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Stabilization design of underactuated AUV based on quaternion
WU Qi, LI Ye
Clledge of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
Abstract: Stabilization control aims at stabilizing the AUV to the designed position and attitude from any initial position under the controlling input. Stabilization is widely used in the abutment of deep-water submarines and location tracking. This paper describes a new time-variable stabilization law with four inputs which was designed based on the simplification of the 6-DOF (degree of freedom) space motion and trace equations of an underactuated AUV and the conversion of the model which was realized by quaternion. The control trial was done to prove that the control law was convergent. The simulation results prove that the control method is effective and the stabilization can be achieved under any initial conditions.
Key words: autonomous underwater vehicles     stabilization     three dimensional     trajectories     linear control systems     time varying systems     motion control     simulation

1 四元数

2 水下机器人空间运动方程

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3 AUV的镇定设计

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h(ηvt)是余下的部分。相比于标准函数δλβτ1τ4τ5τ6是同类的一阶形式，且处处连续。向量场f是连续的时间周期的，且相对于标准函数δλβf是同类型的零阶形式。向量场h(ηvt)也是连续的，是相对于δλβ严格的正阶的同类型函数形式的总和。因此，如果(ηv)=(0，0)是系统(14)局部渐近指数稳定的稳定点，则系统(13)的解(ηv)=(0，0)是局部ρβ—指数镇定的。

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4 镇定仿真

AUV的基本参数为[7]m11=215，m22=265，m33=265，m44=40，m55=80，m66=80，d11=70，d22=100，d33=100，d44=30，d55=50，d66=50，且AUV是中性浮力，不计入重力和浮力(假设重力和浮力平衡，且重心浮心重合)。

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 图 1 平移速度u、v、w Fig. 1 Velocity of vehicle u， v， w
 图 2 旋转速度p、q、r Fig. 2 Rotational speed of vehicle p， q， r
 图 3 位移x、y 、z Fig. 3 Displacement of vehicle x， y， z
 图 4 转换变量ε1，ε2、ε3 Fig. 4 Transformation variables ε1，ε2，ε3
 图 5 实际轨迹图 Fig. 5 Actual path of vehicle
 图 6 名义标准ρα响应 Fig. 6 Response of the dilation ρα

5 结束语

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DOI: 10.3969/j.issn.1673-4785.201210058

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#### 文章信息

WU Qi, LI Ye

Stabilization design of underactuated AUV based on quaternion

CAAI Transactions on Intelligent Systems, 2014, 9(2): 186-191
http://dx.doi.org/10.3969/j.issn.1673-4785.201210058