Underactuated Surface Vehicles Research Articles

Distributed avoidance-accommodating flexible performance approach for adaptive formation tracking of underactuated surface vehicles against moving obstacles

A novel strategy for formation tracking of multiple uncertain underactuated surface vehicles is introduced in this study, to maintain the prescribed formation performance in the presence of moving obstacles with unknown velocities. Unlike the existing methods for prescribed formation performance control, our key contribution is the development of distributed avoidance-accommodating flexible performance functions (FPFs). These functions prevent deviation from the prescribed performance bounds while navigating around moving obstacles, considering input saturation and model uncertainties. We design local adaptive formation controllers by using distributed posture errors and avoidance-accommodating FPFs. Auxiliary signals that facilitate adjustment of the posture errors and performance functions during obstacle avoidance are derived using a recursive design that ensures Lyapunov stability. Additionally, command filters for virtual control laws are redesigned as saturation-compensating filters to solve the input saturation problem. Consequently, the proposed controller ensures the prescribed distributed formation performance, even in scenarios involving moving obstacles and input saturation, a capability lacking in conventional prescribed performance-based formation controllers, which can become unstable in such scenarios. The theoretical findings of this study are validated through comparative simulations.

Prescribed-time adaptive state observer approach for distributed output-feedback formation tracking of networked uncertain underactuated surface vehicles

Prescribed-time adaptive state observer approach for distributed output-feedback formation tracking of networked uncertain underactuated surface vehicles

Disturbance-Observer-Based Adaptive Prescribed Performance Formation Tracking Control for Multiple Underactuated Surface Vehicles

This study proposes a new disturbance-observer-based adaptive distributed formation control scheme for multiple underactuated surface vehicles (USVs) subject to unknown synthesized disturbances under prescribed performance constraints. A modified sliding mode differentiator (MSMD) is applied as a nonlinear disturbance observer to estimate unknown synthesized disturbances, which contain unknown environmental disturbances and system modelling uncertainties, thus enhancing the robustness of the system. Based on this, we impose the time-varying performance constraints on the position tracking error between the neighboring USVs. A novel differentiable error transformation equation is embedded in the prescribed performance control, and an adaptive prescribed performance controller is constructed by employing the backstepping method to ensure that the position tracking error remains within the prescribed transient and steady performance, and each USV realizes collision-free formation motion. Furthermore, a novel second-order nonlinear differentiator is introduced to extract the derivative information of the virtual control law. Finally, the numerical simulation results verify the effectiveness of the proposed control scheme.

Graph Search-Based Path Planning for Automatic Ship Berthing

Ship berthing is one of the most challenging operations for crews, involving optimal trajectory generation and intricate harbor maneuvering at low speed. In this paper, we present a practical path-planning method that generates smooth trajectories for an underactuated surface vehicle (USV) traveling in a confined harbor environment. Our approach introduces a Generalized Voronoi Diagram (GVD)-based path planner to handle the unberthing phase. The hybrid A* search-based path finding method is used for the transportation phase. A simple planner based on a Bézier curve is proposed for the berthing phase. To track the target path, an adaptive pure pursuit method and proportional-derivative (PD) controller is used. The performance of the given method is tested numerically and experimentally on a catamaran with a pair of non-steerable thrusters. The results demonstrate that the proposed algorithm can achieve a successful berthing operation through static obstacle handling and smooth trajectory generation.

Neural Network Control of Underactuated Surface Vehicles With Prescribed Trajectory Tracking Performance.

This article is concerned with the fast and accurate trajectory tracking control problem for a sort of underactuated surface vehicle under model uncertainties and environmental disturbances. A novel neural networks (NNs)-based prescribed performance control strategy is proposed to solve the problem. In the control design, a new type of performance function is constructed which provides a way to predefine the settling time and accuracy, straightforward. Then, a pair of barrier functions are employed to combat not only the position error but also the virtual control input. This evades the possible singularity or discontinuity of the control solution. Next, an initialization technique is exploited, removing the requirement for the initial condition of the control system. Finally, two NNs are employed to deal with the unknown ship nonlinearities. The performance analysis not only demonstrates the effectiveness of the proposed approach but also reveals its robustness against disturbances and unknown reference trajectory derivatives. There is, thus, no need to acquire such knowledge or employ specialized tools to handle disturbances. The theoretical findings are illustrated by a simulation study.

Continuous and Periodic Event-Triggered Sliding-Mode Control for Path Following of Underactuated Surface Vehicles.

This article develops continuous and periodic event-triggered sliding-mode control (SMC) algorithms for path following of underactuated surface vehicles (USVs). Based on the SMC technology, a continuous path-following control law is designed. The upper bounds of quasi-sliding modes for path following of USVs are established for the first time. Subsequently, both continuous and periodic event-triggered mechanisms are considered and added into the proposed continuous SMC scheme. It is demonstrated that with appropriate selecting of control parameters, the use of hyperbolic tangent functions does not affect the boundary layer of quasi-sliding mode caused by event-triggered mechanisms. The proposed continuous and periodic event-triggered SMC strategies can make the sliding variables reach the quasi-sliding modes and stay in there. Moreover, energy consumption can be reduced. Stability analysis shows that the USV can follow a reference path by using the designed method. The simulation results show the effectiveness of the proposed control methods.

Adaptive Finite-Time Trajectory Tracking Control for Underactuated Surface Vehicles Based on Adaptive Disturbance Compensating

Adaptive Finite-Time Trajectory Tracking Control for Underactuated Surface Vehicles Based on Adaptive Disturbance Compensating

Smooth Sliding Mode Control for Path Following of Underactuated Surface Vehicles Based on LOS Guidance

In this paper, a solution to the problem of following a curved path for underactuated unmanned surface vehicles (USVs) with unknown sideslip angle and model uncertainties is studied. A novel smooth sliding mode control (SSMC) based on a finite-time extended state observer (FTESO) for heading control is proposed. Firstly, the model of a USV with rudderless double thrusters is established. Secondly, the path-following error dynamics of a USV is established in a path-tangential reference frame. Thirdly, a finite-time observer is introduced to estimate the unidentified sideslip angle, and the line-of-sight (LOS) guidance law is applied to produce the desired heading angle. Finally, an SSMC controller is proposed to force USV tracking at the desired heading angle and surge speed, in which FTESO is used to estimate and compensate the unknown disturbance in sliding mode dynamics. The theoretical analysis for FTESO-SSMC verifies that the controller can provide finite-time convergence to and stability on the sliding surface. Simulation studies and contrast test are conducted to demonstrate the robustness and rapidity of the proposed FTESO-SSMC controller.

Collision-free flexible performance tracking control against moving obstacles for underactuated surface vehicles with model uncertainty and input saturation

This paper presents a novel tracking control method based on a collision-free flexible performance function (CFPF) that allows us to preset tracking performance bounds for uncertain underactuated surface vehicles in the presence of moving obstacles and input saturation. In contrast to previous studies that have utilized flexible performance functions, we introduce a new CFPF combined with alteration signals to adjust the tracking performance against moving obstacles with unknown velocities. The CFPF-based adaptive control design strategy is established using the coordinate transformation method and auxiliary variables, where the CFPF tuning mechanism is derived from a Lyapunov-based tracker design. By employing the Lyapunov stability theory, we prove that the proposed method allows for the desired tracking performance adjustment, thereby ensuring trajectory tracking and obstacle avoidance despite model uncertainty, input saturation, and unknown moving obstacles.

Disturbance observer-based adaptive neural control for underactuated surface vehicle with constraint of input saturation

In this paper, a robust adaptive neural control algorithm is provided to solve the problem of path-following control for underactuated surface vehicle (USV) subject to input saturation, in the presence of model uncertainties and unknown marine environmental disturbance.In the algorithm, through the application of neural network (NN), an adaptive disturbance observer (ADO) is proposed to observe the unknown disturbance, which does not need the precise information of the upper bound of the disturbance, and the model uncertainty can be appropriated simultaneously. Specially, since the ADO and control law share the same set of NN, the number of adaptive parameters of the controller can be greatly reduced. After that, dynamic surface control (DSC) method is used to avoid repeated derivative in the process of back-stepping, which solve the “calculation explosion” problem. An auxiliary system is designed to compensate errors caused by input saturation, which solve the input saturation problem of actuators. Through Lyapunov stability analysis, it is proved that all signals of the closed-loop system are semi-globally ultimately uniformly bounded (SGUUB). Finally, some experiments are conducted to demonstrate the effectiveness of the algorithm.

Distributed formation tracking control of underactuated surface vehicles based on event-trigged control

In this paper, a distributed formation tracking control problem is investigated for underactuated surface vessels (USVs). The uncertainties induced by model uncertainties and external disturbances are assumed to be unknown. An event-trigged disturbance observer (ETDO) is proposed to provide the estimations of the uncertainties, and an event-triggered mechanism is used to determine when measured velocity information must be sent to the observer. An event-trigged controller (ETC) is designed based on a backstepping technique, dynamic surface control, and the observer. Stability analysis of distributed formation control system is given to prove all signals are bounded. Simulations demonstrate the proposed control strategy.

Leader–Follower Formation Tracking Control of Underactuated Surface Vehicles Based on Event-Trigged Control

This paper investigates the leader–follower formation tracking control of underactuated surface vessels (USVs) with input saturation. Each vessel is subject to the uncertainties induced by model uncertainties and environmental disturbances. First, an event-triggered extended-state observer (ETESO) is used to recover the velocity, yaw rate and uncertainties. Then, an estimator is used to estimate the velocity of the leader. An event-triggered controller (ETC) is constructed based on the estimator, the observer and extra variables. Specifically, extra variables are used to solve the problems of underactuation and input saturation. Stability analysis of the control system is conducted to prove that all signals are bounded. Simulations demonstrate that the ETESO can accurately estimate the uncertainties, velocity and yaw rate, and the ETC can largely reduce the action times of actuator.

Adaptive event-triggered fuzzy tracking control for underactuated surface vehicles under external disturbances

In this paper, the tracking control problem of underactuated surface vehicles with modeling uncertainties and unknown external disturbances is studied. The fuzzy logic system is applied to approximate the uncertainties in the model. A new disturbance observer with a learning factor is introduced to compensate external disturbances. It can improve observation precision and lead to faster tracking of the system. According to this, and combining the adaptive backstepping technique with the command-filter and event-triggered mechanism, the adaptive fuzzy control method is proposed to guarantee the boundedness of all the closed-loop signals. It is also proved that the tracking errors of the position and yaw angle can keep within a certain precision in finite time. Simulation on the surface vessel verifies the feasibility, and the proposed method is insensitive to the main design parameters.

Robust adaptive synchronized event-triggered formation control of USVs with the fault amendment strategy

In this paper, the formation control of the underactuated surface vehicles (USVs) is studied in the presence of the condition of actuator fault and limited communication resources. Considering the performance characteristics of the underactuated surface vehicle (USV), a robust adaptive synchronized event-triggered formation control method is proposed under the usage of the event-triggered control (ETC) and robust neural damping technique. In consideration of the constant energy expenditure of the law of adaptation, the formulated control method is set in the mechanism of triggering by both the controller and the gain related adaptive law, which could cause the communication to reduce more much power consumption. The robust adaptive rule is fault compensated in the way of combining robust neural damping and dynamic surface control (DSC) techniques. Since the fault amendment strategy compresses inconclusive bias fault parameters and model uncertainty parameters, system stability can be enhanced under the premise of reducing the influence of adaptive parameters. A huge volume of work has taken place to ensure semi-global uniform ultimate bounded (SGUUB) stability. To conclude, the effectiveness of the algorithm is verified by two arithmetic examples.

A Novel Cooperative Design for USV–UAV Systems: 3-D Mapping Guidance and Adaptive Fuzzy Control

This note investigates a novel cooperative design for path following of the mixed-order underactuated surface vehicle (USV) and unmanned aerial vehicle (UAV) in presence of the structure uncertainties and external disturbances. The designed cooperative scheme is comprised of the 3 dimension (3D) mapping guidance and adaptive fuzzy control algorithm. The 3D mapping guidance is developed to provide the reference signals of the yaw degree of freedom for the USV and UAV by utilizing the equivalent mapping technique. To control the USV-UAV converge to the desired path, the adaptive fuzzy control algorithm is designed for the position and attitude loops by fusing the dynamic surface control (DSC) and the Backstepping techniques. The position loop can generate the thrust inputs for the USV-UAV and provide the desired rolling and pitching angles for the UAV by using nonlinear decoupling method. In the proposed algorithm, the model uncertainties are approximated by the fuzzy logic system and only eight norm-based adaptive parameters are required to be updated online. Based on the Lyapunov theorem, the stability of the position loop and the attitude loop for the USV-UAV systems is achieved and all signals in the cooperative systems are the semi-global uniform ultimate bounded (SGUUB). The superiorities and the effectiveness of the proposed strategy are verified through the numerical experiment on the MATLAB platform under the external disturbances.

Distributed dynamic obstacle avoidance design to connectivity-preserving formation control of uncertain underactuated surface vehicles under a directed network

This paper presents a Lyapunov-based recursive design approach for unifying distributed connectivity-preserving formation control and dynamic obstacle avoidance problems of uncertain multiple underactuated surface vehicles (USVs) with heterogeneous range constraints. Compared with related works, the main contribution of this study is to develop a novel control design for preserving network connectivity under dynamic obstacle avoidance in the distributed formation tracking framework. Because of the limited communication ranges, it is difficult to maintain the network interactions among USVs during dynamic obstacle avoidance. To deal with this problem, a collision-avoiding function is defined as a local error surface for the recursive control design, and a distributed complementary signal vector is introduced in the connectivity-preserving formation error surface. The complementary signals are designed to prevent network disconnections when the formation error is increased by the avoidance action and to ensure the stability of the collision-avoiding error dynamics, which eventually lead to preventing network disconnections during dynamic obstacle avoidance. An adaptive formation tracking scheme is designed via the neural networks-based command-filtered backstepping. The stability of the overall closed-loop system with preserved network connectivity and obstacle avoidance is proved based on the Lyapunov stability theorem. Finally, the theoretical approach is demonstrated through simulations.

Trajectory Planning of USV: On-Line Computation of the Double S Trajectory Based on Multi-Scale A* Algorithm with Reeds–Shepp Curves

Trajectory planning aims to provide a time-related control target that contains the concerned states. For an underactuated surface vehicle (USV), planning challenges include limitations on curvature, speed, acceleration, and jerk. These challenges are relevant for the precise control of USVs. To solve these problems, an on-line double S method and multi-scale A* trajectory planning algorithm is proposed by integrating Reeds–Shepp curves (RSC), where a quad-tree-based graph is used for path planning and collision detection. Simulations illustrate that the proposed method has a better performance than the smooth rapid-exploration random tree (smooth-RRT) method and jump point search (JPS) method, and that path length and the state limitations are satisfied.

A predictive type-3 fuzzy control for underactuated surface vehicles

In this paper, a path-following control (PFC) problem of an underactuated surface vehicle (USV) is scrutinized based on an interval type-3 fuzzy logic system (IT3FLS). The suggested method is able to tackle the main limitations of the singleton fuzzy controller in terms of the approximation ability for uncertainties and exogenous disturbances of a complex nonlinear USV. Since a novel structure is employed for the FLS, the control policy is capable of ensuring robust performance against uncertainties with a wide range of variations and higher volumes of complex disturbances. Moreover, surge-guided line-of-sight (SGLOS) and auxiliary dynamics are utilized to design surge and heading control policies, adjusting the velocity of a vehicle and its position at each moment respective to the predefined path. Predictive compensators are designed to enhance the robustness by reducing the approximation error signals while the stability analysis of both tracking and approximation error signals are investigated based on the Lyapunov approach and Barbalat’s lemma. Finally, simulation results demonstrate the effectiveness of the suggested improved fuzzy-based control strategy to solve a PFC problem.

Dynamic Event-Triggered Path-Following Control of Underactuated Surface Vehicle With the Experiment Verification

This paper investigated the dynamic event-triggered control scheme for the path-following activity of underactuated surface vehicle (USV) subject to actuator saturation and gain uncertainties. Specifically, a dynamic event-triggered mechanism with the adjustable threshold is developed to reduce the communication burden and the execution wear of actuators. Unlike most existing event-triggered results, in which the threshold parameters are always fixed, the developed mechanism can ensure that the triggering thresholds are updated online in an adaptive manner, so as to achieve better resource efficiency. Furthermore, taking the practical measurable variables (i.e., revolving speed of propeller and rudder angle) as the control input, an auxiliary system is designed to deal with the influence of actuator saturation, which is distinct from most existing saturation-tolerant methods for USV. For merits of the neural damping technique, both the internal and external uncertainties are remodeled and only four adaptive parameters require to be updated online. Considerable effort has been made to guarantee the semi-globally uniform ultimate bounded (SGUUB) stability. Finally, the numerical simulation and physical experiment are illustrated to demonstrate the remarkable performance of the proposed algorithm.

Adaptive distributed fault-tolerant control for underactuated surface vehicles with bridge-to-bridge event-triggered mechanism

This paper investigates an adaptive distributed fault-tolerant formation control scheme for multiple underactuated surface vehicles (USVs) with the bridge-to-bridge event-triggered communication mechanism. In particular, under the directed topology, information from each USV is broadcast to the adjacent vehicles only if the event-triggered condition is satisfied. The benefit of the proposed event-triggered communication mechanism eliminates the requirement of either the continuous monitoring of adjacent vehicles’ states or global graph information, which can address the problem of the limited communication bandwidth in the marine practice. Based on the event-triggered communication, backstepping and directed topology, an adaptive distributed formation controller is developed for each USV. Besides, the unknown structure uncertainty and external disturbances are compressed together to compensate by introducing the neural network (NN) approximator and the neural damping technique. And the derived adaptive law can also compensate the adverse effect of unknown actuator faults and gain uncertainty. Through the Lyapunov theory, all signals in the closed-loop system are proved to be with the semi-global uniform ultimate bounded (SGUUB) stability. Finally, the numerical simulation is illustrated to verify the effectiveness of the control algorithm.