To address the challenges faced by multiple autonomous underwater vehicles (AUVs) in formation control under complex marine environments—such as model uncertainties, external disturbances, dynamic communication topology variations, and limited communication resources—this paper proposes an integrated control framework that combines robust individual control, distributed cooperative formation, and dynamic event-triggered communication. At the individual control level, a robust control method based on a fractional-order sliding mode observer (FOSMO) and a fractional-order terminal sliding mode controller (FOTSMC) is developed. The observer exploits the memory and broadband characteristics of fractional calculus to achieve high-precision estimation of lumped disturbances, while the controller constructs a non-integer-order sliding surface with an adaptive gain law to guarantee finite-time convergence of tracking errors. At the formation coordination level, a distributed trajectory generation method based on dynamic consensus is proposed to achieve reference trajectory planning and formation maintenance in a cooperative manner. At the communication level, a dynamic-threshold event-triggered mechanism is designed, where the triggering condition is adaptively adjusted according to the state errors, thereby significantly reducing communication load and energy consumption. Theoretically, Lyapunov-based analysis rigorously proves the stability and convergence of the closed-loop system. Numerical simulations confirm that the proposed method outperforms several benchmark algorithms in terms of tracking accuracy and disturbance rejection. Moreover, the integrated framework maintains precise formation under communication topology variations, achieving a communication reduction rate exceeding 65% compared to periodic protocols while preserving coordination accuracy.

This paper proposes a control method that combines a fractional-order sliding mode observer and a cooperative control strategy to address the problem of path-following for underactuated autonomous underwater vehicles (AUVs) in complex marine environments. First, a fractional-order sliding mode observer is designed, combining fractional calculus and double-power convergence laws to enhance the estimation accuracy of high-frequency disturbances. An adaptive gain mechanism is introduced to avoid dependence on the upper bound of disturbances. Second, a formation cooperative control strategy based on path parameter coordination is proposed. By setting independent reference points for each AUV and exchanging path parameters, formation consistency is achieved with low communication overhead. For the followers’ speed control problem, an error-based expected speed adjustment mechanism is introduced, and a hyperbolic tangent function is used to replace the traditional arctangent function to improve the response speed of the system. Numerical simulation results show that this control method performs well in terms of path-following accuracy, formation maintenance capability, and disturbance suppression, verifying its effectiveness and robustness in complex marine environments.

This paper addresses the three-dimensional trajectory tracking control problem for the underactuated Autonomous Underwater Vehicle (AUV) operating in complex ocean environments characterized by dynamic disturbances and model uncertainties. A super-twisting extended state observer (STESO) was designed to accurately estimate and compensate for external disturbances and unmodeled dynamics in finite time. A fractional-order proportional–integral–derivative (FOPID) controller was then developed based on the disturbance estimates provided by the STESO. Leveraging the superior frequency-domain tuning flexibility of fractional calculus, the controller enhances tracking precision and robustness against dynamic disturbances. Furthermore, a strict Lyapunov-based stability analysis is presented, and the tracking error converges to zero asymptotically when disturbance estimation errors vanish. Numerical simulations validated the effectiveness and robustness of the proposed control strategy under various disturbance scenarios.

This paper addresses the three-dimensional trajectory tracking problem for underactuated autonomous underwater vehicles subject to external disturbances and model uncertainties in complex ocean environments. A robust control method integrating backstepping dynamic surface control and non-singular terminal sliding mode is proposed. Firstly, based on the kinematic and dynamic models of autonomous underwater vehicle, virtual velocity commands are constructed via backstepping approach to stabilize the position and attitude errors. To circumvent the “differential explosion” problem inherent in conventional backstepping control caused by repeated differentiations of virtual control variables, first-order low-pass filters are introduced to construct dynamic surface control, yielding smooth derivatives of virtual velocity commands. Secondly, to enhance convergence rate and robustness, a non-singular terminal sliding surface is designed at the dynamic level, and a terminal reaching law is formulated to achieve finite-time convergence of velocity tracking errors. Furthermore, to compensate for external disturbances and unmodeled dynamics, a disturbance observer based on the super-twisting algorithm is developed, enabling finite-time high-precision estimation of lumped disturbances, with the estimation results incorporated into the control law for feedforward compensation. Finally, comparative simulations are conducted under two typical disturbance scenarios. The results demonstrate that the proposed method achieves instantaneous disturbance estimation (reducing convergence time from 3 s to near zero), significantly smoother control inputs, and superior tracking accuracy with RMSE as low as 0.6788 m and MAE as low as 0.1468 m, reducing errors by up to 30.6% compared to baseline methods.

Aiming at the problems of traditional Rapidly exploring Random Tree Star (RRT*), its modified algorithms in the three-dimensional complex underwater path planning of autonomous underwater vehicles (AUVs), including sampling redundancy, simplistic expansion mechanism, mismatch between planned paths and AUV motion constraints, and insufficient real-time performance, this paper proposes an improved bidirectional artificial potential field RRT* (Improved BI-APF-RRT*) algorithm. The algorithm adopts a hybrid sampling strategy to concentrate sampling in high-value regions and optimize node distribution. A three-level progressive expansion strategy is designed to balance fast convergence and excellent obstacle avoidance capability. Meanwhile, a dynamic target switching strategy is introduced to enhance the coordination efficiency of bidirectional search trees. Simulation results show that in three-dimensional underwater obstacle environments with different complexity levels, the proposed algorithm outperforms comparative algorithms such as GB-RRT*, BI-RRT*, and APF-RRT* in terms of path length, planning time, number of generated nodes, and iteration times. The proposed algorithm provides an efficient and feasible technical scheme for the deep-sea autonomous navigation of AUVs, and is of great significance for promoting the engineering application of underwater unmanned systems.

To addressthe challenge of attitude control in quad-ducted fan unmanned aerial vehicles (UAVs) under coupled disturbances comprising thrust lag, ground effect and a composite wind field during near-ground flight and to mitigate the inherent trade-off between disturbance rejection and noise suppression in fixed-bandwidth extended state observers (ESOs), this paper proposes a robust attitude control method based on a Sigmoid law adaptive-bandwidth extended state observer (AB-ESO). An attitude dynamic model covering the above multi-source disturbances is established, with all uncertainties uniformly treated as lumped disturbances. An adaptive-bandwidth mechanism with filtering and rate-limiting modules is designed for smooth continuous bandwidth tuning. A composite control framework integrating disturbance feedforward, lag compensation and attitude feedback is constructed, and the uniform ultimate boundedness of the closed-loop system is proved. Comparative simulations are conducted against six baseline controllers, including a cascade proportional–integral–derivative (PID) controller, fixed-bandwidth ESOs, incremental nonlinear dynamic inversion (INDI), fast terminal sliding mode control (FTSMC) and a time-varying bandwidth ESO, in a near-ground composite wind scenario. Results show that the proposed method achieves improved comprehensive performance: the three-axis average tracking root mean square error (RMSE) is approximately 72% lower than of the PID controller and 15.8% lower than that of the high-bandwidth ESO, and the control output total variation is reduced by about 27.8%. Monte Carlo verification with 100 random turbulence groups further validates the strong statistical robustness of the proposed method. All validations in this work are based on numerical simulations. This study provides a technical reference for high-precision control of ducted fan UAVs in near-ground environments.