﻿ 基于指数趋近滑模控制的水下机器人-机械手系统轨迹跟踪
 舰船科学技术  2019, Vol. 41 Issue (1): 54-58 PDF

Trajectory tracking of an underwater vehicle-manipulator system based on sliding mode control with exponential reaching law
TANG Qi-rong, DENG Zhen-qiang, LI Ying-hao, CHEN Di
Laboratory of Robotics and Multibody System, School of Mechanical Engineering, Tongji University, Shanghai 201804, China
Abstract: For the underwater vehicle-manipulator system, it is necessary to reach the predetermined trajectory quickly and accurately, so as to implement tasks. A sliding mode variable structure control method based on the exponential reaching law is proposed to improve the response speed and control accuracy of the underwater vehicle-manipulator system as well as reduce high frequency chattering of the system. Firstly, based on the dynamic model of underwater vehicle-manipulator system, a sliding mode controller combing exponential reaching law and sliding mode variable structure control method is established. Then the stability of the controller is verified with Lyapunov theory. After that, the trajectory tracking control simulation of the system is performed in Matlab environment. The simulation results show that the proposed sliding mode control system has a faster response and smaller control errors. Moreover, it can realize the trajectory control of the underwater vehicle-manipulator system effectively.
Key words: UVMS     trajectory tracking     sliding mode control     exponential reaching law     chattering
0 引　言

1 水下机器人-机械手系统建模

 图 1 水下机器人-机械手系统坐标系 Fig. 1 Coordinate system of UVMS

 \begin{align} & {{\xi }} = {\left[ {x\;y\;z\;\varphi \;\theta \;\psi \;{q_1}\; \cdot \cdot \cdot \;{q_n}} \right]^{\rm T}}, \\ & {{\tau }} = {\left[ {{F_x}\;{F_y}\;{F_z}\;{W_x}\;{W_y}\;{W_z}\;{\tau _1}\; \cdots \;{\tau _n}} \right]^{\rm T}}{\text{。}} \end{align} (1)

 $\frac{{\rm{d}}}{{{\rm{d}}t}}\left( {\frac{{\partial L}}{{\partial \dot {{\xi }}}}} \right) - \frac{{\partial L}}{{\partial {{\xi }}}} = {{Q}}{\text{。}}$ (2)

 ${{M}}\left( {{\xi }} \right)\ddot {{\xi }} + {{C}}\left( {{{\xi }}, \dot {{\xi }}} \right)\dot {{\xi }} + {{D}}\left( {\dot {{\xi }}} \right)\dot {{\xi }} + {{G}}\left( {{\xi }} \right) = {{\tau }}{\text{。}}$ (3)

2 水下机器人-机械手系统滑模控制 2.1 滑模变结构控制

2.2 水下机器人-机械手系统滑模控制器设计，

 ${{e}} = {{{\xi }}_d} - {{\xi }}, \\ \dot {{e}} = {\rm{d}}{{e}}/{\rm{d}}t = {\dot {{\xi }}_d} - \dot {{\xi }}\text{，}$ (4)

 ${{s}} = {{ce}} + \dot {{e}}{\text{。}}$ (5)

 ${{s}} = {\left[ {{s_1}\;{s_2}\; \cdot \cdot \cdot \;{s_N}} \right]^{\rm T}}, \\ {{c}} = {\rm diag}\left\{ {{c_1}\;{c_2}\; \cdot \cdot \cdot \;{c_N}} \right\}\text{。}$ (6)

 $\dot {{s}} = {\rm{d}}{{s}}/{\rm{d}}t = - \varepsilon {\rm{sgn}} \left( {{s}} \right) - k{{s}}, \varepsilon > 0, k > 0,$ (7)

 ${\rm{sgn}} \left( {{s}} \right) = \left\{ {\begin{array}{*{20}{c}} {{I}}\text{，}&{{{s}} > {{0}}} \text{，}\\ {{0}}\text{，}&{{{s}} = {{0}}}\text{，} \\ { - {{I}}}\text{，}&{{{s}} < {{0}}} \text{。} \end{array}} \right.。$ (8)

 $\begin{split}{l} & {{u}} = {{\tau }} = {{M}}\left( {{\xi }} \right)\left( {{{c\dot e}} + \varepsilon {{\rm sgn}} \left( {{s}} \right) + k{{s}} + {{{{\ddot \xi }}}_d}} \right)+\\ & {{C}}\left( {{{\xi }}, {{\dot \xi }}} \right)\left( {{{ce}} - {{s}} + {{{{\dot \xi }}}_d}} \right)+\\ & {{D}}\left( {{{\dot \xi }}} \right)\left( {{{ce}} - {{s}} + {{{{\dot \xi }}}_d}} \right)+\\ & {{G}}\left( {{\xi }} \right)\text{。} \end{split}$ (9)

 ${{V}} = {{{{{s}}^2}}/2},$ (10)

 $\dot {{V}} = {{s\dot s}}\text{。}$ (11)

 $\dot {{V}} = - \varepsilon \left| {{s}} \right| - k{{{s}}^2}\text{。}$ (12)

 图 2 基于指数趋近律的UVMS滑模控制系统 Fig. 2 SMC of UVMS based on exponential reaching law
3 仿真研究 3.1 仿真对象

 图 3 水下机器人-机械手系统三维模型 Fig. 3 Three dimensional model of UVMS

 图 4 本文研究的三自由度水下机械手D-H坐标系 Fig. 4 D-H coordinate system of our 3-DOFs manipulator

 ${{{\xi }}_d} = {[{x_d}\;{y_d}\;{z_d}\;{\varphi _d}\;{\theta _d}\;{\psi _d}\;{q_{1d}}\;{q_{2d}}\;{q_{3d}}]^{\rm T}}{\text{，}}$

 ${x_d} = 4\cos \left( {0.04{{\text{π}}}t} \right),$
 ${y_d} = 4\sin \left( {0.04{{\text{π}}}t} \right),$
 ${z_d} = 0.5t,$
 ${\varphi _d} = {{0}^ \circ },$
 ${\theta _d} = {{0}^ \circ },$
 ${\psi _d} = {{0}^ \circ },$
 ${q_{1d}} = {10^ \circ },$
 ${q_{2d}} = {20^ \circ },$
 ${q_{3d}} = - {3}{{0}^ \circ }{\text{。}}$

3.2 仿真结果

 图 5 UVMS艇体空间运动轨迹跟踪 Fig. 5 Trajectory tracking of UVMS in 3-dimensional space

 图 6 UVMS首向运动轨迹跟踪 Fig. 6 Sway motion tracking of UVMS

 图 7 UVMS侧向运动轨迹跟踪 Fig. 7 Surge motion tracking of UVMS

 图 8 UVMS纵向运动轨迹跟踪 Fig. 8 Heave motion tracking of UVMS

 图 9 UVMS姿态角控制 Fig. 9 Control of attitude angles in UVMS

 图 10 UVMS机械手关节角度控制 Fig. 10 Control of manipulator joints in UVMS

4 结　语

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