Underactuated Marine Vehicles Research Articles

PCLOS based fractional-order sliding mode stochastic path following control for underactuated marine vehicles with multiple disturbances and constraints

This paper investigates the stochastic path following control of underactuated marine vehicles (UMVs) subject to multiple disturbances and constraints. Firstly, the complex marine environment in which UMVs navigate typically contains stochastic components, thus the multiple disturbances are categorized as slow-varying deterministic disturbances and stochastic disturbances. Secondly, a position-constrained line-of-sight (PCLOS) based fractional-order sliding mode stochastic (FSMS) control strategy is established to achieve path following control of UMVs. A PCLOS guidance law based on universal barrier Lyapunov function is proposed to ensure that the position errors remain within the constraint ranges, which is versatile for systems with symmetric constraints or without constraints. An FSMS controller based on fractional-order theory and sliding mode control is designed to improve the dynamic response speed of the system and effectively attenuate chattering phenomenon. A stochastic disturbance observer is developed to estimate the slow-varying deterministic disturbances in the stochastic system, and auxiliary dynamic compensators are used to mitigate the impact of input constraints. Lastly, theoretical analysis indicates that the closed-loop system is stable and the position constraint requirements are satisfied. Comparative simulations illustrate the effectiveness of the proposed control strategy.

Model Simplification for Asymmetric Marine Vehicles in Horizontal Motion—Verification of Selected Tracking Control Algorithms

This paper addresses a trajectory tracking control algorithm for underactuated marine vehicles moving horizontally in which the current in the North–East–Down frame is constant. This algorithm is a modification of a control scheme based on the input-output feedback linearization method, for which the application condition was that the vehicle was symmetric with respect to the left and right sides. The proposed control scheme can be applied to a fully asymmetric model, and, therefore, the geometric center can be different from the center of mass in both the longitudinal and lateral directions. A velocity transformation to generalized vehicle equations of motion was used to develop a suitable controller. Theoretical considerations were supported by simulation tests performed for a model with 3 degrees of freedom, in which the performance of the proposed algorithm was compared with that of the original algorithm and the selected control scheme based on a combination of backstepping and integral sliding mode control approaches.

Learning Optimal Guidance Schemes with Safety Guarantees for Underactuated Marine Vehicles

In this paper, we propose a guidance scheme for underactuated marine vehicles with collision-avoidance guarantees. The guidance scheme is based on a line-of-sight approach and ensures path-following when safety allows it, but deviates from the desired path if safety mandates it. We provide formal safety guarantees by proving forward invariance of the collision-free safe set using a barrier function. However, while barrier-function-based control schemes provide formal safety guarantees, the real-life performance is often lacking due to the challenge of manually tuning such controllers. We demonstrate that the performance of the control law can be improved by replacing a part of the control law by a neural network, while retaining the same formal safety guarantees.

Robust trajectory tracking control scheme using transformed velocities for asymmetric underactuated marine vehicles

The paper addresses the issue of trajectory tracking control for underactuated underwater vehicles whose model is described by quasi-velocities resulting from the decomposition of the inertia matrix. The control algorithm takes into account unmodeled dynamics and external disturbances. It is shown that such mathematical models can be diagonalized and described by inertial quasi-velocities (IQV). The control scheme consists of a kinematic velocity controller and a dynamic adaptive integral sliding mode control algorithm. The paper extends the concept based on velocity transformation and backstepping methods to systems with a symmetric inertia matrix. A proof of the stability of a closed system in IQV space was carried out. The proposed approach was verified on two 3 DOF models of underwater vehicles with constraints due to the application of thruster force limitations.

Modification of Nonlinear Controller for Asymmetric Marine Vehicles Moving in Horizontal Plane

This paper considers a trajectory-tracking control algorithm for underactuated marine vehicles moving horizontally in which the current in the North-East-Down frame is constant. This algorithm is a modification of a control scheme based on the input-output feedback linearization method for which the application condition is that the vehicle is symmetric with respect to the left and right sides. The proposed control scheme can be applied to a fully asymmetric model, and, therefore, the geometric center can be different from the center of mass in both the longitudinal and lateral directions. A velocity transformation to generalized vehicle equations of motion was used to develop a suitable controller. Theoretical considerations were supported by simulation tests performed for a model with 3 degrees of freedom, in which the performance of the proposed algorithm was compared with that of the original algorithm and the selected control scheme based on a combination of backstepping and integral sliding mode control approaches.

Trajectory Tracking Nonlinear Controller for Underactuated Underwater Vehicles Based on Velocity Transformation

This paper proposes an algorithm that performs the task of tracking the desired trajectory for underactuated marine vehicles (primarily underwater) that move horizontally. The control scheme, which takes into account model inaccuracies and external disturbances, was designed using the quantities obtained after the transformation of the dynamic equations of motion resulting from the decomposition of the inertia matrix. This, in turn, led to the equation of dynamics with a diagonal inertia matrix. A specific feature of the offered controller is its dual role. It not only allows tracking the desired trajectory, but at the same time, makes it possible to estimate the impact of dynamic couplings when the vehicle is in motion. Such an approach to the tracking task is important at the initial design stage when the choice of the control algorithm has not yet been decided and experimental tests have not been performed. This is feasible because the new variables after the velocity transformation include not only vehicle parameters, but also actual velocities and forces. Therefore, it is also possible to track the original variables. The theoretical results were followed up with simulation tests conducted on a model with three degrees of freedom for two underwater vehicles.

DOPH∞-based path-following control for underactuated marine vehicles with multiple disturbances and constraints

This paper presents a new robust path-following (PF) control method for underactuated marine vehicles with multiple disturbances and constraints. To improve the control performance and reduce the conservativeness of many PF control strategies described in the previous literature, which treated the multiple disturbances of the underactuated marine vehicle as a single equivalent disturbance, the multiple disturbances are categorized into two types according to their characteristics in this paper, i.e., the slowly varying disturbance and the H2-norm bounded disturbance. Then, a composite controller combining Disturbance-Observer-based control with H∞ control, which can be abbreviated as DOPH∞-based controller, is constructed for the control model. A disturbance observer is designed for estimating and eliminating the slowly varying disturbance, and the H∞ theory is used to attenuate the H2-norm bounded disturbance. Moreover, to improve the practicability of the control method in engineering applications, the virtual yaw angular velocity constraint and the actuator constraints are considered, and the auxiliary dynamic compensators are used to compensate for them. Finally, the closed-loop stability of the whole system is guaranteed. Simulations and comparative analyses are presented to demonstrate the effectiveness and robustness of the presented strategy.

A Quasi-Velocity-Based Tracking Controller for a Class of Underactuated Marine Vehicles

This paper investigates the trajectory tracking control problem for underactuated underwater vehicles, for which a model is expressed in terms of quasi-velocities arising from the inertia matrix decomposition. The control approach takes into account non-modeled dynamics and external disturbances and is suitable for symmetric vehicles. It is shown that such systems can be diagonalized using inertial quasi-velocities (IQVs). The strategy consists of the velocity controller and two adaptive integral sliding mode control algorithms. The proposed approach, introducing velocity transformation and using backstepping methods and integral sliding mode control, allows trajectory tracking for vehicles in described models with symmetric inertia matrix. Proof of the stability of the closed system was carried out using IQV. The proposed scheme has been verified on two 3 DOF models of underwater vehicles with thruster limitations. A brief discussion of the results is also given.

Application of a Trajectory Tracking Algorithm for Underactuated Underwater Vehicles Using Quasi-Velocities

In this work, an application of the trajectory tracking algorithm proposed in the literature for underactuated marine vehicles is presented. The main difference relies on that here the dynamics of the vehicle are expressed in terms of some quasi-velocities (QV). This fact has a double meaning. First of all, it is shown that using the QV, it is possible to control a vehicle in the absence of one variable because the works related to marine vehicles have only concerned fully actuated systems. In addition, a controller using QV provides information that gives some insight into vehicle dynamics and that is not available in classical equations of motion. The simulations done on two 3-DOF models of different underwater vehicles and using two desired trajectories show performance of the considered control strategy. A discussion of the presented control scheme and selected control approaches from recent years was also conducted, and the benefits of the proposed approach were pointed out.

Path Following of Underactuated Marine Vehicles Based on Model Predictive Control

Path Following of Underactuated Marine Vehicles Based on Model Predictive Control

Modified Line-of-Sight Guidance Law With Adaptive Neural Network Control of Underactuated Marine Vehicles With State and Input Constraints

This article presents a modified line-of-sight (LOS) guidance law and an adaptive neural network (NN) controller for underactuated marine vehicles in the presence of uncertainties and constraints. Unlike conventional LOS guidance, the proposed guidance law counteracts the drift caused by external disturbances to maintain zero cross-track error. Furthermore, an adaptive NN controller is designed using the barrier Lyapunov function (BLF) to deal with the system constraints and disturbances affecting unknown vehicle dynamics. The stability analysis of the adaptive controller guarantees the uniform ultimate boundedness of the closed-loop system. The proposed control strategy is verified in the simulation and experimental environment in the presence of external disturbances. Both simulation and experimental results confirm that the proposed modified LOS guidance law and adaptive NN controller guarantees asymptotic convergence to the desired path and maintains zero cross-track error despite environmental disturbances.

Nonlinear Model Predictive Trajectory Tracking Control of Underactuated Marine Vehicles: Theory and Experiment

The article studies the trajectory tracking control problem of underactuated marine vehicles via the nonlinear model predictive control (NMPC) strategy, where practical control and state constraints present. It is a well-known challenging issue that the conventional NMPC is not applicable for underactuated marine vehicles, due to the fact that there does not exist a local static continuous state-feedback controller to stabilize the underactuated dynamics. To resolve this issue, this article proposes to construct an auxiliary time-varying tracking controller to aid terminal constraint design in the NMPC framework, where the time-varying tracking controller borrows the ideas from Lyapunov's direct method and backstepping approach. Based on this, a novel NMPC algorithm is designed to ensure trajectory tracking control of underactuated marine vehicles. Furthermore, a systematic parameter design approach is developed. Under the designed parameters, we show that the tracking error system is input-to-state stable (ISS). Finally, the effectiveness of the designed algorithm is verified by thorough simulation and hardware experiments.

Hyperbolic-Tangent LOS Guidance-Based Finite-Time Path Following of Underactuated Marine Vehicles

In this article, a novel hyperbolic-tangent line-of-sight (LOS) guidance-based finite-time path following (HLOS-FPF) framework is created to render an underactuated marine vehicle (UMV) rapidly and accurately follow the desired path, in the presence of complex unknowns including internal dynamics, external disturbances, and arbitrary sideslip. By defining a virtually desired sideslip angle of which the tangent-nonlinearity is exactly identified by a finite-time sideslip observer, the hyperbolic-tangent LOS (HLOS) guidance laws collaboratively governing heading, surge, and virtual ship velocity are devised in a finite-time manner such that cross-track error sensitively excites heading guidance. With the aid of nonsmooth auxiliary dynamics, guidance errors are finely dominated with finite-time convergence. Finite-time heading and surge controllers are further synthesized by integral and nonsingular terminal sliding-mode techniques, and ensure that HLOS guidance signals can be exactly tracked, whereby complex unknowns are exactly compensated by finite-time unknown observer. Eventually, nonsmooth analysis together with Lyapunov approach guarantees that the entire HLOS-FPF scheme is globally finite-time stable and contributes to exact path-following under heading-surge collaborative guidance. Simulation results and comprehensive comparisons with typical methods demonstrate remarkable superiority of the innovative HLOS-FPF scheme.

Surge-Heading Guidance-Based Finite-Time Path Following of Underactuated Marine Vehicles

In this paper, a surge-heading guidance-based finite-time path-following control (SHG-FPC) scheme is created for an underactuated marine vehicle with complex unknowns. In lieu of line-of-sight guidance, both surge and heading can be guided by adapting to path-following errors and this can greatly enhance the decision-making autonomy pertaining to guidance of kinematics and dynamics, simultaneously. Complex unknowns can be exactly identified by virtue of the devised finite-time uncertainty observer (FUO), by which FUO-based nonsmooth control laws are able to achieve accurate guidance tracking, and thereby, contributing to entire finite-time path-following performance with strong robustness. Simulation results demonstrate the remarkable performance of the proposed SHG-FPC scheme.

Path following control of an underactuated unmanned marine vehicle with model asymmetry in the presence of ocean current disturbances

Path following control system of an underactuated unmanned marine vehicle is an important guarantee for its successful operation, the path following control problem of an underactuated and asymmetrical unmanned marine vehicle sailing in the presence of ocean current disturbances is addressed. Asymmetry of the unmanned marine vehicle model and higher order velocity coupling terms of damping coefficients of the unmanned marine vehicle are discussed, which would improve the accuracy of the path following control system. A kind of global differential homeomorphism transformation design is proposed to solve the difficulty of nonzero term appearing in the non-diagonal elements of the system inertia coefficient matrix and damping coefficient matrix, which is caused by the model asymmetry of unmanned marine vehicle. An improved line-of-sight guidance algorithm is presented by introducing longitudinal position error and tracking error weight factor into traditional line-of-sight algorithm, which could speed up the path following process, meanwhile the method could be extended to the application of curve path following. Virtual velocity in the tangent direction of the path to be followed is designed for the control system, by increasing a virtual control input, the underactuated control system is simplified, and the higher order velocity coupling terms of damping coefficients are integrated considered in the virtual control law. Stability of the path following control algorithm proposed for unmanned marine vehicle is proved by Lyapunov theory, and some simulation experiments are carried out to verify the effectiveness of the path following control system designed.

Experimental Verification of a Coordinated Path-Following Strategy for Underactuated Marine Vehicles.

This work presents the results of an experimental verification of a coordinated path following strategy for underactuated marine vehicles. The coordinated path following strategy is presented, and is then experimentally verified using three autonomous underwater vehicles. The vehicles are required to coordinate their motion along spatially separated straight-line paths to obtain a desired formation. The vehicles are steered to the paths using an integral line-of-sight guidance approach that allows the vehicles to reject constant ocean currents. Simultaneously, the coordination is achieved by adjusting the velocity based on the along-path distance. First, simulation results are presented, which serve as benchmarks for the experimental results. Furthermore, the simulations are used to show the effect of changing different parameters. The simulation results are performed using high-fidelity hardware simulation models. The results obtained from experiments in the harbor of Porto are then presented and compared with the results of the simulation.

Transverse function control with prescribed performance guarantees for underactuated marine surface vehicles

SummaryThis paper studies the problem of stabilizing reference trajectories (also called as the trajectory tracking problem) for underactuated marine vehicles under predefined tracking error constraints. The boundary functions of the predefined constraints are asymmetric and time‐varying. The time‐varying boundary functions allow us to quantify prescribed performance of tracking errors on both transient and steady‐state stages. To overcome difficulties raised by underactuation and nonzero off‐diagonal terms in the system matrices, we develop a novel transverse function control approach to introduce an additional control input in backstepping procedure. This approach provides practical stabilization of any smooth reference trajectory, whether this trajectory is feasible or not. By practical stabilization, we mean that the tracking errors of vehicle position and orientation converge to a small neighborhood of zero. With the introduction of an error transformation function, we construct an inverse‐hyperbolic‐tangent‐like barrier Lyapunov function to show practical stability of the closed‐loop systems with prescribed transient and steady‐state performances. To deal with unmodeled dynamic uncertainties and external disturbances, we employ neural network (NN) approximators to estimate uncertain dynamics and present disturbance observers to estimate unknown disturbances. Subsequently, we develop adaptive control, based on NN approximators and disturbance estimates, that guarantees the prescribed performance of tracking errors during the transient stage of on‐line NN weight adaptations and disturbance estimates. Simulation results show the performance of the proposed tracking control.

Fuzzy Uncertainty Observer-Based Path-Following Control of Underactuated Marine Vehicles with Unmodeled Dynamics and Disturbances

Subject to complex unknown nonlinearities including unmodeled dynamics, uncertainties, and unknown disturbances, a novel fuzzy uncertainty observer-based path-following control (FUO-PFC) scheme for an underactuated marine vehicle is proposed in this paper. Main contributions are as follows: (1) A surge-varying line-of-sight guidance law is devised innovatively where the guided surge velocity adapts to cross-track error, thereby significantly enhancing robustness and agility of the guidance system; (2) unknown nonlinearities are compositely estimated by the constructed fuzzy uncertainty observer and compensated accurately in the control system; (3) robust surge and heading tracking controllers based on the FUO are developed to ensure that surge and heading tracking errors and uncertainty observation errors are uniformly ultimately bounded. Simulation studies are conducted to demonstrate remarkable performance of the proposed FUO-PFC scheme.

Trajectory Tracking and Path Following for Underactuated Marine Vehicles

In this paper, we present a control strategy for trajectory tracking and path following of generic paths for underactuated marine vehicles. Our work is inspired and motivated by previous works on ground vehicles. In particular, we extend the definition of the hand position point, introduced for ground vehicles, to autonomous surface vehicles and autonomous underwater vehicles, and then use the hand position point as output for a control strategy based on the input–output feedback linearization method. The presented strategy is able to deal with external disturbances affecting the vehicle, e.g., constant and irrotational ocean currents. Using the Lyapunov analysis, we are able to prove that the closed-loop system has an external dynamics that is globally exponentially stable and an internal dynamics that has ultimately bounded states, both for the trajectory tracking and the path following control problems. Finally, we present a simulation case study and experimental results in order to validate the theoretical results.

Semiglobal Exponential Stability of a Counter-Current and Co-Current Guidance Scheme

A control technique for counter-current and co-current guidance of underactuated marine vehicles is revisited and stronger stability properties are shown. In particular, the stronger property of uniform semiglobal exponential stability is shown for the complete multiple-equilibria closed loop system, that has previously been shown to be uniformly semiglobally asymptotically stable and uniformly locally exponentially stable. Compared to the original proof, the analysis presented in this paper does not invoke the theory developed for cascaded systems; it follows instead a direct approach where a Lyapunov function for the full system is identified. This shows that analysing stability of a complex non-linear system by means of proper Lyapunov function candidates can yield significant results, leaving however the designer with the challenging task of identifying the right candidate. The theory is supported by simulations.