Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Neural Sliding Mode Control for Path Tracking of Underactuated Ships Considering Input Saturation
He Zhang, Ji Zeng, Shu-kang Tong, Pan Gao, Qing-wei Wang
Merchant Marine College, Shanghai Maritime University
Shanghai , China

dynamic models via the transformation of frames or the geometricprinciples, such as the line-of-sight and the framework of Serret-Frenet.
A guidance strategy of the switching LOS proposed in the references of(Borhaug, Pavlov et al. 2011, Liu, N Eg Enborn et al. 2018) improved
the convergence of path tracking error and reduced the calculation of
LOS angle. LOS and reduced-ordered extended state observer (ESO)
technologies were combined in the reference (Liu, Wang et al. 2016).
The time-varying sideslip angle induced by the disturbance of external
environments could be accurately identified via the reduced-orderedESO. The references of (Zhao and Dong 2020) applied the SerretFrenet framework to reduce the dimension of controlling output, andsimplified the design of controller to complete the accurate pathtracking. The other strategy was to build an ideal virtual ship which
could sail along the reference path without considering the inertia anddamping, thus turning the problem of the path tracking into the trackingof the virtual ship. A guidance algorithm of dynamics virtual ship
(DVS) was proposed in references of (Zhang and Zhang 2014, Deng,Zhang et al. 2019). The introduce of DVS between the guiding ship andthe actual ship ensured the ships could return to the planned track
through the steering device with the maintenance of the velocity when
the ships deviated from the reference track greatly.

ABSTRACT
Aiming at the path tracking problem of underactuated ships, a neuralnetwork sliding mode control method considering the saturation
characteristics of control input is proposed in this paper. In order tobetter integrate with navigation practice, the influence of non diagonal
elements of mass matrix and damping matrix is considered in theestablishment of underactuated ship model. The input saturation
problem is considered in the design of the controller, and the additional
virtual control rate can be designed to simultaneously deal with theinput saturation and underdrive problems. At the same time, thedynamic surface control (DSC) is introduced to estimate the derivativeof the virtual control law to avoid the computational burden of direct
derivation. The neural network minimum parameter learning method isused to deal with the uncertainty of the model and approximate thenonlinear term of the system. The adaptive law and practical control
law of the system are designed with sliding mode control. The stabilityof the closed-loop system is proved by Lyapunov direct method. The
simulation experiment results show that the control strategy proposedin this paper is more in line with actual engineering requirements while
ensuring fast and efficient path tracking.

KEY WORDS: Underactuated ships; path following; input saturation;neural network; sliding mode.

INTRODUCTION
Path tracking is one of the typical scenarios for the research of ship
controlling, which usually includes three parts, i.e., path planning,
guidance strategy and control strategy. Among these, the controlstrategy is the most challenging problem, which requires thecomprehensive consideration of underactuated characteristics, theinterference of external environments and the uncertainty of shipmodels (Li, Tong et al. 2016). With assistance of modern advanced
control theory, great research achievements have been obtained for theabove problems. However, some research results are not compatible
with the actual ships due to the imbalance of information between thecomplex algorithms and the practical applications.
The guidance strategies to solve the problem of the path tracking ofunderactuated ships can be classified into two categories (Li, Chen et al.
2017). One category was to reduce the tracking error under the1913

The above methods were not applicable in the actual navigation
practice although these methods solved the problem of underactuatedship tracking in the mathematical derivation successfully. The
references of (Perera and Soares 2012, Qin, Lin et al. 2016) assumed
that the mass matrix and damping matrix of underactuated ships werediagonal matrices. The cascade structure was destroyed under thisassumption, resulting in many problems in the design of the controller.
Whereas, the mass matrix and damping matrix of underactuated ships
were not diagonal in the actual situation, leading to the invalidation ofthe assumption. An approach to solve this problem was proposedconsidering the non-diagonal matrix in the references of (Meng, Chenet al. 2017, Zhu and Du 2020). The reference of (Do 2010) proposed
the concept of actual control. Most previous studies ignored theconstraint produced by the actuators, and the analysis of these
constraints was a necessary condition to ensure the applicability of thecontrol schemes. The references of (Shojaei and Khoshnam 2015,
Zheng and Sun 2016, Qiu, Wang et al. 2018) regarded the input
saturation constraint of actuators as one of the important researchcontents. The reference of (Liang, Lin et al. 2021) proposed that theneglection of the input saturation in the design of controllers would