly, a novel fixed-time extended state observer (FxTESO) is established to estimate the pitch angular velocity and lumped disturbances within a fixed time. Furthermore, a novel adaptive fixed-time saturation compensation system (AFxTSCS) is proposed to mitigate the effect caused by actuator saturation, and it can adjust the parameter adaptively when the actuator is in saturation or out of saturation. Finally, the AFTCC scheme, which is based on the NFTSMC framework and combines FxTESO and AFxTSCS, is designed to achieve the pitch angle trajectory tracking of UG, and the finite-time convergence of the whole closed-loop system is proved by the Lyapunov stability theory, and the simulations verify the availability and superiority of the proposed AFTCC scheme.

Heading and velocity guidance based path following of autonomous surface vehicle with uncertainty attenuation and asymmetric saturated constraints

The path following of underactuated autonomous surface vehicle (ASV) with line-of-sight (LOS)-based heading and velocity guidance is studied thoroughly in the presence of complex uncertainties and asymmetric input saturation that actuators are likely to suffer from. On the basis of the extended-state-observer-based LOS (ELOS) principle and guided velocity design strategies, a finite-time heading and velocity guidance control (HVG) scheme is presented. Firstly, an improved ELOS (IELOS) is developed such that the unknown sideslip angle can be estimated directly, instead of requiring one more step to calculate it by the output of observers and relying on the equivalent assumption between actual heading angle and guidance angle. Secondly, a new form of velocity guidance is designed by considering magnitude and rate constraints and path's curvature, keeping in line with ASV's manoeuvrability and agility. Then asymmetric saturation is considered and studied by designing projection-based finite-time auxiliary systems to avoid parameter drift. All error signals of the closed-loop system of ASV are forced to converge to an arbitrarily small neighbourhood of the origin within a finite settling time by the HVG scheme. The expected performance of the presented strategy is demonstrated via a series of simulations and comparisons. In addition, to show the strong robustness of the presented scheme, stochastic noises modelled by Markov process, bidirectional step signals and faults both multiplication and addition types are considered in simulations.

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.

Fault-tolerant trajectory tracking control for unmanned surface vehicle with actuator faults based on a fast fixed-time system

In this paper, an observer-based fixed-time tracking control strategy is presented for unmanned surface vehicles (USVs) with model uncertainties, external disturbances, and actuator faults. Firstly, as the theory foundation, a fast fixed-time stable system that has a shorter settling time than the existing systems is proposed. According to this system and the motion characteristics of an USV, a fast fixed-time disturbance observer is developed to obtain the unknown effects caused by lumped uncertainties. By combining the estimated knowledge and a nonsingular fast fixed-time terminal sliding surface, a robust fast fixed-time trajectory tracking controller is designed for the USV. According to Lyapunov stability theory, the fast fixed-time convergence of the proposed controller is proved. Finally, the simulation results demonstrate the effectiveness of the developed control scheme.

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.

Data-driven model-free resilient speed control of an autonomous surface vehicle in the presence of actuator anomalies

This paper is concerned with the resilient speed control of an autonomous surface vehicle (ASV) in the presence of actuator anomalies. A data-driven model-free resilient speed control method is presented based on available input and output data only with pulse-width-modulation inputs. Specifically, a data-driven neural predictor is designed to learn the unknown system dynamics of the speed control system of the ASV. Then, a resilient speed control law is designed based on the learned dynamics obtained from the neural network predictor, where a cost function is designed for selecting the optimal duty cycle for the motor. The stability of the data-driven neural predictor is analyzed by using input-state stability (ISS) theory. The advantage of the developed data-driven model-free resilient control method is that the optimal speed control performance can be achieved in the presence of actuator anomalies without any modeling process. Simulation results show the learning ability of the data-driven neural predictor and the effectiveness of the proposed data-driven model-free resilient speed control method for the ASV subject to actuator anomalies.

Robust Fixed-Time H∞ Trajectory Tracking Control for Marine Surface Vessels Based on a Self-Structuring Neural Network

In this study, a robust fixed-time H∞ trajectory tracking controller for marine surface vessels (MSVs) is proposed based on self-structuring neural network (SSNN). First, a fixed-time H_∞ Lyapunov stability theorem is proposed to guarantee that the MSV closed-loop system is fixed-time stable (FTS) and the L₂ gain is less than or equal to γ. This shows high accuracy and strong robustness to the approximation errors. Second, the SSNN is designed to compensate for the model uncertainties of the MSV system, marine environment disturbances, and lumped disturbances term constituted by the actuator faults (AFs). The SSNN can adjust the network structure in real time through elimination rules and split rules. This reduces the computational burden while ensuring the control performance. It is proven by Lyapunov stability that all signals in the MSV system are stable and bounded within a predetermined time. Finally, theoretical analysis and numerical simulation verify the feasibility and effectiveness of the control scheme.

Multiple missiles fixed-time cooperative guidance without measuring radial velocity for maneuvering targets interception

For multiple missile simultaneously intercepting a maneuvering target, under the directed communication topologies between missiles, this paper designs a fixed-time cooperative guidance law based on three-dimensional guidance system. Furthermore, the radial velocity measurements are not required for the designed method. First, we construct the cooperative guidance model by using the three-dimensional missile-target intercepting geometry. Then, based on the fixed-time differentiator and the bi-limit homogeneity theory, a consensus protocol is designed in line-of-sight (LOS) direction, which can ensure missile's impact time achieve fixed-time consensus. Next, in normal direction of LOS, two continuous adaptive fixed-time guidance laws are designed to guarantee LOS angular rates achieve fixed-time convergence. Finally, the excellent performance of the designed method is validated by simulation results.

Adaptive formation control for autonomous surface vessels with prescribed-time convergence

This article is dedicated to solving the problem of predefined-time cooperative control for autonomous surface vessels encountering model uncertainties and external perturbations. By virtue of the prescribed-time stable theory, a robust formation controller is constructed, with which the settling time of the cooperative system can be prescribed in advance. The controller is developed under the backstepping framework, where the dynamic surface control is applied to generate the real-time command. Considering the unmodeled autonomous surface vessel dynamics, the neural network-based nonlinear approximator is incorporated with minimum-learning-parameter technique. Under this scenario, the real-time control can be pursed with one parameter being estimated. Finally, comparative simulation examples are provided to exhibit the effectiveness and advantages of designed control strategies.

Swarm Control for Connectivity-Preserving and Collision-Avoiding Unmanned Surface Vehicles Subject to Multiple Constraints

This paper investigates swarm control for unmanned surface vessels subject to multiple constraints. These constraints can be summarized as model parameter uncertainty, the unavailability of velocity measurements, time-varying environmental disturbances, input saturation and output constraints. Firstly, to recover unmeasured velocity information, to identify unknown vehicle dynamics and to estimate time-varying environmental disturbances, a neural adaptive state observer is designed for each vessel. Secondly, to avoid complex calculations, a second-order linear tracking differentiator is employed to generate a smooth reference signal and to extract the time derivative of the kinematic control law. Thirdly, to solve the input saturation, an auxiliary dynamic system is introduced. Fourthly, the barrier Lyapunov function is used to achieve connectivity preservation, collision avoidance and swarm control. Meanwhile, by using the estimated velocities of vessels, an output feedback controller is designed. The stability of the closed-loop system is proved. The simulation results show the effectiveness of the proposed swarm control strategy.

Line-of-sight-based global finite-time stable path following control of unmanned surface vehicles with actuator saturation

This paper focuses on the path following problem of unmanned surface vehicles (USVs) with unknown velocities, model uncertainties, and actuator saturation. To steer a USV rapidly and accurately follow the desired parameterized path, a line-of-sight (LOS)-based finite-time path following scheme is constructed in which the finite-time technique can ensure the fast error convergence, such that some intelligent operations, including patrolling, fuel supplying, and formation control, can be promptly performed. First, USV kinematic and kinetic models are established, and finite-time observers are subsequently employed to identify the unmeasured USV velocities and model uncertainties. Then, an LOS guidance law is designed to achieve the finite-time convergence of the position errors. In addition, an optimized look-ahead distance is developed using a fuzzy algorithm. Meanwhile, the control subsystem is designed at the kinetic level by combining the backstepping sliding mode method and a novel auxiliary dynamic system, where the auxiliary system is applied to address actuator saturation. Subsequently, theoretical analysis is conducted to verify that the entire system is uniformly global finite-time stable (UGFTS). Finally, the simulation studies confirms the availability of the developed method.

Disturbance Observer-Based Tracking Controller for Uncertain Marine Surface Vessel

In this study, a novel control framework is proposed to improve the tracking performance of uncertain marine vessels which work in enhanced sea states. The proposed control strategy is based on incorporating a fixed-time nonlinear disturbance observer (FTNDO) in a fixed-time convergent backstepping control. More specifically, the FTNDO is developed to reconstruct the total uncertainties due to the system uncertainty and unknown time-varying exterior disturbances. In comparison with the existing disturbance observers, the FTNDO guarantees that the estimation errors will converge to the origin within a predefined time even if the initial estimation errors tend toward infinity. This feature is quite important in the closed-loop system stability analysis as the separation principle does not hold in nonlinear systems. Besides, it does not require the restricting assumption that the upper bound of the lumped uncertainty or its time derivative has to be bounded or known. A backstepping control with a compensation control part is then designed to make the tracking errors converge to the origin within a finite time regardless of initial tracking errors. The compensation control is developed by means of the estimated signal and applied to totally reject the total uncertainty. The global fixed-time stabilization of the closed-loop system is investigated through the Lyapunov stability criterion. Numerical simulation results conducted on an uncertain marine surface vessel confirm the superior control performance and efficiency of the planned method in comparison with the existing disturbance observer-based tracking control strategies.

Fixed-time terminal sliding mode tracking protocol design for high-order multiagent systems with directed communication topology

This paper presents a novel fixed-time consensus tracking protocol for high order multi-agent system (MAS) with directed communication topology. A new distributed observer is proposed such that fixed-time leader's state estimation can be achieved, which overcomes the difficulty arising from asymmetry of communication topology. A series of terminal sliding surfaces are constructed and a singularity-free sliding mode fixed-time tracking protocol is developed. It is proved that the proposed tracking protocol achieves fixed-time consensus tracking. Particularly, we can obtain the controller gain from the pre-specified time, which helps to tune the gain in accordance with consensus time requirement. Moreover, a less conservative convergence time bound estimation is attained. Simulation examples demonstrate the effectiveness of the presented scheme.

Robust Adaptive Self-Structuring Neural Network Bounded Target Tracking Control of Underactuated Surface Vessels

This paper studies the target-tracking problem of underactuated surface vessels with model uncertainties and external unknown disturbances. A composite robust adaptive self-structuring neural-network-bounded controller is proposed to improve system performance and avoid input saturation. An extended state observer is proposed to estimate the uncertain nonlinear term, including the unknown velocity of the tracking target, when only the measurement values of the line-of-sight range and angle can be obtained. An adaptive self-structuring neural network is developed to approximate model uncertainties and external unknown disturbances, which can effectively optimize the structure of the neural network to reduce the computational burden by adjusting the number of neurons online. The input-to-state stability of the total closed-loop system is analyzed by the cascade stability theorem. The simulation results verify the effectiveness of the proposed method.

Adaptive synchronization of marine surface ships using disturbance rejection without leader velocity

This work realizes the adaptive neural disturbance rejection for the leader-follower cooperative synchronization of surface ships with model perturbations and ocean disturbances without leader velocity measurements. The virtual ship alleviates the requirements on leader ship's velocities such that the information requirements are only position and heading on the leader ship. The adaptive neural networks approximate model perturbations. The robustifying term attenuates neural network approximation errors. The adaptive neural network-based disturbance observer achieves the disturbance rejection which is integrated with the dynamic surface control technique. The supply ship synchronization control system is ensured to be practical stable. The synchronization control realizes the ship's cooperative synchronization navigation. Simulations with comparisons validate the synchronization scheme.

Trajectory linearization-based robust course keeping control of unmanned surface vehicle with disturbances and input saturation

This article addresses the problem of course keeping for unmanned surface vehicle (USV) subject to rudder servo characteristics, disturbances, uncertainties and rudder saturation. A double loop robust compound control strategy is developed by incorporating finite-time uncertainty observer (FUO) and auxiliary dynamic system into trajectory linearization control (TLC). TLC is an effective robust control technique with simple design structure, which is used in the course control experiment of USV for the first time. In each loop, the FUO and auxiliary system are designed to compensate unknown lumped disturbances and input saturation, respectively. A nonlinear tracking differentiator (NTD) is concurrently introduced to realize differentiation and filtering for the reference command. Strict stability analysis indicates that the entire system is uniformly ultimately bounded (UUB). Results from simulations and experiments are presented to validate the developed strategy.

A Self-triggered Position Based Visual Servoing Model Predictive Control Scheme for Underwater Robotic Vehicles

An efficient position based visual sevroing control approach for Autonomous Underwater Vehicles (AUVs) by employing Non-linear Model Predictive Control (N-MPC) is designed and presented in this work. In the proposed scheme, a mechanism is incorporated within the vision-based controller that determines when the Visual Tracking Algorithm (VTA) should be activated and new control inputs should be calculated. More specifically, the control loop does not close periodically, i.e., between two consecutive activations (triggering instants), the control inputs calculated by the N-MPC at the previous triggering time instant are applied to the underwater robot in an open-loop mode. This results in a significantly smaller number of requested measurements from the vision tracking algorithm, as well as less frequent computations of the non-linear predictive control law. This results in a reduction in processing time as well as energy consumption and, therefore, increases the accuracy and autonomy of the Autonomous Underwater Vehicle. The latter is of paramount importance for persistent underwater inspection tasks. Moreover, the Field of View constraints (FoV), control input saturation, the kinematic limitations due to the underactuated degree of freedom in sway direction, and the effect of the model uncertainties as well as external disturbances have been considered during the control design. In addition, the stability and convergence of the closed-loop system has been guaranteed analytically. Finally, the efficiency and performance of the proposed vision-based control framework is demonstrated through a comparative real-time experimental study while using a small underwater vehicle.

Underactuated AUV Nonlinear Finite-Time Tracking Control Based on Command Filter and Disturbance Observer

The three-dimensional (3D) path following problem of an underactuated autonomous underwater vehicle with ocean currents disturbances is addressed in this paper. Firstly, the motion equation under the ocean currents disturbance is established, and the dynamic model of 3D tracking error is constructed based on virtual guidance method. Then, a finite-time control scheme based on super-twisting observer and command filtered backstepping technology is proposed. We adopt super-twisting observer based on finite-time theory to observe the ocean currents disturbances for improving the system robust. A command filtered backstepping is proposed to replace the differential process in the conventional backstepping method for avoiding the differential expansion problem. The filter compensation loop is designed to ensure the accuracy of the filtered signal, and the anti-integration saturation link is designed considering the influence of integral saturation. Lyapunov stability theory is used to prove the stability of the underactuated AUV. Simulation studies are conducted to show the effectiveness and robustness of the controller.