﻿ 基于LOS导航算法的无人船路径跟踪控制
 舰船科学技术  2024, Vol. 46 Issue (5): 109-114    DOI: 10.3404/j.issn.1672-7649.2024.05.020 PDF

Unmanned vessel path tracking control based on LOS navigation algorithm
LI Shao-peng, HUANG Li-hua, ZHANG Lei, GAO Yang
Wuhan Second Ship Design and Research Institute, Wuhan 430000, China
Abstract: In order to solve the path tracking control issue of unmanned vessel, an adaptive path tracking control algorithm based on line-of sight(LOS) navigation algorithm and fuzzy PID control is proposed. Firstly, the path planning problem is transformed into a heading control problem according to the LOS algorithm. Then the heading control of unmanned vessel is carried out by fuzzy PID control algorithm. Simulation results show that the proposed algorithm has high path following accuracy, small lateral offset and smooth tracking path, which have some reference value for the path tracking control of unmanned vessel.
Key words: unmanned vessel     LOS     path tracking     PID
0 引　言

1 无人船运动模型 1.1 船体运动模型

 图 1 水平面运动坐标系 Fig. 1 Motion coordinate system of horizontal

 ${\scriptsize T = \left[ \begin{gathered} \cos \psi \cos \theta {\text{ cos}}\psi {\text{sin}}\theta {\text{sin}}\phi - \sin \psi \cos \phi {\text{ }}\cos \psi \sin \theta \cos \phi + \sin \psi \sin \phi {\text{ }} \\ \sin \psi \cos \theta {\text{ sin}}\psi {\text{sin}}\theta {\text{sin}}\phi {\text{ + cos}}\psi {\text{cos}}\phi {\text{ }}\sin \psi \sin \theta \cos \phi - \cos \psi \sin \phi \\ {\text{ }} - \sin \theta {\text{ }}\cos \theta \sin \phi {\text{ }}\cos \theta \cos \phi \\ \end{gathered} \right]。}$ (1)

 $R(\psi ) = \left[ \begin{array}{cccccccccccccc} \cos \psi & - {\text{sin}}\psi & 0 \\ \sin \psi& {\text{ cos}}\psi & {\text{ 0}} \\ 0 & 0 & 1 \end{array} \right]，$ (2)

 $\dot \xi = u\cos \psi - v\sin \psi ，$ (3)
 $\dot \eta = u\sin \psi + v{\text{cos}}\psi ，$ (4)

 $\dot \psi = r。$ (5)

 $\begin{split} & m\left[ {\dot u - vr - {x_G}{r^2} - {y_G}\dot r} \right] = X = {X_H} + {X_E} + {X_T} ，\\ & m\left[ {\dot v + ur - {y_G}{r^2} + {x_G}\dot r} \right] = Y = {Y_H} + {Y_E} + {Y_T}，\\ & {I_z}\dot r + m\left[ {{x_G}(\dot v + ur) - {y_G}(\dot u - vr)} \right] = N = {N_H} + {N_E} + {N_T} 。\end{split}$ (6)

 $G = G(u,v,r,\dot u,\dot v,\dot r)。$ (7)

 $u = U{\text{ }}v = r = \dot u = \dot v = \dot r = 0。$ (8)

 $\begin{split} (m - {X_{\dot u}})\dot u =& {X_u}u + {X_{uu}}{u^2} + {X_{uuu}}{u^3} + {X_{vv}}{v^2} + {X_{rr}}{r^2} +\\ & {X_{vr}}vr + {X_E} + {X_T}，\end{split}$ (9)
 $\begin{split} (m - {Y_{\dot v}})\dot v + (m{x_G} - {Y_{\dot r}})\dot r = & {Y_v}v + {Y_r}r + {Y_{vvv}}{v^3} + {Y_{vvr}}{v^2}r +\\ & {Y_{uv}}uv + {Y_{ur}}ur + {Y_E} + {Y_T}，\\[-1pt] \end{split}$ (10)
 $\begin{split} &(m{x_G} - {N_{\dot v}})\dot v + ({I_z} - {N_{\dot r}})\dot r = {N_v}v + {N_r}r + {N_{vvv}}{v^3} +\\ & {N_{vvr}}{v^2}r + {N_{uv}}uv + {N_{ur}}ur + {N_E} + {N_T}。\end{split}$ (11)

 $\begin{split} & {f_m} = (m - {Y_{\dot v}})({I_z} - {N_{\dot r}}) - (m{x_G} - {Y_{\dot r}})(m{x_G} - {N_{\dot v}}) ，\\ & {f_x} = {X_u}u + {X_{uu}}{u^2} + {X_{uuu}}{u^3} + {X_{vv}}{v^2} + {X_{rr}}{r^2} + {X_{vr}}vr + {X_E} + {X_T}，\\ & {f_y} = {Y_v}v + {Y_r}r + {Y_{vvv}}{v^3} + {Y_{vvr}}{v^2}r + {Y_{uv}}uv + {Y_{ur}}ur + {Y_E} + {Y_T}，\\ & {f_n} = {N_v}v + {N_r}r + {N_{vvv}}{v^3} + {N_{vvr}}{v^2}r + {N_{uv}}uv + \\ & \qquad {N_{ur}}ur + {N_E} + {N_T}。\\[-1pt] \end{split}$ (12)
 $\begin{split} & \dot u = {f_x}/(m - {X_{\dot u}})，{\text{ }}\; \dot \xi = u\cos \psi - v\sin \psi，\\ & {\text{ }}\dot v = {f_y} \cdot ({I_z} - {N_{\dot r}})/{f_m} - {f_n} \cdot (m{x_G} - {Y_{\dot r}})/{f_m}，\\ & \dot \eta = u\sin \psi + v{\text{cos}}\psi，{\text{ }} \\ & \dot r = {f_n} \cdot (m - {Y_{\dot v}})/{f_m} - {f_y} \cdot (m{x_G} - {N_{\dot v}})/{f_m}，{\text{ }}\; \dot \psi = r 。\end{split}$ (13)
1.2 海洋环境风、浪、流数学模型

1）海风干扰力

 $\begin{split} & {u_R} = {V_T}\cos ({\psi _T} - \psi ) + u，\\ & {v_R} = {V_T}\sin ({\psi _T} - \psi ) - v 。\end{split}$ (14)

 $\left\{ \begin{gathered} {X_{wind}} = \frac{1}{2}{C_X}({\alpha _R}){\rho _a}V_R^2{A_T} ，\\ {Y_{wind}} = \frac{1}{2}{C_Y}({\alpha _R}){\rho _a}V_R^2{A_L}，\\ {N_{wind}} = \frac{1}{2}{C_N}({\alpha _R}){\rho _a}V_R^2{A_L}L 。\end{gathered} \right.$ (17)

3 仿真结果分析

1）无接纳圆LOS导航算法+经典PID控制轨迹跟踪仿真。目标路径为夹角90°的折线路径，从图可以看出在转角处没有接纳圆的时候转向不平滑，会有较大的超调和波动，但一段时间后也能完成路径跟踪目标，转向部分有较大的偏移量。

2）有接纳圆LOS导航算法+经典PID控制轨迹跟踪仿真。对比图7可知，转向处增加接纳圆后会根据接纳圆的引导提前转向，从而使得转向过程更平滑，横向偏移量减小。

 图 6 无接纳圆轨迹跟踪仿真结果 Fig. 6 Simulation results of trajectory tracking without acceptance circle

 图 7 有接纳圆经典PID控制轨迹跟踪仿真结果 Fig. 7 Simulation results of classic PID control trajectory tracking with acceptance circle

3）有接纳圆LOS导航算法+模糊PID控制轨迹跟踪仿真。在使用模糊PID控制后，无人船可以根据航行状态实时改变PID参数大小，从而改善控制器精度，对比图7图8可知，控制过程的横向偏移量有了明显减少。

 图 8 有接纳圆模糊PID控制轨迹跟踪仿真结果 Fig. 8 Simulation results of fuzzy PID control trajectory tracking with acceptance circle

4 结　语

 [1] LEFEBER E, PETTERSEN K Y, NIJMEIJER H. Tracking control of an underactuated ship[J]. IEEE Transactions on Control Systems Technology, 2003, 11(1): 52-61. DOI:10.1109/TCST.2002.806465 [2] FOSSEN T I, LEKKAS A M. Direct and indirect adaptive integral line-of-sight path-following controllers for marine craft exposed to ocean currents[J]. International Journal of Adaptive Control and Signal Processing, 2017, 31(4): 445-463. DOI:10.1002/acs.2550 [3] 韩鹏, 刘志林, 周泽, 等. 基于LOS法的自航模航迹跟踪控制算法实现[J]. 应用科技, 2018, 45(3): 66-70. [4] SPERRY E. Directional stability of automatically steered bodies. Journal of American Society of Naval Engineers, 1922, 42(1): 2−13 [5] SUGIMOTO A. A new autopilot system with condition adaptivity. Proceedings 5th ship Control systems symposium, Annapolis, Maryland, USA, 1978, 105−111 [6] 张旋武. 基于强化学习的无人船路径跟随控制[D]. 武汉: 武汉理工大学, 2021. [7] 李超. 基于CMAC的无人船模糊PID航迹控制技术研究[D]. 武汉: 湖北工业大学, 2019. [8] 柳晨光. 基于预测控制的无人船运动控制方法研究[D]. 武汉: 武汉理工大学, 2019. [9] 刘陆. 欠驱动无人船的路径跟踪与协同控制[D]. 大连: 大连海事大学, 2018. [10] 秦晋盟. 无人船路径跟踪滑模控制研究[D]. 大连: 大连海事大学, 2021. [11] 张薇. 船舶运动智能PID控制研究[D]. 哈尔滨: 哈尔滨工程大学, 2009. [12] 王艳. 无人船建模及路径跟踪控制[D]. 杭州: 浙江大学, 2020.