﻿ 矢量推进水下机器人的推力分配方法
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 哈尔滨工程大学学报  2018, Vol. 39 Issue (10): 1605-1611  DOI: 10.11990/jheu.201702042 0

### 引用本文

LI Xinfei, MA Qiang, YUAN Lihao, et al. Thrust allocation method of underwater robots with vector propulsion[J]. Journal of Harbin Engineering University, 2018, 39(10), 1605-1611. DOI: 10.11990/jheu.201702042.

### 文章历史

1. 哈尔滨工程大学 船舶工程学院, 黑龙江 哈尔滨 150001;
2. 哈尔滨建成集团有限公司, 黑龙江 哈尔滨 150030

Thrust allocation method of underwater robots with vector propulsion
LI Xinfei1, MA Qiang2, YUAN Lihao1, WANG Hongwei1
1. College of Ship Engineering, Harbin Engineering University, Harbin 150001, China;
2. Harbin Construction Group Co., LTD, Harbin 150030, China
Abstract: In order to study the thrust allocation method of the remotely operated vehicles (ROV) in deep sea, a mathematics model of the over-actuated vector thrust system is constructed according to the ROV characteristics, i.e. several thrusters are arranged as vectors symetrically. The direct logic thrust allocation technology is applied in the model, which first normalizes the six degrees of freedom motion control voltage, then amplifies the voltage, and then allocates the thrust by direct logic method on the horizontal plane and vertical plane respectively. The numerical simulation and analysis shows this thrust allocation method can achieve the optimized distribution and output of thrust and the six degrees of freedom motion control for the over-actuated ROV, having the simple, accurate, and real-time merits, besides, it avoids saturated output of thrust allocation, therefore, the method has certain guidance significance and engineering value on the research of underwater robot and over-actuated ship thrust allocation.
Keywords: underwater robot    motion control    over-actuated    hydraulic thruster    vector arrangement    thrust allocation

Fossen[3]针对过驱动海上航行器的推力分配方法进行深入分析，指出直接分配法和伪逆法是一种实时性较性高的推力分配方法，但必须解决推进器推力的饱和输出问题[4]。李新飞等[2]针对某作业型ROV所安装的液压推进器建立了控制电压和推力响应之间对应关系，为推力分配方法的研究奠定基础。俞建成[5]针对过驱动矢量推进载人潜器，对每个推进器的期望控制量进行归一化处理后，研究了过驱动推力分配问题。贾立娟[6]针对某观测型ROV的推进器进行动力学建模，分析了螺旋桨动力学响应问题。范士波[7]使用原始对偶路径跟踪方法解决了过驱动ROV推力分配时可能出现的饱和问题，但是该方法计算过程复杂，且实时性不高。Soylu等[8]研究了考虑饱和约束特性的推力优化分配方法，但是没有考虑该方法的实时性问题。Akmal等[9]针对某性ROV研究了一种主动容错的推力分配方法。黄海等[10]建立了一种矢量推进微型ROV的推力分配模型，基于递归神经网络设计了推力容错分配控制器，但是没有考虑推力饱和问题。魏延辉[11]研究了一种基于能量最优原则的推力分配方法，但没有考虑推力饱和问题。可以看出：国内外一些学者在对矢量推进系统和推力分配方法进行研究时，往往没有考虑推进器饱和约束条件，或者虽然考虑了推进器约束条件[12]，但使用推力分配方法复杂、计算量大、实时性不高。

1 ROV推进系统建模及推力分配 1.1 ROV运动控制系统组成及工作原理

 Download: 图 1 作业型ROV运动控制系统的组成及其工作原理 Fig. 1 The working principle of Work-Class ROV

1.2 ROV矢量推进系统的数学建模 1.2.1 水平面矢量推进系统的数学建模

1) 水平推进器的合推力

 $\left\{ \begin{array}{l} {X_{\rm{h}}} = {T_1}\cos {\beta _{\rm{h}}} + {T_2}\cos {\beta _{\rm{h}}} - {T_3}\cos {\beta _{\rm{h}}} - {T_4}\cos {\beta _{\rm{h}}}\\ {Y_{\rm{h}}} = {T_1}\sin {\beta _{\rm{h}}} - {T_2}\sin {\beta _{\rm{h}}} + {T_3}\sin {\beta _{\rm{h}}} - {T_4}\sin {\beta _{\rm{h}}}\\ {Z_{\rm{h}}} = 0 \end{array} \right.$ (1)

2) 水平推进器的合推力矩。

 $\left\{ \begin{array}{l} {K_{\rm{h}}} = - {T_{1y}}{z_{\rm{h}}} + {T_{2y}}{z_{\rm{h}}} - {T_{3y}}{z_{\rm{h}}} + {T_{4y}}{z_{\rm{h}}}\\ {M_{\rm{h}}} = {T_{1x}}{z_{\rm{h}}} + {T_{2x}}{z_{\rm{h}}} - {T_{3x}}{z_{\rm{h}}} - {T_{4x}}{z_{\rm{h}}}\\ {N_{\rm{h}}} = {T_{1x}}{y_{\rm{h}}} + {T_{1y}}{x_{\rm{h}}} - {T_{2x}}{y_{\rm{h}}} - {T_{2y}}{x_{\rm{h}}} - {T_{3x}}{y_{\rm{h}}} - \\ \;\;\;\;\;\;\;\;{T_{3y}}{x_{\rm{h}}} + {T_{4x}}{y_{\rm{h}}} + {T_{4y}}{x_{\rm{h}}} \end{array} \right.$ (2)
 Download: 图 2 水平推进器的推力对ROV本体的推力矩示意图 Fig. 2 The thrust moment of horizontal propeller on ROV

1.2.2 垂直面矢量推进系统的数学建模

1) 垂直推进器的合推力。

 $\left\{ \begin{array}{l} {X_{\rm{v}}} = 0\\ {Y_{\rm{v}}} = - {T_5}\sin {\beta _{\rm{v}}} + {T_6}\sin {\beta _{\rm{v}}} - {T_7}\sin {\beta _{\rm{v}}} + {T_8}\sin {\beta _{\rm{v}}}\\ {Z_{\rm{v}}} = {T_5}\cos {\beta _{\rm{v}}} + {T_6}\cos {\beta _{\rm{v}}} + {T_7}\cos {\beta _{\rm{v}}} + {T_8}\cos {\beta _{\rm{v}}} \end{array} \right.$ (3)
 Download: 图 3 垂直推进器的推力对ROV本体的推力矩示意图 Fig. 3 The thrust moment of vertical propeller on ROV

2) 垂直推进器的合推力矩。

4台垂直推进器的推力经过力的分解后，其各自分解力的正方向如图 3所示。则4台垂直推进器推力对ROV本体产生的合推力矩在坐标系{b}上的三个轴上可用下式表示：

 $\left\{ \begin{array}{l} {K_{\rm{v}}} = - {T_{5y}}{z_{\rm{v}}} - {T_{5z}}{y_{\rm{v}}} + {T_{6y}}{z_{\rm{v}}} + {T_{6z}}{y_{\rm{v}}} - {T_{7y}}{z_{\rm{v}}} - \\ \;\;\;\;\;\;\;{T_{7z}}{y_{\rm{v}}} + {T_{8y}}{z_{\rm{v}}} + {T_{8z}}{y_{\rm{v}}}\\ {M_{\rm{v}}} = - {T_{5z}}{x_{\rm{v}}} - {T_{6z}}{x_{\rm{v}}} + {T_{7z}}{x_{\rm{v}}} + {T_{8z}}{x_{\rm{v}}}\\ {N_{\rm{v}}} = - {T_{5y}}{x_{\rm{v}}} + {T_{6y}}{x_{\rm{v}}} + {T_{7y}}{x_{\rm{v}}} - {T_{8y}}{x_{\rm{v}}} \end{array} \right.$ (4)

1.2.3 过驱动推进系统合推力

 $\left\{ \begin{array}{l} {X_{\rm{T}}} = {X_{\rm{h}}} + {X_{\rm{v}}}\\ {Y_{\rm{T}}} = {Y_{\rm{h}}} + {Y_{\rm{v}}}\\ {Z_{\rm{T}}} = {Z_{\rm{h}}} + {Z_{\rm{v}}}\\ {K_{\rm{T}}} = {K_{\rm{h}}} + {K_{\rm{v}}}\\ {M_{\rm{T}}} = {M_{\rm{h}}} + {M_{\rm{v}}}\\ {N_{\rm{T}}} = {N_{\rm{h}}} + {N_{\rm{v}}} \end{array} \right.$ (5)

 $\mathit{\boldsymbol{\tau }} = \mathit{\boldsymbol{B}}\left( \beta \right)\mathit{\boldsymbol{T}}$ (6)

1.3 ROV推力分配方法 1.3.1 水平面运动推力分配方法

 $\left\{ \begin{array}{l} {\delta _1} = \left| {{u_X}} \right|/{u_{\rm{H}}}\\ {\delta _2} = \left| {{u_Y}} \right|/{u_{\rm{H}}}\\ {\delta _3} = \left| {{u_Z}} \right|/{u_{\rm{H}}} \end{array} \right.$ (7)

 $\left\{ \begin{array}{l} X = {k_1}{u_X}{\delta _1}\\ Y = {k_2}{u_Y}{\delta _2}\\ N = {k_3}{u_N}{\delta _3} \end{array} \right.$ (8)

 $\left\{ \begin{array}{l} {T_{{e_1}}} = X + Y + N\\ {T_{{e_2}}} = X - Y - N\\ {T_{{e_3}}} = - X + Y - N\\ {T_{{e_4}}} = - X - Y + N \end{array} \right.$ (9)

1.3.2 垂直面运动推力分配方法

 $\left\{ \begin{array}{l} {\varepsilon _1} = \left| {{u_Z}} \right|/{u_{\rm{V}}}\\ {\varepsilon _2} = \left| {{u_K}} \right|/{u_{\rm{V}}}\\ {\varepsilon _3} = \left| {{u_M}} \right|/{u_{\rm{V}}} \end{array} \right.$ (10)

 $\left\{ \begin{array}{l} Z = {l_1}{u_Z}{\varepsilon _1}\\ K = {l_2}{u_K}{\varepsilon _2}\\ M = {l_3}{u_M}{\varepsilon _3} \end{array} \right.$ (11)

 $\left\{ \begin{array}{l} {T_{{e_5}}} = Z - K - M\\ {T_{{e_6}}} = Z + K - M\\ {T_{{e_7}}} = Z - K + M\\ {T_{{e_8}}} = Z + K + M \end{array} \right.$ (12)

1.3.3 螺旋桨数学模型

 $Q = {K_{\rm{Q}}}\rho {n^2}{D^5}$ (13)

 $T = {K_{\rm{T}}}\rho {n^2}{D^4}$ (14)

 $P = Q\omega$ (15)

3 仿真结果及分析 3.1 仿真初始条件

 Download: 图 4 期望推力及控制电压 Fig. 4 Expected thrust and control voltage

3.2 未归一化伪逆推力分配仿真

 Download: 图 5 未归一化伪逆法的推进器响应 Fig. 5 Thrust response based on pseudo inverse method

3.3 归一化直接逻辑推力分配仿真

 Download: 图 6 归一化后期望推力及推力矩 Fig. 6 The normalized desired forces and moments

 Download: 图 7 归一化直接逻辑法的推力分配结果 Fig. 7 Thrust allocation by normalized direct logical

3.4 归一化伪逆推力分配仿真

 Download: 图 8 归一化伪逆法的面推进器响应 Fig. 8 Thrust allocation of normalized pseudo inverse method

3.5 三种推力分配方法消耗功率对比

 Download: 图 9 三种分配方法消耗功率对比 Fig. 9 Power consumption of three allocation methods

4 结论

1) 根据过驱动作业型ROV总体结构中推进器的空间分布关系，推导出推进器的推力和作用到ROV本体上合力之间的关系，建立了过驱动ROV推进系统的数学模型。

2) 先将水平面控制电压和垂直面控制电压进行归一化，然后分别按照权重进行放大后，再对ROV进行推力分配，可有效解决推进器饱和问题。

3) 根据多个推进器成矢量对称布置的特点，提出一种先将控制电压归一化，再进行直接逻辑推力分配方法，可实现ROV的六自由度运动控制。

4) 直接逻辑分配法是一种非常接近最优能耗的推力分配方法，具有直观、简单、效率高和实时性强等显著优点。

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