Aiming at the model uncertainty and the complexity of trajectory tracking control of underactuated unmanned surface vehicles (USVs) in complex marine environments, an underactuated USV trajectory tracking control strategy with signal quantization based on the extended state observers (ESOs) is proposed in this paper. According to the inner and outer loop control strategy, the guidance law is designed in the kinematic subsystem to solve the underactuated problem of the USV. In the kinetic subsystem, the ESOs are utilized to resolve the unknown terms in the system and smooth the quantized state signals. Moreover, the input quantization process is represented through a linear model, while the controller has not acquired any prior parameter knowledge of quantization. A Lyapunov-based stability analysis was conducted to demonstrate the stability of the entire closed-loop system. The effectiveness of the proposed strategy was validated through the simulation.

Ensuring collision-free navigation is essential for the safe operation of multiple autonomous surface vehicles. This paper addresses the problem of safe containment maneuvering of multiple underactuated ASVs in unknown environments. A distributed containment maneuvering controller based on local LiDAR perception is proposed, which allows the ASVs to move into the convex hull formed by multiple virtual leaders following parameterized paths, achieving coordinated formations while maintaining collision-free behavior. First, the containment maneuvering control law is developed based on the information of the neighbor information. Then, by introducing path parameter deviations among multiple virtual leaders, a path parameter update law is designed. Finally, obstacle information is obtained through LiDAR perception, and a Gaussian process is employed to construct a control barrier function-based safety constraint. The designed containment maneuvering control law is optimized via quadratic programming to ensure real-time safety. Lyapunov stability analysis demonstrates that the overall control system is asymptotically stable, ensuring the safety of the system. The simulation results confirm the effectiveness of the proposed approach.

This paper addresses the distributed containment control problem for autonomous surface vehicles (ASVs) with model uncertainties and external environmental disturbances under a structured cost index. A distributed fuzzy optimal control method based on a predictor-actor-critic architecture is proposed to achieve containment tracking control for ASVs. First, a finite-time data-driven fuzzy predictor is developed using integral concurrent learning to estimate the lumped uncertainties. Next, using the predictor and reference trajectories information, a performance index including tracking errors and control inputs is constructed. The corresponding Hamilton-Jacobi-Bellman (HJB) equation is derived to obtain the optimal control solution. Then, critic fuzzy logic systems (FLSs) are developed to approximate the unknown partial derivatives coupled with the control input in the HJB equation. Furthermore, actor FLSs are trained using a gradient descent method to approximate the critic FLSs. Finally, a distributed fuzzy optimal controller is designed based on the actor FLSs. Through Lyapunov stability analysis, it is proven that the closed-loop system is input-to-state practically stable. Simulation results demonstrate that the proposed distributed containment tracking control method is effective for ASVs based on the predictor-actor-critic architecture.

This study investigates the resilient adaptive synchronization control problem of multi-agent systems (MASs) under a probabilistic data-driven algorithm (PDDA). First, to address the vulnerability of communication links, a MAS model incorporating random link failures (RLFs) is established. Second, to reduce redundant inter-agent communication, a PDDA is introduced by embedding random sampling intervals into the triggering mechanism. Then, to achieve resilient adaptive synchronization, sufficient conditions are derived, wherein algebraic Riccati equations and a suitably constructed Lyapunov–Krasovskii functional (LKF) are employed. Finally, simulation studies based on helicopter flight data demonstrate the effectiveness and robustness of the proposed strategy under PDDA and RLFs.

A binocular vision system with Scheimpflug cameras provides an effective solution for the deformation measurement of a metal sheet after bulging experiments with a hemispherical rigid punch. The calibration accuracy of the binocular vision deformation measurement system is crucial. The intrinsic parameter calibration of a Scheimpflug camera should consider its tilted imaging plane. The structural parameters need to be optimized before measurement. The traditional optimization of structural parameters through a nonlinear objective function is not always accurate or efficient. In this paper, we proposed a calibration method for a binocular vision deformation measurement system with Scheimpflug cameras. The intrinsic parameters, including the tilted Scheimpflug angles, are first calibrated. Through the tilted Scheimpflug angles, the image points from the tilted imaging plane can be projected to the ideal imaging plane. Then, the in-plane distance constraints of a planar target are merged with the correspondences of the calibration points to optimize the structural parameters linearly. We designed length and displacement measurement experiments to compare the performance of the proposed method with that of other methods. The average length measurement error of the proposed method is 0.013 mm, and those of other methods range from 0.031 mm to 0.065 mm. The average displacement measurement error of the proposed is 0.027 mm, and those of other methods range from 0.037 mm to 0.064 mm. Furthermore, we measured metal sheets under different deformation states to verify the feasibility of the proposed method. Experimental results demonstrate that the proposed method can effectively improve the calibration accuracy and robustness of the binocular vision deformation measurement system with Scheimpflug cameras, thereby improving the deformation measurement accuracy of metal sheets.

This paper studies the collision-free cluster formation control of autonomous surface vehicles subject to unknown internal uncertainties and unknown external disturbances. A collision-free cluster formation control method is presented based on fuzzy predictor to achieve safe formation tracking control in obstacle environments. Specifically, a fuzzy predictor is designed by using the fuzzy logic system. Then, a collision-free cluster formation controller based on artificial potential functions is proposed, which can autonomously avoid inter-agent collisions and static obstacle. By using the Lyapunov stability analysis, the closed system is input-to-state. Simulation results verify the effectiveness of the proposed method.

This paper addresses the adaptive trajectory tracking control problem for unmanned surface vehicle (USV) operating under challenging conditions, including thruster saturation, unknown dynamics, state constraints, and unavailable velocity measurements. An adaptive quantized feedback control strategy based on a neural network observer is proposed. To address the challenge of limited maritime communication resources, a signal quantization and event-triggered mechanism was introduced. The input quantization process is described by a linear analytical model. A neural network observer is designed to estimate the unavailable velocity states. Neural networks are employed to approximate the unknown system dynamics, and a low-frequency gain learning method is introduced to effectively suppress control signal chattering induced by external disturbances. A dynamic auxiliary system is designed to compensate for the effects of thruster saturation. Furthermore, a constraint-handling mechanism based on a logarithmic barrier function is incorporated to ensure that all state variables remain strictly within the prescribed safe boundaries. Rigorous stability analysis of the resulting closed-loop system is conducted based on Lyapunov stability theory. Comprehensive simulation studies validate the effectiveness of the proposed control strategy.

This article addresses the collision-free cooperative path following (CPF) problem of multiple underactuated unmanned surface vehicles (USVs) in the presence of stationary and dynamic obstacles. The position and velocity of the obstacles are unknown, and only the relative angle and relative distance are measured. A collision-free control method is proposed for achieving collision avoidance and CPF for USVs. Specifically, at the kinematic level, collision-free guidance laws are proposed for CPF based on time-to-collision feedback and fixed-time coordination. Both stationary and dynamic obstacles can be avoided by incorporating time-to-collision feedback into the desired yaw rate. A fixed-time path variable update law is applied to synchronize the path variables in fixed time. At the dynamic level, concurrent learning switching extended state observers are proposed for estimating the model uncertainties including the unknown control input. As a result, the proposed data-driven kinetic controller does not need any parameter information. The hardware-in-loop simulation and experiment results demonstrate the effectiveness of the proposed collision-free CPF controller for USVs.

This article addresses the safety-certified cooperative path following of networked underactuated autonomous surface vehicles (ASVs) with individual interests navigating complex marine environments. Each ASV operates under static/dynamic obstacle constraints, neighboring ASV constraints, and input constraints. A three-layer safety-certified path-following architecture is proposed based on control barrier functions and Nash equilibrium seeking. At the communication layer, a path variable update law based on distributed Nash equilibrium seeking is designed to achieve path variable cooperation. At the nominal layer, a line-of-sight-based principle is employed to design guidance laws for each ASV to achieve path following. At the optimization layer, three heading-constrained control barrier functions are developed for mapping safety constraints to constraints on yaw rates of ASVs, and a quadratic program is constructed to optimize the guidance yaw rate signal. The distinct features of the proposed method are two aspects: each ASV is allowed to consider its individual interest when performing a group task; static/dynamic obstacles and neighboring ASVs can be avoided by changing the yaw rate only. Stability analysis demonstrates that the feedback control system exhibits input-to-state stability. The efficacy of the novel method is validated through both hardware-in-the-loop simulation results and field experiment results.

This paper presents a high-execution efficient anti-disturbance formation scheme with collision-obstacle avoidance for under-actuated ships with signal quantization. The formation scheme is built on an improved artificial potential field method and an event-triggered mechanism for underactuated unmanned surface vehicles (USVs), incorporating signal quantization and actuator fault tolerance simultaneously. Firstly, this scheme introduces an improved artificial potential field repulsive function to achieve collaborative collision avoidance and obstacle avoidance at the dynamic level. Secondly, the strategy uses an extended state observer (ESO) to estimate each USV's quantized state and model uncertainty without needing quantizer parameters. A linear model to describe input quantization with actuator faults is also considered. Subsequently, an event-triggered collision avoidance control strategy is proposed to further reduce the communication burden. The proposed formation control strategy's stability and effectiveness are rigorously proven via input-to-state stability theory and validated through simulations.

This paper studies the trajectory tracking control of second-order uncertain nonlinear systems in the presence of internal uncertainty and external disturbances. Trajectory tracking control method is presented based on integral concurrent learning predictor. Specifically, an integral concurrent learning predictor is designed by using the historical data and real-time data information, which can estimate the unknown system parameters without persistency of excitation. Then, a trajectory tracking controller is developed by combining the estimated information. By using the Lyapunov stability analysis, the closed system is input-to-state stable. Simulation results verify the effectiveness of the proposed method.

This paper addresses the formation reconfiguration problem of multiple unmanned surface vehicles (USVs) subject to static and dynamic obstacles. The locations and shapes of the obstacles are unknown, and only the closest collision points and collision vectors can be locally measured. A safe-critical control method is proposed for achieving collision avoidance and formation reconfiguration for USVs. Specifically, hybrid artificial potential fields are designed based on safe space artificial potential fields and repulsion space artificial potential fields using the collision vectors, and nominal guidance laws are proposed based on the hybrid artificial potential fields to guide each USV toward the target position while avoiding static obstacles. A reciprocal control barrier function is designed based on the closest collision points, and a constrained quadratic programming problem incorporating the reciprocal control barrier function is established to calculate optimal yaw rate guidance signals. The optimal yaw rate guidance signals direct each USV to avoid dynamic obstacles and neighboring USVs. The stability and safety analyses show that USVs can avoid collision and achieve formation reconfiguration. The effectiveness of the proposed control method for safe-critical formation reconfiguration of USVs is validated through both simulation and experiment results.

This paper investigates the design of perimeterdefense guidance laws for a defending autonomous surface vehicle (ASV) under input and collision avoidance constraints. A safety-critical perimeter-defense guidance method based on nonlinear model predictive control is proposed. Using the concept of dual optimization design, the optimal attack strategy of the attacker is first estimated by the defending ASV, utilizing information on the dynamics and intent of the attacking ASV. Subsequently, the predicted strategy is embedded into the cost function of the defending ASV, and constraints related to collision avoidance with static obstacles, as well as upper bounds on surge and angular velocities, are incorporated into the optimization framework. By solving this optimization problem, real-time guidance commands are generated that satisfy all constraints, ensuring effective interception of the attacker while guaranteeing safe navigation and avoiding collisions. Finally, the effectiveness of the proposed safety-critical perimeter-defense guidance method is illustrated by the simulation results.

This paper is concerned with the hunting problem of unmanned surface vehicles (USVs) subject to measurement noise. First, uncertainty-aware Voronoi-partioning among USVs and between USVs and obstacles are generated based on the best linear separator and max-margin hyperplane, respectively. Next, considering the factors of USV size and collision avoidance probability, buffers are introduced to the boundaries of the constructed Voronoi cells. Then, a series of hunting centorid points are generated based a buffered evader-centered uncertainty-Aware Voronoi cells (B-ECUAVCs) strategy including an encircling and a capture phases. Finally, a line-of-sight guidance method is proposed for pursuing USVs to achieve the tracking of hunting centorid points, such that the evading USV can be hunting in an unbounded area.

This paper addresses the parallel cooperative path-following control of multiple underactuated cyber-physical maritime autonomous surface ships (MASSs) with unknown dynamics and modeling errors. The proposed control architecture enables virtual-reality interaction by integrating artificial systems, computational experiments, and parallel execution. First, we develop a high-fidelity artificial system using the proposed deep neural-extended state observer (DN-ESO) with an online dual time-scale deep neural network architecture to replicate and predict the behavior of multiple MASSs under complex ocean conditions. Next, we design a parallel cooperative path following controller that leverages the information obtained from DN-ESO through computational experiments. Finally, we employ the controller to simultaneously drive both the artificial and actual systems during parallel execution. Using cascade theory, we prove that the entire closed-loop system achieves input-to-state stability, ensuring that all signals remain uniformly ultimately bounded. Simulation results demonstrate the reliability and effectiveness of the proposed method.

This paper investigates fault-tolerant course control of the unmanned surface vehicle (USV) in the presence of input and state quantization. In the design of the controller, the failure factor of sensors and actuators is considered for the fault-tolerant system of USV. An extended state observer (ESO) is adopted to estimate the variables and uncertainties of the system, and quantized state variables are reconstructed. In addition, the input quantization process is described linearly, so that the controller does not require any prior knowledge of the quantized parameters. The stability of the controller and the observer are proved by using the Lyapunov stability theory, the entire closed-loop system is ultimately uniformly bounded. During the simulation, the saturation function is used instead of the sign function in the control law to prevent jitter, and the effectiveness of the proposed strategy is verified.

This paper presents a safety-certified target-reaching method for multiple underactuated autonomous surface vehicles (ASVs) operating in environments with both stationary and moving obstacles. Specifically, a nominal guidance law based on the guiding vector fields (GVFs) are employed for target-reaching, while a safety-certified guidance law based on the control barrier functions (CBFs) ensure safety. The CBFs dynamically adjust according to the type of encountered obstacle, selecting the optimal collision avoidance heading. A quadratic programming (QP) problem with guidance signal changes as the objective function and CBFs as constraints is formulated. Collision avoidance is achieved by optimizing both the ASV's velocity and heading rate. This method guarantees that safe distances are maintained between ASVs, neighbors and obstacles while achieving target positions. Numerical simulation results substantiate the effectiveness of the proposed safety-certified control method.

This article focuses on the trajectory tracking control of under-actuated unmanned surface vehicles subject to unknown ocean current and input quantization. Regarding kinematics, we devise an extended-state-observer-based guidance law capable of compensating for ocean currents to track the intended trajectory. Concerning kinetics, we propose an event-triggered adaptive fuzzy quantization control law using a linear analytical model to depict input quantization, eliminating the need for prior quantization parameter information. A notable aspect is the reduction in both execution frequency and magnitude, thereby mitigating communication burdens. The stability of this control strategy is proofed through input-to-state stability analysis. Simulation experiments are conducted to affirm the viability of the event-triggered adaptive fuzzy quantization control strategy.

This paper addresses the flocking control problem for a group of unmanned surface vehicles (USVs) to follow a leader USV guided by a parameterized path in an environment with obstacles. The locations and shapes of the obstacles are unknown, and only the closest collision points and collision vectors can be locally measured. A safety-critical flocking control method is proposed for achieving collision avoidance and establishing a flocking behavior for USVs. Specifically, control inputs of virtual reference points are designed based on an artificial potential function. For the leader USV, a nominal path following guidance law is designed to follow a predefined parameterized path. For the follower USVs, a flocking guidance law is designed to follow the virtual reference points. An exponential control barrier function is designed based on the closest collision points. A constrained quadratic programming problem incorporating exponential control barrier function is established to calculate optimal yaw rate guidance signals. The effectiveness of the proposed control method for safety-critical flocking control of USVs is validated through simulation results.

This paper focuses on the problem of safe guidance and control for under-actuated ASVs (autonomous surface vehicles) subject to input constraints. A model predictive control method is presented with a safe guidance strategy to achieve the trajectory tracking control of under-actuated ASVs. In specifically, a safe guidance law is proposed with control barrier functions to yield the guidance signals, such that the objectives of collision avoidance and trajectory tracking can be realized. An extended-state-observer is utilized to estimate the model uncertainty and external disturbance. The estimated information is incorporated into the model predictive control loop for ASVs to track the safe guidance within input constraints. Simulation outcomes are expounded to illustrate the effectiveness of the developed safe guidance and control method.