Lyapunov-LMPC: 水下自主航行器轨迹跟踪控制的优化策略

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本篇研究论文探讨了自主水下航行器(AUV)的轨迹跟踪控制问题，着重于利用Lyapunov模型预测控制(LMPC)方法来提升AUV的导航性能。Lyapunov理论在控制领域中具有重要意义，因为它能够确保系统的稳定性，尤其是在处理非线性系统时。作者Chao Shen、Yang Shi和Brad Buckham针对AUV设计了一种新颖的基于Lyapunov的模型预测控制器框架。这个框架的关键在于考虑实际操作限制，如推进器的饱和问题，通过在线优化算法将这些约束纳入控制器的设计过程，从而提高了轨迹跟踪的精确性和鲁棒性。通过采用非线性反步跟踪控制策略，研究人员能够在建立的LMPC问题中构建收缩约束，理论上保证了闭环系统的稳定性。论文的核心内容包括对满足递归可行性的充分条件的分析，这关系到控制器的连续运行和闭环系统的稳定状态。这些条件提供了对系统行为的深入理解，使得控制器能够在不断变化的环境中保持稳定并有效跟踪预设的轨迹。此外，该研究还可能探讨了控制算法的实时性能、计算效率以及如何在有限的计算资源下实现最佳的控制决策。这篇论文通过Lyapunov理论与模型预测控制的结合，为AUV的轨迹跟踪控制提供了一个创新且实用的方法，有助于提高AUV在水下环境中的自主导航能力，同时兼顾了实际操作中的复杂约束和动态性能需求。这对于水下探索、海洋科研以及潜在的工业应用具有重要的理论和实践价值。

5796 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 65, NO. 7, JULY 2018

Trajectory Tracking Control of an Autonomous

Underwater Vehicle Using Lyapunov-Based

Model Predictive Control

Chao Shen , Member, IEEE, Yang Shi , Fellow, IEEE, and Brad Buckham, Member, IEEE

Abstract—This paper studies the trajectory tracking con-

trol problem of an autonomous underwater vehicle (AUV).

We develop a novel Lyapunov-based model predictive con-

trol (LMPC) framework for the AUV to utilize computa-

tional resource (online optimization) to improve the trajec-

tory tracking performance. Within the LMPC framework, the

practical constraints, such as actuator saturation, can be

explicitly considered. Also, the thrust allocation subprob-

lem can be addressed simultaneously with the LMPC con-

troller design. Taking advantage of a nonlinear backstep-

ping tracking control law, we construct the contraction con-

straint in the formulated LMPC problem so that the closed-

loop stability is theoretically guaranteed. Sufﬁcient condi-

tions that ensure the recursive feasibility, and hence the

closed-loop stability, are provided analytically. A guaran-

teed region of attraction is explicitly characterized. In the

meantime, the robustness of the tracking control can be

improved by the receding horizon implementation that is

adopted in the LMPC control algorithm. Simulation results

on the Saab SeaEye Falcon model AUV demonstrate the sig-

niﬁcantly enhance trajectory tracking control performance

via the proposed LMPC method.

Index Terms—Autonomous underwater vehicle (AUV),

backstepping, Lyapunov-based nonlinear control, model

predictive control (MPC), thrust allocation (TA), trajectory

tracking.

I. INTRODUCTION

HE autonomous underwater vehicles (AUVs) exemplify

the recent advances in the marine robotics ﬁeld and

has been receiving a growing interest from both industry and

academia due to their potential to substantially reduce risks and

operational costs in various submarine projects [1]. The core

feature of the AUV refers to the capability of reacting appro-

priately during the missions without intervention from human

Manuscript received June 19, 2017; revised September 6, 2017, and

October 24, 2017; accepted November 5, 2017. Date of publication De-

cember 4, 2017; date of current version March 6, 2018. This work was

supported in par t by the Natural Sciences and Engineering Research

Council of Canada, and in part by the National Natural Science Foun-

dation of China under Grant 61473116. (Corresponding author: Yang

Shi)

The authors are with the Department of Mechanical Engineering

and the Institute for Integrated Energy Systems (IESVic), University of

Victoria, Victoria, BC V8W 3P6, Canada (e-mail: shenchao@uvic.ca;

yshi@uvic.ca; bbuckham@uvic.ca).

Color versions of one or more of the ﬁgures in this paper are available

online at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TIE.2017.2779442

operators, which, on the other hand, justiﬁes an elaborated con-

trol system [2]–[4].

The trajectory tracking is one fundamental functionality of

the AUV control system, but is never an easy task. The highly

nonlinear and cross-coupled system dynamics together with the

unpredictable complex underwater environment, which intro-

duces considerable disturbances and uncertainties challenges

the controller design. There exist plenty of research studies in

the literature devoted to the AUV trajectory tracking control.

When the desired trajectory is piecewise linear (i.e., way-point

tracking), the assumptions for l ocal linearization can hold, and

the classic linear control techniques are applied to solve the tra-

jectory tracking problem [5]. The linear control methods, such as

the proportional-integral-derivative (PID) and linear-quadratic-

regulator are often preferred due to their easy implementation.

However, linear control techniques will be no longer effective

if the desired trajectory represents a curve in the workspace,

because the curve trajectory, by nature, emphasizes the non-

linearity of the AUV motion. Therefore, the nonlinear control

techniques are often resorted to for the tracking controller de-

sign. The Lyapunov-based backstepping control (BSC) repre-

sents the mainstream method for the AUV tracking control be-

cause the control law exploits those “good” nonlinearities in the

system dynamics, which gains additional robustness compared

to the inverse dynamics control (feedback linearization). Ex-

amples include [6] and [7]. In [6], the AUV trajectory tracking

control considers the complete kinematics and dynamics of the

motion and design the control law using the backstepping tech-

nique. An output feedback tracking control via Lyapunov-based

backstepping can be found in [7]. Due to the insensitivity to

model uncertainties, the sliding model control (SMC) becomes

the other mainstream nonlinear method for the AUV trajectory

tracking control. In [8], an enhanced trajectory tracking perfor-

mance is obtained by the combining the SMC, PID, and robust

control. To eliminate the main drawback associated with the

SMC, known as the “chattering” effect, in [9], an adaptive law

is incorporated in the control law design. In [10], the higher

order sliding mode is used for the chattering-free trajectory

tracking control. Most recent studies on autonomous vehicle

tracking control try to address more practical issues [11]–[13].

The system constraints, such as thrust limit and safe operat-

ing area are inevitable in real AUV applications, hence, it is

desired to consider these constraints in the tracking controller

design.

See http://www.ieee.org/publications

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