舰船科学技术  2020, Vol. 42 Issue (2): 98-102 PDF

Attitude tracking control of negative-buoyancy quad tilt-rotor autonomous underwater vehicle
WANG Tao, WU Chao, GE Tong
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, China
Abstract: The attitude tracking control of negative-buoyancy quad tilt-rotor autonomous underwater vehicle (NQTAUV) is influenced by many disturbances, which results in the attitude tracking error. A disturbance observer and an attitude tracking controller are designed to estimate the disturbance and compensate it for high attitude tracking performance. The attitude tracking error model is derived, a disturbance observer is designed to estimate the disturbance, an attitude tracking controller is designed to track the target attitude under disturbance, the performance of the controller is validated by experiments. The experiments show that the estimation of the disturbance is near the real value, and precise attitude tracking is achieved. The research shows that the disturbance observer based attitude control can compensate the disturbance and improve the attitude tracking accuracy.
Key words: negative-buoyancy     quad tilt-rotor     autonomous underwater vehicle     disturbance observer     attitude tracking
0 引　言

NQTAUV有独特的机身倾转悬停（body-tilt-hover, BTH）功能，即在机身实现大幅度俯仰角机动的时候，能够悬停在水中一个位置点，而不产生水平的分力，不会引起水平的位移。对于普通AUV来说，一般是在艇体尾部有一个推进器，部分在艇体上还有垂向和横向的推进器，实现垂向和水平机动。不过，这些推进器一般固定在艇体上，只能提供固定方向的力或力矩，不能提供矢量推力，所以不能做机身倾转悬停。然而，NQTAUV可以借助自身的矢量推力进行机身倾转悬停[7-8]。BTH是一项有用的功能。比如，AUV前部一般安装有摄像机，用以提供视频信息。通常来讲，为了更大的视角，摄像机安装在一个二自由度云台上。然而，当云台损坏后，相机的视角被限制，此时，可以采用BTH功能，操作手可以重新获得原来的视角。不过，当工作在BTH模式时，因为舵机会随着俯仰角而转动，引起转动惯量的变化，同时产生一定的干扰力矩，且不能计算或测量得到干扰量幅值。因此，需要更鲁棒的姿态控制器，实现姿态的跟踪。此外，在BTH模式下，水动力矩也会随着机身的旋转运动而改变。因此，研究干扰的估计和补偿策略，以及在干扰下的姿态跟踪，是符合实际应用需要的。

1 NQTAUV数学模型 1.1 运动学和动力学

 图 1 坐标系 Fig. 1 Coordinates

BTH模式示意图如图2所示。

 图 2 机身倾转悬停模式 Fig. 2 Body-tilt-hover mode

NQTAUV的运动学和动力学方程为：

 $\dot \sigma = G(\sigma )\omega$ (1)
 $J\dot \omega {\rm{ }} = - S(\omega )J\omega - {{ I}_A}\dot \omega - { C}(\omega )\omega - D(\omega ) + \tau$ (2)

 $S(\lambda ) = \left[ {\begin{array}{*{20}{c}} 0&{ - {\lambda _3}}&{{\lambda _2}} \\ {{\lambda _3}}&0&{ - {\lambda _1}} \\ { - {\lambda _2}}&{{\lambda _1}}&0 \end{array}} \right] {\text{，}}$ (3)

 $G(\sigma ) = \frac{1}{4}[(1 - {\sigma ^T}\sigma )I + 2S(\sigma ) + 2\sigma {\sigma ^{\rm T}}] {\text{，}}$ (4)

$G(\sigma )$ 有性质：

 $\sigma G(\sigma ) = \frac{1}{4}(1 + {\sigma ^T}\sigma )\sigma {\text{。}}$ (5)
1.2 姿态跟踪误差模型

 $\tilde \sigma = \sigma \otimes \sigma _d^{ - 1} = \frac{{{\sigma _d}({\sigma ^{\rm T}}\sigma - 1) + \sigma (1 - \sigma _d^{\rm T}{\sigma _d}) - 2S({\sigma _d})\sigma }}{{1 + \sigma _d^{\rm T}{\sigma _d}{\sigma ^{\rm T}}\sigma + 2\sigma _d^{\rm T}\sigma }} {\text{，}}$ (6)

 $\tilde \omega = \omega - \tilde { R}{\omega _d} {\text{，}}$ (7)

 $\tilde { R} = \frac{{(1 - 6{{\tilde \sigma }^{\rm T}}\tilde \sigma + {{({{\tilde \sigma }^{\rm T}}\tilde \sigma )}^2})I + 8\tilde \sigma {{\tilde \sigma }^{\rm T}} - 4(1 - {{\tilde \sigma }^{\rm T}}\tilde \sigma )S(\tilde \sigma )}}{{{{(1 + {{\tilde \sigma }^{\rm T}}\tilde \sigma )}^2}}}{\text{，}}$ (8)

$\tilde { R}$ 的导数为：

 $\dot {\tilde { R}} = - S(\tilde \omega )\tilde { R} {\text{，}}$ (9)

$\tilde \omega$ 的导数为：

 $\dot {\tilde \omega} = \dot \omega - (\dot{ \tilde { R}}{\omega _d} + \tilde { R}{{\dot {\tilde \omega}} _d}) = \dot \omega - [ - S(\tilde \omega )\tilde { R}{\omega _d} + \tilde{ R}{{\dot{ \tilde \omega}} _d}] {\text{，}}$ (10)

 $\dot {\tilde \sigma} = G(\tilde \sigma )\tilde \omega {\text{，}}$ (11)
 $\begin{split} \dot {\tilde \omega} = & {J^{ - 1}}[ - S(\omega )J\omega - {{ I}_A}\dot \omega - { C}(\omega )\omega - { D}(\omega ) + \tau ] - \\ &( - S(\tilde \omega )\tilde R{\omega _d} + \tilde R{{\dot {\tilde \omega}} _d}){\text{，}} \end{split}$ (12)

 $\begin{split} \tau = & \nu + [S(\omega )J\omega + {I_A}\dot \omega + C(\omega )\omega + { D}(\omega )] +\\ & J( - S(\tilde \omega )\tilde R{\omega _d} + \tilde R{{\dot {\tilde \omega}} _d}) {\text{，}} \end{split}$ (13)

 $\dot {\tilde \omega} = {J^{ - 1}}(\nu + d) {\text{。}}$ (14)

 $\dot {\tilde \omega} = {J^{ - 1}}\nu + d' {\text{。}}$ (15)
2 控制器和干扰观测器设计

 图 3 控制框架 Fig. 3 Control scheme
2.1 干扰观测器设计

 $\dot z{\rm{ }} = - l(\tilde \omega )[z + p(\tilde \omega ) + {J^{ - 1}}\nu ] {\text{，}}$ (16)
 $\hat d'{\rm{ }} = z + p(\tilde \omega ) {\text{，}}$ (17)

 $l(\tilde \omega ) = \frac{{\partial p(\tilde \omega )}}{{\partial \tilde \omega }} {\text{。}}$ (18)

 $\begin{split} & \dot {\tilde d'} = \dot d' - \dot {\hat d'} = 0 - [\dot z + \frac{{\partial p(\tilde \omega )}}{{\partial \tilde \omega }}\dot {\tilde \omega} ]= \\ & l(\tilde \omega )[z + p(\tilde \omega ) + {J^{ - 1}}\nu ] + l(\tilde \omega )\dot {\tilde \omega} = \\ & l(\tilde \omega )[\hat d' + {J^{ - 1}}\nu ] - l(\tilde \omega )({J^{ - 1}}\nu + d') =\\ & - l(\tilde \omega )[d' - \hat d']= \\ & - l(\tilde \omega )\tilde d' {\text{。}} \end{split}$ (19)

 $\dot {\tilde d }= - l(\tilde \omega )\tilde d {\text{。}}$ (20)

 $l(\tilde \omega ) = {k_3},{k_3} > 0 {\text{，}}$ (21)

 $p(\tilde \omega ) = \int l (\tilde \omega ){\rm d}\tilde \omega = {k_3}\tilde \omega {\text{。}}$ (22)
2.2 控制器设计

 ${V_1}{\rm{ }} = 2{k_1}\ln (1 + {\tilde \sigma ^{\rm T}}\tilde \sigma ) + \frac{1}{2}{\tilde \omega ^{\rm T}}J\tilde \omega {\text{，}}$ (23)

 $\begin{split} {{\dot V}_1} =& 4{k_1}\frac{{{{\tilde \sigma }^{\rm T}}\dot {\tilde \sigma} }}{{1 + {{\tilde \sigma }^T}\tilde \sigma }} + {{\tilde \omega }^{\rm T}}J\dot {\tilde \omega} = \\ & {k_1}{{\tilde \omega }^{\rm T}}\tilde \sigma + {{\tilde \omega }^{\rm T}}(\nu + d) = {{\tilde \omega }^{\rm T}}({k_1}\tilde \sigma + \nu + d) {\text{，}} \end{split}$ (24)

 $\nu = - {k_1}\tilde \sigma - {k_2}\tilde \omega - \hat d {\text{，}}$ (25)

 ${{\dot V}_1}{\rm{ }} = - {k_2}{{\tilde \omega }^{\rm T}}\tilde \omega + {{\tilde \omega }^{\rm T}}\tilde d \leqslant - {k_2}||\tilde \omega |{|^2} + ||\tilde \omega ||||\tilde d|| {\text{。}}$ (26)
2.3 稳定性分析

 ${V_2} = \frac{1}{2}{\tilde d^2} {\text{，}}$ (27)

${V_2}$ 的导数为：

 ${{\dot V}_2} = \tilde d\dot {\tilde d} = - {k_3}{{\tilde d}^2} {\text{，}}$ (28)

 ${\dot V_3} = {\dot V_1} + {\dot V_2} \le - {k_2}||\tilde \omega |{|^2} + ||\tilde \omega ||||\tilde d|| - {k_3}{\tilde d^{'2}} {\text{。}}$ (29)

3 实验结果和分析 3.1 测试平台

3.2 姿态跟踪实验

 ${\sigma _d} = \left[ {\begin{array}{*{20}{c}} 0 \\ {\tan\left(\dfrac{{\text{π}} }{{72}}\right)\sin\left(\frac{{\text{π}}}{{10}}t\right)} \\ 0 \end{array}} \right]{\text{。}}$ (30)

$x$ $y$ 轴施加约0.008 N.m的常值干扰力矩。为了验证所提干扰观测器和姿态跟踪控制器的有效性，在实验的 $0 \sim 50\;$ s内，将干扰观测器关闭；在 $50 \sim 100\;$ s内，将干扰观测器激活。实验结果如图4图6所示。其中，图4显示姿态跟踪效果，图5显示控制力矩，图6显示干扰估计值。

 图 4 正弦信号姿态跟踪结果 Fig. 4 Sinusoidal attitude tracking performance

 图 5 控制输入 Fig. 5 Control input

 图 6 干扰观测值 Fig. 6 Disturbance estimation

4 结　语

 [1] FOSSEN, T. Guidance and control of ocean vehicles[M]. John Willey & Sons: 1994. [2] BROWN, C. L. In Deep sea mining and robotics: Assessing legal, societal and ethical implications[C]// 2017 IEEE Workshop on Advanced Robotics and its Social Impacts (ARSO), Austin, TX, USA, 2017: 1-2. [3] LI Y, PAN D, ZHAO Q, et al. Hydrodynamic performance of an autonomous underwater glider with a pair of bioinspired hydro wings–a numerical investigation[J]. Ocean Engineering, 2018, 163: 51-57. DOI:10.1016/j.oceaneng.2018.05.052 [4] WYNN R B, HUVENNE V A I, LE BAS T P, et al. Autonomous underwater vehicles (auvs): Their past, present and future contributions to the advancement of marine geoscience[J]. Marine Geology, 2014, 352: 451-468. DOI:10.1016/j.margeo.2014.03.012 [5] WANG T, WU C, WANG J, et al. Modeling and control of negative-buoyancy tri-tilt-rotor autonomous underwater vehicles based on immersion and invariance methodology[J]. Applied Sciences, 2018, 8. [6] HUI Y, TONG G, JIA-WANG L, et al. In Prediction of mode and static stability of negative buoyancy vehicle[C]// 2011 Chinese Control and Decision Conference (CCDC), 2011: 1903-1909. [7] WU N, WU C, GE, T, et al. Pitch channel control of a remus auv with input saturation and coupling disturbances[J]. Applied Sciences, 2018, 8. [8] XIANG X, LAPIERRE L, JOUVENCEL B. Smooth transition of auv motion control: From fully-actuated to under-actuated configuration[J]. Robotics and Autonomous Systems, 2015, 67: 14-22. DOI:10.1016/j.robot.2014.09.024 [9] LI X, ZHAO M, GE T. A nonlinear observer for remotely operated vehicles with cable effect in ocean currents[J]. Applied Sciences, 2018, 8. [10] YUAN Y, YU Y, GUO L. Nonlinear active disturbance rejection control for the pneumatic muscle actuators with discrete-time measurements[J]. Ieee Transactions on Industrial Electronics, 2019, 66: 2044-2053. [11] CUI R, YANG C, LI Y, SHARMA S. Adaptive neural network control of auvs with control input nonlinearities using reinforcement learning[J]. Ieee Transactions on Systems Man Cybernetics-Systems, 2017, 47: 1019-1029. DOI:10.1109/TSMC.2016.2645699 [12] LIU C, MCAREE O, CHEN W H. Path following for small uavs in the presence of wind disturbance, Control [C]// (Control), 2012 UKACC International Conference on, Cardiff, UK, 2012: 613-618. [13] PALOMERAS N, VALLICROSA G, MALLIOS A, et al. Auv homing and docking for remote operations[J]. Ocean Engineering, 2018, 154: 106-120. DOI:10.1016/j.oceaneng.2018.01.114 [14] XING G Q, SHABBIR A P. Alternate forms of relative attitude kinematics and dynamics equations[C]// 2001 Flight Mechanics Symposium, Greenbelt, MD, USA, 2001: 83-97.