In cooperative target tracking missions involving multiple unmanned surface vehicles, maintaining a prescribed formation is often challenged by the presence of obstacles in the marine environment, which increases the risk of collision and disrupts vehicle motion. Traditional collision avoidance methods can prevent collision avoidance but tend to disrupt the original tracking formation. Meanwhile, conventional formation transformation methods typically neglect the influence of the target state on the tracking formation, limiting their adaptability in dynamic tracking scenarios. To address these problems, this study proposes an adaptive formation transformation and control method for target tracking based on the hyperbolic tangent (Tanh) function.

First, collision detection is formulated based on the overlap between formation and obstacles, and then three formation transformation strategies are designed based on the collision detection results, namely, contraction, rotation and a combined transformation. Then, considering that the Tanh function can map the positive real values to the range of 0 to 1 with a smooth transformation curve, it is introduced to integrate the critical distance and safe distance in order to define an adaptive formation transformation law. According to different strategies and transformation degrees, this method enables flexible realization of multiple tracking formations, while smoothing the formation transformation process. Then, to ensure coordinated tracking and synchronization with the target’s motion, a consistency deviation model is established based on the expected formation and target velocity. A distributed kinematics controller is designed using the inverse step method, which enables stable target tracking and enhances the system’s response speed. In addition, a dynamic controller based on the super-twisting sliding mode method is implemented, and the stability of the closed-loop system is rigorously verified.

Taking a system of four USVs as an example, the proposed algorithm is validated through simulation experiments under the integrated scenarios involving telescopic, rotational, combined telescopic-rotational, and dense obstacle conditions. The results show that the USV formation can adaptively track the desired formation transformations according to the obstacle distribution. The proposed approach significantly reduces tracking errors in position, heading and speed, while producing smoother outputs for both longitudinal control forces and turning control moments compared with the artificial potential field method.

The proposed design method not only meets the requirements for formation transformation in USV cooperative target tracking under obstacle-rich environments, but also realizes the stable formation transformation, ensuring the safety of multi-USV system and the integrity of tracking formation.

Due to mixed-frequency multi-source disturbances, unmanned surface vehicles (USVs) encounter challenges in accurately capturing state information and ensuring path-tracking precision. To address this issue, a composite anti-disturbance control method based on an extended state observer combined with Kalman filter (KFESO) is proposed for distributed cooperative path following of multiple USVs.

Firstly, an extended state observer combined with Kalman filter is constructed to estimate the state variables and lumped disturbances of USVs. Secondly, a distributed state observer is designed to obtain the speed information of the virtual leader. Based on the consistency theory and the line-of-sight guidance law, a kinematic cooperative controller is designed by combining the output of the KFESO and the estimated reference speed. Furthermore, a kinetic anti-disturbance controller is designed using the backstepping method and the dynamic surface control technique. The Lyapunov stability theory is employed to prove that all error signals in the control system are uniformly ultimately bounded.

Simulation experiments show that the proposed method can accurately obtain the states of USVs. Under mixed-frequency multi-source disturbances, compared with the standard ESO-based control method, it has higher tracking precision and stronger anti-disturbance ability. Regarding path tracking trajectories, the proposed method achieves reduced lateral deviations and more stable trajectories. For position errors, the convergence times are comparable, but the proposed method effectively eliminates oscillations. In terms of path parameter coordination error, the proposed method can stabilize the formation, whereas the comparison method suffers from high-frequency oscillations. In terms of state estimation accuracy, the proposed method significantly improves the estimation accuracy of various state variables, enables the distributed state observer to effectively estimate the speed of the virtual leader, and achieves smaller errors in speed and control force (moment), effectively mitigating the frequent actuator response to noise.

This method can resolve the trade-off between estimation speed and accuracy in ESO, and improve the precision of multi-USV cooperative path following.

In the process of marine resource development, some thrusters of over-actuated ships are prone to failures during operation, resulting in a decrease in propulsion power. This paper aims to propose a fault-tolerant control method based on improved adaptive control allocation to enhance the fault tolerance and the safety reliability of ship operations.

Firstly, an adaptive control allocation algorithm is designed to online reconstruct the configuration matrix of the faulty propulsion system based on the current propulsion capacity, reducing the thrust deviation. Additionally, a differential term is added to the adaptive update law to suppress the thrust jitter. Then, the unprocessed control allocation error is regarded as a lumped disturbance, which is estimated and compensated by a modified extended state observer. Finally, the boundedness of the error in the closed-loop control system is proved using Lyapunov theory, ensuring the theoretical feasibility of the method.

Simulation and modeling experiments are carried out using a self-developed over-actuated ship experimental prototype. In terms of the upper limit of positioning error, the IACA method demonstrates a significantly lower upper limit of positioning error across all directions when compared to the ACA and QPCA methods. Furthermore, regarding system dynamic performance, the IACA method facilitates rapid stabilization of the system to a steady state following thruster failure. In the simulation experiments, the abrupt changes in disturbance estimation values, actual force, and thrust deviation associated with the IACA method were minimal post-failure, indicating a rapid recovery. Additionally, the adaptive parameter updates were both faster and more stable, exhibiting minimal jitter, effectively enhancing the system's performance in terms of jitter reduction.

The results show that the proposed method can effectively handle the failure of over-actuated ship thrusters. Verified by experiments, it can reduce operation errors, help the system quickly return to stability, improve the jitter, enhance the fault tolerance of the ship, provide an effective strategy for the fault-tolerant control of ship thrusters, and is of great significance for the safe and stable operation of the ship. However, further research and optimization are needed in the future.

This paper proposes a null-space-based active disturbance rejection control（ADRC）allocation method to analyze the influence of multi-source disturbances encountered during the autonomous berthing of ships, such as environmental loads, bank effects, model uncertainties and control allocation errors.

First, a ship berthing motion model, multi-source disturbance model and control allocation model are established, and a neural network extended state observer (NNESO) is designed to estimate ship states and multi-source disturbances in real time. Second, null-space technology is introduced to design the control allocation algorithm. Based on this method, a scheme for stabilization control outside the berth and parallel berthing is realized. Finally, it is proven that all error signals of the autonomous berthing system under the proposed method remain uniformly ultimately bounded, ensuring the safety of the autonomous berthing process.

The comparative simulation results show that the proposed method has a trajectory tracking effect similar to that of the quadratic programming (QP) method, with a solution time of about 1.3% and a yaw maximum allocation error of 36.51% of the pseudo inverse (PI) method.

The proposed method not only ensures the accuracy of berthing motion control, but also significantly reduces the solution time and maximum allocation error, thereby ensuring real-time control allocation with high accuracy.