Underactuated Surface Vessels Research Articles

LPVS guidance and adaptive event-triggered control for an underactuated surface vessel with the prevention of obstacle’s vicious maneuvering

This paper investigates the adaptive neural event-triggered control for an underactuated surface vessel (USV), considering constraints of the obstacle’s vicious maneuvering and the limited communication channel. In the algorithm, a novel logical phantom virtual ship (LPVS) guidance principle is developed to generate the global path following reference and the obstacle avoidance order in the simulation results, where the corresponding operation comply to the suggestion in international regulations for prevention collision at sea (COLREGs). The improved design of velocity obstacle (VO) method can guarantee its predictive capability to prevent the obstacle’s vicious maneuvering. As for the control module, the adaptive event-triggered control algorithm is proposed by employing the robust neural damping technique and the input event-triggered mechanism. And the derived adaptive law can effectively solve perturbations from the gain uncertainty and the external disturbances. Through the theoretical analysis, all signals of the closed-loop control system are with the semi-globally uniform ultimate bounded (SGUUB) stability. The simulation experiments have been presented to verify the obstacle avoidance effectiveness and the burden-some superiority of the algorithm.

Robust Bearing-Based Formation Tracking Control of Underactuated Surface Vessels: An Output Regulation Approach

This article is concerned with the robust formation tracking control of a group of underactuated surface vessels whose formation is characterized by the relative bearings between the vessels. Control protocols are proposed to asymptotically steer certain points on the vessels, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">hand points</i> , which lie ahead of their centers of mass along the longitudinal axes, to track the desired moving formation; such a control method is called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">an output regulation approach</i> . The moving formation is guided by the motions of two or more agents, which are referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">leaders</i> , and the other <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">follower</i> agents track the leaders by maintaining bearing constraints to neighbors. The proposed control schemes are designed based on a backstepping technique and sliding mode control. The latter is employed to attenuate known bounded disturbances present in the vessels' dynamics. When the bounds of the disturbances are unknown, an adaptive control protocol is subsequently investigated, under which the system is shown to converge to a small neighborhood of the target formation. Further, sufficient conditions on the upper bound of the hand points' desired velocities are provided for the uniform ultimate boundedness of the vessels' internal sway-yaw dynamics. Simulation results are provided to support the theoretical analysis.

Event-triggered path tracking control with obstacle avoidance for underactuated surface vessel compliant with COLREGs-constraints: Theory and experiments

Event-triggered path tracking control with obstacle avoidance for underactuated surface vessel compliant with COLREGs-constraints: Theory and experiments

Event-triggered trajectory tracking control of underactuated surface vessels with performance-improving mechanisms under input saturation and actuator faults

This paper deals with the improvement for the tracking performance of underactuated surface vessels (USVs) under input saturation and actuator faults. The neural networks (NNs) are used to reconstruct the dynamic uncertainty of the ship, and an adaptive law is designed to compensate the adverse effects of external unknown disturbances and bias faults on the system. To improve the tracking performance of the system, a nonlinear link is added in the design process of the control scheme to adjust the system error feedback, and the finite-time control (FTC) technology is used to further improve the steady-state performance and transient performance of the system. In addition, to solve the problem of communication resource limitation, an event-triggered mechanism for switching thresholds is introduced, which reduces the update frequency of controller signals. Based on the above techniques, a trajectory tracking control scheme with a performance improvement mechanism is designed. A rigorous stability analysis is provided for the control scheme using Lyapunov stability theory. Finally, the effectiveness of the control scheme is verified by two sets of simulations.

Adaptive Finite-Time Trajectory Tracking Event-Triggered Control Scheme for Underactuated Surface Vessels Subject to Input Saturation

In this paper, the trajectory tracking problem of underactuated surface vessels (USVs) that is subject to input saturation, unmodeled dynamics, and marine environmental disturbances is investigated. Firstly, USVs underactuation problem is handled by constructing a coordinate transformation. An auxiliary dynamic system is adopted to deal with input saturation. The adaptive law is presented to online update the upper bounds of the composite disturbances. The event-triggering condition is introduced to reduce drastically control execution frequency and the transmission load. By combining the auxiliary dynamic system, an adaptive technique, a first-order command filtered technique and an event-triggered condition, a novel adaptive finite time event-triggered control (AFETC) scheme is proposed, which has the following significant characteristics compared to most existing schemes: 1) the artfully constructed coordinate transformation not only avoids computational complexity but also simplifies the design; 2) the first-order command filtering vector-backstepping control method not only circumvents “explosion of complexity” in the traditional backstepping approach, but also ensures the finite-time settling of position tracking errors of USVs; 3) with the event triggered control, it reduces the control execution frequency, thereby decreasing the communication transmission load; and 4) it ensures stable tracking without requiring a priori information of the unmodelled dynamics of USVs or external disturbances. The designed robust adaptive control has proven to enable USVs to track the desired trajectory while guaranteeing the closed-loop stability in a finite time and avoiding Zeno behavior. Simulation and comparation results demonstrate the effectiveness and superiority of the proposed control strategy.

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.

Prescribed performance control of underactuated surface vessels' trajectory using a neural network and integral time-delay sliding mode

Prescribed performance control of underactuated surface vessels' trajectory using a neural network and integral time-delay sliding mode

FXESO based FNMPC path following control for underactuated surface vessels with roll stabilisation

External ocean disturbances result in the roll motion of underactuated surface vessels (USVs), which probably have severe effects. To improve the USV capability of path following and speed maintenance in rudder roll stabilisation (RRS) control, a fixed-time extended state observer (FXESO) based fuzzy nonlinear model predictive control (FNMPC) scheme was proposed. A 4-degrees of freedom (DOF) nonlinear USV model is established for investigation. Subsequently, the FXESO is designed to estimate the velocity states and lumped disturbance terms of the USV model, which are used to simplify the predictive model. Subsequently, the disturbance compensation nonlinear model predictive control (NMPC) with fuzzy rules is designed to handle multi-objective cooperative control problems between path following and RRS. Fuzzy rules are designed to improve the performance of path following and speed maintenance by altering the objective function weights in MPC. The stability of proposed scheme was theoretically proven. The effectiveness of proposed algorithm was verified through simulations and comparisons.

Improved iterative learning path-following control for USV via the potential-based DVS guidance

Considering navigation scenarios in elaborate waters, the high-precision waypoints-based path-following problem of underactuated surface vessel (USV) is investigated by combining the iterative learning control (ILC) and the artificial potential field (APF) in this note. A potential-based dynamic virtual ship (DVS) guidance, considering the challenge of preventing collisions with irregular barriers, is designed with the path following module and the collision avoidance module. A virtual potential field is constructed in the guidance strategy to provide the desired heading signal In particular, the desired heading signal will force that to navigate to one secure location, where the USV approaches the barrier. On the basis of guidance, the iterative control algorithm is selected to design the controller of the system due to the advantages of high accuracy. The dynamic surface control (DSC) and the robust neural damping techniques are utilized to constraint the intrinsic problem of “explosion of complexity” in ILC. The merits of the method involve concise form and controllable precision. Through the Lyapunov criterion, the corresponding closed-loop system is with the semi-global uniformly ultimately bounded (SGUUB) stability. The simulation results are illustrated to verify the effectiveness of the proposed algorithm.

Fixed-time self-structuring neural network fault-tolerant tracking control of underactuated surface vessels with state constraints

In this paper, a fixed-time fault-tolerant control strategy is proposed for trajectory tracking of underactuated surface vessels (USVs) with input saturation. A predefined region boundary function is proposed, which has all predefined fixed-time convergence properties and provides predefined specifications for tracking errors. To achieve the predetermined tracking performance, a fixed-time adaptive neural network state constrained fault-tolerant controller is proposed based on dynamic surface control technology, a back-stepping program, and an asymmetric time-varying tangent barrier Lyapunov function (ATVTBLF). The unknown external environment disturbances and complex continuous unknown nonlinear terms are approximated by a self-structuring neural network (SSNN), which can improve the robustness of the control system to unknown parameters and guarantee the tracking performance of the control system. The number of neurons of the SSNN can be adjusted online according to the approximation efficiency, which can reduce the amount of calculation of the control system. Based on Lyapunov stability theory, it is proven that the closed-loop system is bounded and stable in a fixed time, and the tracking error is always kept within the constraint range. The simulation results show that the underactuated surface vessel control system has good tracking performance.

Event-triggered predefined-time H∞ formation control for multiple underactuated surface vessels with error constraints and input quantization

In this paper, an event-triggered predefined-time H∞ formation control strategy is proposed for multiple underactuated surface vessels (USVs) with error constraints and input quantization. A modified asymmetric barrier Lyapunov function (MABLF) is employed to constrain the tracking errors to a predefined range. Both event-triggered and input quantization are simultaneously employed to guarantee that the controller achieves satisfactory performance even with a limited network bandwidth. H∞ control is introduced to ensure that the system L2 gain is less than or equal to a given ς, which effectively improves the robustness to the lumped disturbance. Theorem analysis shows that the proposed controller guarantees that the tracking errors of the system converge to an arbitrarily small region in a predefined time. The effectiveness of the proposed controller is confirmed by simulation examples and comparisons.

Minimum-learning-parameter-based adaptive finite-time trajectory tracking event-triggered control for underactuated surface vessels with parametric uncertainties

For the problem of trajectory tracking control of underactuated surface vessels (USVs) affected by input saturation, parametric uncertainties, time-varying marine environmental disturbances, and limited transmission resources, a robust adaptive finite-time event-triggered control scheme is presented in this paper. First, a coordinate transformation is constructed to tackle the underactuation problem of the USV and enables the USV control law to be devised in vector form, which simplifies the design and makes it more suitable for computer processing. A continuous auxiliary dynamic system is constructed to handle the input saturation problem. The minimum learning parameter (MLP) technique is used to approximate the parametric uncertainties of the model. An adaptive law is devised to update online the upper bound of the combination of external disturbances and the approximation error generated by the MLP. Additionally, a finite-time control scheme is presented by introducing a robustifying term in the virtual control law, which improves the control performance; an introduced event triggering mechanism in the channel from the controller to the actuator decreases both the transmission burden and the control execution frequency without affecting the control performance. The theoretical analysis reveals that the devised robust adaptive finite-time event-triggered control scheme enables the USVs to track the desired trajectory in a finite time with a small number of control executions, while ensuring the closed-loop stability of the system and avoiding Zeno behavior. The simulations verify the effectiveness and the superiority of the presented control scheme.

Approximation-free design for distributed formation tracking of networked uncertain underactuated surface vessels under fully quantized environment

Distributed formation tracking results have been studied in the literature for networked underactuated surface vessels (NUSVs) at the dynamic level. The distributed formation tracker design of NUSVs under a fully quantized environment remains an open problem. This paper provides a solution to this problem in the low-complexity control framework that ensures prescribed performance without the help of any adaptive approximation tools. State variables and underactuated control inputs of followers are quantized and communicated under a directed network. Distributed formation controllers using quantized state feedback signals are constructed for NUSV followers. The design conditions that lead to establishing the prescribed performance of local tracking errors in the presence of state and input quantization are newly derived via distributed quantization errors. It is shown from the recursive analysis of closed-loop quantization errors that although all states and inputs of followers and the communicated position information under a directed network are quantized, the prescribed performance of the presented formation system is ensured.

Roto-Translation Invariant Formation of Multiple Underactuated Planar Rigid Bodies

This article investigates the roto-translation invariant (RTI) formation of multiple underactuated planar rigid bodies, which are established under the framework of matrix Lie groups. The main contribution is that we define the RTI and pseudo RTI (P-RTI) formation of planar rigid bodies. Different from the common formation given in the earth-fixed frame, the RTI formation is defined in the body-fixed frame so that it possesses a rigid-body motion obtained by composing rotation and translation simultaneously. Moreover, regarding fully actuated planar rigid bodies, we propose the velocity and force requirements to maintain the RTI formation, which are derived based on the kinematic and dynamic model, respectively. Another contribution of this article is that the RTI formation feasibility is investigated for underactuated planar rigid bodies subject to nonholonomic constraints on velocities and accelerations. To be more specific, we study the occasions when wheeled mobile robots and underactuated surface vessels can maintain the RTI or P-RTI formation. Finally, the results of the simulation and experiment are presented so as to exhibit the RTI and P-RTI formation intuitively.

ESHLOS guidance for neuro-adaptive path following control of underactuated surface vessels

This paper proposes a neuro-adaptive path following control scheme based on ESHLOS guidance law for underactuated surface vessels with unmeasured linear velocities. Based on two extended state observers, an ESHLOS guidance law is designed, where the guidance law not only calculates the desired heading angle and surge velocity signals, but also compensates the unknown sideslip angle. Then, neuro-adaptive path following controllers are proposed to track the desired signals via backstepping technique. The hyperbolic tangent function is applied to model input saturation nonlinearity, and adaptive radial basis function neural networks are used to offset the lumped disturbances including external environmental disturbances, model uncertainties. Besides, a high-order tracking differentiator is introduced to generate derivatives of desired heading angle, so that the computational burden inherent in backstepping technique is reduced. Based on the Lyapunov functions, it is proven that all error signals of the closed-loop system are bounded. Finally, simulation results are utilized to reveal the efficacy of the presented approach.

Singularity-Free Continuous Adaptive Control of Uncertain Underactuated Surface Vessels With Prescribed Performance

This article is dealt with the problem of trajectory tracking with prescribed performance for a family of underactuated surface vessels (USVs) under model uncertainties and disturbances. The prescribed performance means that the USV tracks a given trajectory with the arbitrarily predefined speed of response and accuracy. The existing prescribed performance control (PPC) solutions and the traditional robust control approaches for USVs may have the singularity issue or cause a discontinuous control signal. Thereby, a new-type adaptive PPC strategy is put forward in this article. The adaptive technique is devoted to tackling model imperfections as usual, whereas the constraint-handling technique is adopted in a novel way. Herein, we first construct an auxiliary variable instead of using the approach angle or azimuth angle. Then, we impose constraints on the position error, not the tracking error, and the auxiliary variable, simultaneously. In this way, the predefined performance is achieved by moreover a singularity-free continuous control action. These theoretical findings are illustrated via a comparative simulation study.

Formation Control of Multiple Underactuated Surface Vessels with a Disturbance Observer

To maintain the formation of underactuated surface vessels (USVs), this study designs a formation controller based on a virtual structure strategy. The problem of formation control is transformed into the problems of tracking the USV position and the virtual structure point position. Meanwhile, to eliminate the effects of model parameter uncertainties and external environment disturbances on USV tracking control, a compensation control algorithm based on disturbance estimation is proposed. The Lyapunov theorem is introduced to ensure that the trajectory tracking error of the proposed control algorithm eventually converges to any small region, which confirms global stability of the designed tracking error. The simulation results demonstrate that the proposed controller can eliminate the effect of external uncertain interference and maintain the formation of multiple USVs.

Distributed observer based event‐triggered affine formation maneuver control for underactuated surface vessels with positive minimum inter‐event times

AbstractThis article investigates the distributed event‐triggered affine formation maneuver control problem for multiple underactuated surface vessel (USV) systems with positive minimum inter‐event times (MIET). Unlike common formation control methods that only ensure the formation system to keep a fixed geometric shape, the proposed scheme enables multiple USVs maneuver as a group in translation, shearing, rotation, or combinations of them. The proposed control strategy is composed of two parts. First, a distributed event‐triggered observer (DETO) is proposed to observe the time‐varying target formation under the lack of global leaders' information and govern the inter‐vessel communications among the formation group. Besides, the MIET of the designed communication strategy is proved to be strictly positive and computable from formation configurations and control parameters. With these guarantees, the maximum communication frequency can be known in advance. Then, upon the DETO signals, the adaptive local tracking controller is subsequently synthesized for each vessel to realize the target formation track. Rigorous theoretical analysis and simulation results are finally conducted to verify the validness and effectiveness of the proposed algorithm.

Design of distributed event-triggered circumnavigation control of a moving target by a group of underactuated surface vessels

This paper investigates the localization and circumnavigation problem for a group of underactuated surface vessels (USVs). In particular, the USVs collaboratively locate an unknown moving target and then circumnavigate it isometrically with desired spacing angle and velocity. In this strategy, the target information is assumed to be known to only some vehicles in the group. First, a solution to the localization problem, is addressed from the perspective of event triggered distributed estimator (ETDE) to save limited communication resources. In terms of the Lyapunov functional method, it is shown through a novel sufficient criterion that the proposed distributed protocol guarantees the achievement of the localization while ensuring the exclusion of the Zeno-behavior. Second, due to the underactuation, actuators saturation and the uncertainties in the USVs model dynamics, existing distributed algorithms cannot be extended directly to achieve the circumnavigation objective. Under a dynamic event triggering strategy, a fully distributed exponential adaptive backstepping based control scheme is derived to ensure that the USVs move around the estimated target isometrically with a prescribed radius, circular velocity and inter-robot angular spacing. Moreover, to ensure prescribed transient behavior for line-of-sight range and heading tracking errors, an improved barrier function with time-varying scaling transformation is employed and incorporated within the control scheme. We show that under the event triggered communication, the proposed distributed control method, in the presence of uncertainties and actuator saturation, the circumnavigation problem is achieved with the tracking errors converging exponentially to a neighborhood of zero, while the constraint requirements on the line of sight (LOS) range and heading angle will never be violated.