﻿ 基于滑模控制的欠驱动微型AUV轨迹跟踪控制
 舰船科学技术  2023, Vol. 45 Issue (24): 97-101    DOI: 10.3404/j.issn.1672-7649.2023.24.018 PDF

1. 上海工程技术大学 机械与汽车工程学院 智能协作机器人研究所 上海 201620;
2. 同济大学 机械与能源工程学院 机器人技术与多体系统实验室 上海 201804

Trajectory tracking control of underactuated micro-AUV based on sliding mode control
SUN Dong1, TANG Qi-rong2, LI Jiang2, LIU Ming-hao2, CUI Guo-hua1
1. Intelligent Collaborative Robot Research Institute, School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai 201620, China;
2. Laboratory of Robotics and Multibody System, School of Mechanical Engineering, Tongji University, Shanghai 201804, China
Abstract: For the characteristics of the micro autonomous underwater vehicle (AUV), a sliding mode variable structure control method based on dynamic sliding modulus is proposed to improve the response speed and control accuracy of 3D trajectory tracking. Firstly, based on the dynamic model of micro-AUV, a trajectory tracking controller based on the sliding mode dynamic characteristics is established. Then the stability of the controller is verified with Lyapunov theory. Finally, the simulation experiment is carried out on the 3D trajectory tracking of the micro AUV in Matlab environment. The result shows that the proposed sliding mode controller has high control effect and fast response, and can effectively realize the trajectory tracking control in the underwater 3D space.
Key words: autonomous underwater vehicle     trajectory tracking     sliding mode control     Lyapunov theory
0 引　言

1 微型自主式水下航行器建模

 图 1 微型AUV坐标系及轨迹跟踪 Fig. 1 Coordinate system and trajectory tracking of micro AUV
 $\left\{ \begin{gathered} \dot \eta = J(\eta )\mu ，\\ {\boldsymbol{M}}(\mu )\dot \mu + {\boldsymbol{C}}(\mu ,\dot \mu )\mu + {\boldsymbol{D}}(\mu ,\dot \mu )\mu + g(\eta ) = \tau - {\tau _d}。\\ \end{gathered} \right.$ (1)

 $\left\{ {\begin{array}{*{20}{l}} {\dot x = {U_B}\cos {\gamma _Q}\cos {\chi _Q}}，\\ {\dot y = {U_B}\sin {\gamma _Q}\cos {\chi _Q}} ，\\ {\dot z = {U_B}\sin {\chi _Q}} ，\\ {{{\dot \chi }_Q} = q + \dot \alpha }，\\ {{{\dot \gamma }_Q} = r/\cos \theta + \dot \beta } 。\end{array}} \right.$ (2)

 $\left\{ {\begin{array}{*{20}{l}} {{{\dot x}_e} = {y_e}{{\dot \gamma }_P}\cos {\chi _P} - {z_e}{{\dot \chi }_P} + {U_{{B}}}\cos {\gamma _e}\cos {\chi _e} - {U_P}} ，\\ {{{\dot y}_e} = - {x_e}{{\dot \gamma }_P}\cos {\chi _P} - {z_e}{{\dot \gamma }_P}\sin {\chi _P} + {U_{{B}}}\sin {\gamma _e}\cos {\chi _e}}，\\ {{{\dot z}_e} = {x_e}{{\dot \chi }_P} - {y_e}{{\dot \gamma }_P}\sin {\chi _P} - {U_{{B}}}\sin {\chi _e}}，\\ {{{\dot \theta }_e} = q + {{\dot \alpha }_e} - {{\dot \chi }_P}}，\\ {{{\dot \psi }_e} = r/\cos \theta + {{\dot \beta }_e} - {{\dot \gamma }_P}} 。\end{array}} \right.$ (6)

 ${U_P} = {U_{{B}}}\cos {\psi _e}\cos {\theta _e} + \kappa {x_e} \text{，}$ (7)

 $\dot \mu = \frac{{{U_{\text{B}}}\cos {\psi _e}\cos {\theta _e} + \kappa {x_e}}}{{\sqrt {\dot x_P^2 + \dot y_P^2 + \dot z_P^2} }} \text{。}$ (8)

${\theta _e} = \arctan \left( {{z_e}/\Delta z} \right) $${\psi _e} = \arctan \left( { - {y_e}/\Delta y} \right) 代入式(8)可得：  {U_P} = {U_{\text{B}}}\frac{{\Delta y}}{{\sqrt {y_e^2 + \Delta {y^2}} }}\frac{{\Delta z}}{{\sqrt {z_e^2 + \Delta {z^2}} }} + \kappa {x_e} \text{。} (9) 式中， \Delta y$$ \Delta z$为附加的时变扰动参数。

2 微型自主式水下航行器滑模控制

2.1 纵向轨迹跟踪控制器

 $\left\{ \begin{gathered} {s_{11}}({x_e}) = {k_{11}}{\text{sat}}({k_{12}}{x_e}) + {{\dot x}_e}，\\ {s_{12}}({s_{11}}) = {k_{13}}{\text{sat}}({k_{14}}{s_{11}}) + {{\dot s}_{11}}。\\ \end{gathered} \right.$ (10)

 $\dot n = - {k_{15}}{s_{12}} - {k_{16}}{{\rm{sgn}}} ({s_{12}}) \text{，}$ (11)

 $\dot n = {K_M}({n_r} - n)/{T_M} \text{。}$ (12)

 ${X_{{\text{prop}}}} = \rho {n^2}Df\left( {J,{R_e},{F_n}} \right) \text{。}$ (13)

 ${n_r} = n - {T_M}[{k_{15}}{s_{12}} + {k_{16}}{{\rm{sgn}}} ({s_{12}})] 。$ (14)

 ${V_1} = \frac{{s_{12}^2}}{2} \text{。}$ (15)

 ${\dot V_1} = {s_{12}}{\dot s_{12}} = {s_{12}}\frac{{\partial {s_{12}}}}{{\partial n}}\dot n \text{。}$ (16)

 $\frac{{\partial {s_{12}}}}{{\partial n}} = \frac{{\partial {{\ddot x}_e}}}{{\partial n}} = \frac{\partial }{{\partial n}}({\dot v_t}\cos {\theta _e}) \geqslant {\text{0}} \text{。}$ (17)

3 仿真验证 3.1 对象

 图 2 微型AUV三维模型 Fig. 2 3D model of micro AUV

3.2 结果及分析

 图 3 微型AUV螺旋下潜空间运动轨迹跟踪 Fig. 3 Trajectory tracking of micro AUV in spiral diving

 图 4 微型AUV纵向运动轨迹跟踪 Fig. 4 Trajectory tracking of micro AUV in forward motion

 图 5 微型AUV横向运动轨迹跟踪 Fig. 5 Trajectory tracking of micro AUV in lateral motion

 图 6 微型AUV垂向运动轨迹跟踪 Fig. 6 Trajectory tracking of minor AUV in vertical motion

 图 7 微型AUV姿态偏航角控制 Fig. 7 Yaw angle control of micro AUV attitude

 图 8 微型AUV姿态纵倾角控制 Fig. 8 Pitch angle control of micro AUV attitude

 图 9 微型AUV姿态横滚角控制 Fig. 9 Roll angle control of micro AUV attitude
4 结　语

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