﻿ 水下机器人-机械手末端精度测量方法及误差分析
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 哈尔滨工程大学学报  2019, Vol. 40 Issue (6): 1155-1162  DOI: 10.11990/jheu.201805034 0

引用本文

YAO Feng, YANG Chao, ZHANG Mingjun, et al. End-precision measurement method for autonomous underwater vehicle manipulator systems and its principle error analysis[J]. Journal of Harbin Engineering University, 2019, 40(6), 1155-1162. DOI: 10.11990/jheu.201805034.

文章历史

End-precision measurement method for autonomous underwater vehicle manipulator systems and its principle error analysis
YAO Feng , YANG Chao , ZHANG Mingjun , WANG Lianqiang
College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China
Abstract: Two end-precision measurement methods for autonomous underwater vehicle manipulator systems (AUVMSs) were addressed in this work. The two methods were based on different principles:First, a noncontact end-precision range measurement method was proposed to detect whether the end movement precision of AUVMS is within a certain range. Second, a contact-type end-precision measurement method was proposed to solve the problems encountered in end-precision measurement in the underwater environment. An error analysis method based on numerical iteration for the principle error problem of the end-precision measurement method was proposed by analyzing the factors that influence errors. Finally, pool experiments on end-precision measurement under the conditions of the fixed and dynamic positioning of AUVMSs were conducted to verify the effectiveness of the proposed method. Experimental results showed that the proposed method can effectively measure the end precision of manipulators in real time.
Keywords: underwater vehicle    underwater manipulator    autonomous underwater vehicle manipulator systems (AUVMS)    precision measurement    coordinate transformation    principle error    static precision    dynamic precision

1 AUVMS结构与精度要求

AUVMS样机如图 1所示，由AUV(艇体)和机械手组成[13-14]；外形为椭圆流线型，尺寸为2.0 m×0.6 m×0.6 m，空重约205.0 kg；共有2个水平主推进器、2个侧向推进器及4个垂直推进器；配置深度、速度、姿态角度等传感器和视觉系统。

2 AUVMS末端精度测量方法 2.1 末端精度范围测量方法

 Download: 图 2 水下视觉方法原理 Fig. 2 Schematic diagram of underwater stereo vision

1) AUVMS动力悬停状态下，控制机械手末端运动向目标点(立方体区域中心O)运动；

2) 通过摄像机C1观察，机械手末端如果处于图 3(b)xOz平面内，则xz方向满足机械手末端精度范围在±150 mm以内；反之，则不满足；

 Download: 图 3 精度测量方法原理 Fig. 3 Schematic diagram of precision measurement method

3) 通过摄像机C2观察，机械手末端如果处于图 3(b)xOy平面内，则xy方向满足机械手末端精度范围在±150 mm以内；反之，则不满足。

2.2 接触式末端精度测量方法

1) 方法测量原理。

2) 大地坐标系中实际点坐标测量。

 $\left\{ {\begin{array}{*{20}{l}} {x_b^2 + y_b^2 + {{\left( {{z_b} - a \cdot \cos \theta } \right)}^2} = L_1^2} \\ {x_b^2 + {{\left( {{y_b} - a \cdot \sin \theta } \right)}^2} + z_b^2 = L_2^2} \\ {x_b^2 + y_b^2 + {{\left( {{z_b} - a \cdot \cos \theta + b} \right)}^2} = L_3^2} \end{array}} \right.$ (1)

 $\left\{ {\begin{array}{*{20}{c}} {{x_b} = \pm \sqrt {L_1^2 - y_b^2 - {{\left( {{z_b} - a \cdot \cos \theta } \right)}^2}} } \\ {{y_b} = \left( {L_1^2 - L_2^2 + {a^2} - 2 \cdot {{(a \cdot \cos \theta )}^2} + } \right.} \\ {2a \cdot {z_b} \cdot \cos \theta )/2a \cdot \sin \theta } \\ {{z_b} = \left( {L_3^2 - L_1^2 - {b^2} + 2a \cdot b \cdot \cos \theta } \right)/2b} \end{array}} \right.$ (2)

3) 艇体坐标系中目标点坐标转换。

 Download: 图 4 坐标系{C}与{O}、{E}位置关系 Fig. 4 The position relation diagram of coordinate system {C} and {O}, {E}

① 目标点位置转换到媒介坐标系{C}。

 $_o^c{\bf{P}} = \left[ {\begin{array}{*{20}{c}} {c{\rm{ \mathsf{ α} }} c{\rm{ \mathsf{ β} }} }&{c{\rm{ \mathsf{ α} }} s{\rm{ \mathsf{ β} }} s\gamma - s{\rm{ \mathsf{ α} }} c\gamma }&{c{\rm{ \mathsf{ α} }} s{\rm{ \mathsf{ β} }} c\gamma + s{\rm{ \mathsf{ α} }} s\gamma } \\ {s{\rm{ \mathsf{ α} }} c{\rm{ \mathsf{ β} }} }&{s{\rm{ \mathsf{ α} }} s{\rm{ \mathsf{ β} }} s\gamma + c{\rm{ \mathsf{ α} }} c\gamma }&{s{\rm{ \mathsf{ α} }} s{\rm{ \mathsf{ β} }} c\gamma - c{\rm{ \mathsf{ α} }} s\gamma } \\ { - s{\rm{ \mathsf{ β} }} }&{c{\rm{ \mathsf{ β} }} s\gamma }&{c{\rm{ \mathsf{ β} }}c\gamma } \end{array}} \right]$ (3)

 $^c\mathit{\boldsymbol{P}}{ = ^o}\mathit{\boldsymbol{P}} \cdot _o^c\mathit{\boldsymbol{P}}$ (4)

② 媒介坐标系{C}转换到大地坐标系{E}。

 $_C^E\mathit{\boldsymbol{P}} = {\left[ {\begin{array}{*{20}{c}} d&e&f \end{array}} \right]^{\text{T}}}$ (5)

 $^\mathit{\boldsymbol{E}}\mathit{\boldsymbol{P}}{ = ^C}\mathit{\boldsymbol{P}} + _C^E\mathit{\boldsymbol{P}}$ (6)

 $\begin{array}{l} \left[ {\begin{array}{*{20}{l}} \xi \\ \eta \\ \zeta \end{array}} \right] = \left[ {\begin{array}{*{20}{l}} {{\rm{c}}\alpha {\rm{c}}\beta \quad \;\;\;{\rm{c}}\alpha {\rm{s}}\beta {\rm{s}}\gamma - {\rm{s}}\alpha {\rm{c}}\gamma \;\;\;\quad \;{\rm{c}}\alpha {\rm{s}}\beta {\rm{c}}\gamma + {\rm{s}}\alpha {\rm{s}}\gamma }\\ {{\rm{s}}\alpha {\rm{c}}\beta \quad {\rm{s}}\alpha {\rm{s}}\beta {\rm{s}}\gamma + {\rm{c}}\alpha {\rm{c}}\gamma \;\quad \;\;\;\;\;\;\;{\rm{s}}\alpha {\rm{s}}\beta {\rm{c}}\gamma - {\rm{c}}\alpha {\rm{s}}\gamma }\\ { - {\rm{s}}\beta \quad \;\;\;\;\;\;\;\;\;{\rm{c}}\beta {\rm{s}}\gamma \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\rm{c}}\beta {\rm{c}}\gamma } \end{array}} \right] \cdot \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{y_1}}\\ {{z_1}} \end{array}} \right] + \left[ {\begin{array}{*{20}{l}} d\\ e\\ f \end{array}} \right] \end{array}$ (7)

① 坐标系{O}中，选取机械手关节上的OPQ，此三点坐标值通过接触式传感器测量得出；

② 坐标系{E}中，通过实际点测量过程，测量得到OPQ的坐标值，表示为O′、P′、Q′；

③ 将OPQ点作为目标点，O′、P′、Q′作为目标点转换点，分别代入式(7)左右端，联立可得αβγdef

4) 方法测量步骤。

① 艇体坐标系{O}中，给定目标点坐标A(x1, y1, z1)，控制机械手向目标点运动，稳定后的机械手末端在大地坐标系{E}中实际点为A′；

② 通过实际点坐标测量，得到实际点A′的坐标值A′(xb, yb, zb)；

③ 将艇体坐标系{O}中目标点A，通过媒介坐标系{C}转换，得到大地坐标系{E}中目标点转换坐标AZ(ξ, η, ζ)；

④ 大地坐标系{E}中，通过实际点A′、目标点转换坐标AZ，得出末端精度δ

 $\delta = \left| { \pm \sqrt {{{\left( {{x_b} - \xi } \right)}^2} + {{\left( {{y_b} - \eta } \right)}^2} + {{\left( {{z_b} - \zeta } \right)}^2}} } \right|$ (8)
2.3 接触式末端精度测量方法原理性误差分析

2.3.1 坐标测量误差分析

1) 受传感器测量精度影响，传感器测量值L1L2L3中存在测量误差，具体数值为±0.001%·L(传感器测量精度与测量长度L为正比例关系)；

2) 由于abc的数值通过接触式拉伸传感器测量得出，受传感器测量精度影响，abc中存在测量误差，其误差分别为±0.001%·a、±0.001%·b、±0.001%·c

 $\left\{ {\begin{array}{*{20}{l}} {{L_{{\rm{e}}\;1}} = {L_1} \pm 0.001\% \cdot {L_1}, }&{{a_{\rm{e}}} = a \pm 0.001\% \cdot a}\\ {{L_{{\rm{e}}\;2}} = {L_2} \pm 0.001\% \cdot {L_2}, }&{{b_{\rm{e}}} = b \pm 0.001\% \cdot b}\\ {{L_{{\rm{e}}\;3}} = {L_3} \pm 0.001\% \cdot {L_3}, }&{{c_{\rm{e}}} = c \pm 0.001\% \cdot c} \end{array}} \right.$ (9)

 $\left\{ {\begin{array}{*{20}{l}} {{x_{{\rm{be}}}} = \pm \sqrt {L_{{\rm{e}}1}^2 - y_{{\rm{be}}}^2 - {{\left( {{z_{{\rm{be}}}} - {a_{\rm{e}}} \cdot \cos {\theta _{\rm{e}}}} \right)}^2}} }\\ {{y_{{\rm{be}}}} = \frac{{L_{{\rm{e}}1}^2 - L_{{\rm{e}}2}^2 + a_{\rm{e}}^2 - 2 \cdot {{\left( {{a_{\rm{e}}} \cdot \cos {\theta _{\rm{e}}}} \right)}^2} + 2{a_{\rm{e}}} \cdot {z_{{\rm{be}}}} \cdot \cos {\theta _{\rm{e}}}}}{{2{a_{\rm{e}}} \cdot \sin {\theta _{\rm{e}}}}}}\\ {{z_{{\rm{be}}}} = \frac{{L_{{{\rm{e}}3}}^2 - L_{{\rm{e}}1}^2 - b_{\rm{e}}^2 + 2{a_{\rm{e}}} \cdot {b_{\rm{e}}} \cdot \cos {\theta _{\rm{e}}}}}{{2{b_{\rm{e}}}}}} \end{array}} \right.$ (10)
 $cos\ {\theta _{\rm{e}}} = \left( {a_{\rm{e}}^2 + b_{\rm{e}}^2 - c_{\rm{e}}^2} \right)/2{a_{\rm{e}}}{b_{\rm{e}}}$ (11)

 ${\delta _{\rm{C}}} = \left| { \pm \sqrt {{{\left( {{x_{{\rm{be}}}} - {x_{\rm{b}}}} \right)}^2} + {{\left( {{y_{{\rm{be}}}} - {y_{\rm{b}}}} \right)}^2} + {{\left( {{z_{{\rm{be}}}} - {z_{\rm{b}}}} \right)}^2}} } \right|$ (12)

1) 在艇体坐标系{OO-x1y1z1}，x1y1z1 3个方向，每个方向各自间隔1 mm取点，机械手可达空间内共取50 000个坐标点；

2) 将上述坐标点A′，代入式(1)得到坐标点对应的L1L2L3参数值；

3) 将L1L2L3代入式(9~11)，得到坐标点A′对应的包含了误差因素的坐标Ae′；

4) 将A′和Ae′代入式(12)，可得当前坐标点的坐标测量误差δC

5) 重复迭代50 000次上述2)~4)过程，得到50 000个坐标点测量误差组成区间，即为机械手可达空间内精确的坐标测量误差范围。

 Download: 图 5 坐标测量误数值范围 Fig. 5 The numerical range of coordinate measurement error

2.3.2 坐标转换误差

1) 转换参数求解过程，O′、P′、Q′坐标值通过空间坐标测量方法测量，其包含坐标测量误差；

2) 转换参数求解过程，受传感器测量精度影响，OPQ坐标值中存在传感器测量误差。

1) 大地坐标系{E}中，O′、P′、Q′坐标值中坐标测量误差为0~0.325 mm(2.3.1节推导得出)；

2) 艇体坐标系{O}中，OPQ的坐标值中传感器测量误差为±0.001%·L

1) 包含了误差因素的OPQO′、P′、Q′坐标值表示为OePeQeOe′、Pe′、Qe′；

2) 将OePeQeOe′、Pe′、Qe′代入式(4)左右端，联立求解得出包含误差影响因素的坐标转换参数αeβeγedeeefe

3) 基于此组坐标转换参数αeβeγedeeefe数值，将目标点A转换到大地坐标系{E}下，得到包含误差影响因素的转换值AZe(ξe, ηe, ζe)；

4) AZe(ξe, ηe, ζe)与AZ(ξ, η, ζ)的差值，即为坐标转换误差δZ

 ${\delta _z} = \left| { \pm \sqrt {{{\left( {{\xi _e} - \xi } \right)}^2} + {{\left( {{\eta _e} - \eta } \right)}^2} + {{\left( {{\zeta _e} - \zeta } \right)}^2}} } \right|$ (13)

 Download: 图 6 坐标转换误差数值范围 Fig. 6 The numerical range of coordinate conversion error

3 精度测量水池实验验证 3.1 末端精度范围测量方法实验

 Download: 图 7 水下视觉末端精度范围测量实验 Fig. 7 Experimental diagram of the end precision range measurement based on underwater vision

3.2 接触式末端精度测量方法实验

3.2.1 静态末端精度测量实验

 Download: 图 8 静态末端精度测量实验 Fig. 8 The static end precision measurement experiment

3.2.2 动态末端精度测量实验

4 结论

1) 为检测AUVMS机械手末端运动是否到达某一规定的范围内，提出了一种水下视觉末端精度范围测量方法。水池实验结果表明：本文方法能够准确的测量AUVMS机械手末端精度范围，验证了本文方法的有效性。

2) 为检测AUVMS机械手末端精度的具体数值，提出了一种接触式水下机械手末端精度测量方法；在AUVMS艇体固定和艇体动力悬停状态下。水池实验结果表明：本文方法能够实时、有效测量机械手作业范围内部不同目标点的末端精度，验证了本文方法的有效性。

3) 本文提出基于数值迭代方式的原理性误差分析思路，得出本文方法原理性误差为0.088~1.380 mm。本文原理性误差分析思路与测量装置结构无关，该思路可为与本文测量原理相近的测量方法进行误差分析时参考。

 [1] 徐玉如, 李彭超. 水下机器人发展趋势[J]. 自然杂志, 2011, 33(3): 125-132. XU Yuru, LI Pengchao. Developing tendency of unmanned underwater vehicles[J]. Chinese journal of nature, 2011, 33(3): 125-132. (0) [2] SIMETTI E, CASALINO G, TORELLI S, et al. Floating underwater manipulation:developed control methodology and experimental validation within the TRIDENT project[J]. Journal of field robotics, 2014, 31(3): 364-385. DOI:10.1002/rob.2014.31.issue-3 (0) [3] MARANI G, CHOI S K, YUH J. Underwater autonomous manipulation for intervention missions AUVs[J]. Ocean engineering, 2009, 36(1): 15-23. DOI:10.1016/j.oceaneng.2008.08.007 (0) [4] YANG Chao, WANG Yujia, YAO Feng. Driving performance of underwater long-arm hydraulic manipulator system for small autonomous underwater vehicle and its positioning accuracy[J]. International journal of advanced robotic systems, 2017, 14(6): 1-18. (0) [5] LYNCH B, ELLERY A. Efficient control of an AUV-manipulator system:an application for the exploration of Europa[J]. IEEE journal of oceanic engineering, 2014, 39(3): 552-570. DOI:10.1109/JOE.2013.2271390 (0) [6] 丁雅斌, 梅江平, 张文昌, 等. 基于单目视觉的并联机器人末端位姿检测[J]. 机械工程学报, 2014, 50(21): 174-179. DING Yabin, MEI Jiangping, ZHANG Wenchang, et al. Position and orientation measurement of parallel robot based on monocular vision[J]. Journal of mechanical engineering, 2014, 50(21): 174-179. (0) [7] 王一, 刘常杰, 任永杰, 等. 工业坐标测量机器人定位误差补偿技术[J]. 机械工程学报, 2011, 47(15): 31-36. WANG Yi, LIU Changjie, REN Yongjie, et al. Compensation for positioning error of industrial coordinate measurement robot[J]. Journal of mechanical engineering, 2011, 47(15): 31-36. (0) [8] 孙天慧, 田文杰, 王辉, 等. 基于球杆仪的三坐标并联动力头运动学标定方法[J]. 机械工程学报, 2012, 48(5): 22-27. SUN Tianhui, TIAN Wenjie, WANG Hui, et al. Kinematic calibration of 3-DOF spindle head using double-ball bar[J]. Journal of mechanical engineering, 2012, 48(5): 22-27. (0) [9] 解则晓, 辛少辉, 李绪勇, 等. 基于单目视觉的机器人标定方法[J]. 机械工程学报, 2011, 47(5): 35-39. XIE Zexiao, XIN Shaohui, LI Xuyong, et al. Method of robot calibration based on monocular vision[J]. Journal of mechanical engineering, 2011, 47(5): 35-39. (0) [10] 刘常杰, 马爽, 郭寅, 等. 高精度柔性坐标测量系统及其校准技术研究[J]. 光学学报, 2013, 33(10): 120-126. LIU Changjie, MA Shuang, GUO Yin, et al. Study on calibration technology of high-precision flexible coordinate measurement system[J]. Acta optica sinica, 2013, 33(10): 120-126. (0) [11] 李煊, 张铭钧. 水下双目视觉系统中的目标分割和目标定位[J]. 华中科技大学学报(自然科学版), 2017, 45(12): 53-59. LI Xuan, ZHANG Mingjun. Target segmentation and target positioning of underwater binocular vision system[J]. Journal of Huazhong University of Science & Technology (natural science edition), 2017, 45(12): 53-59. (0) [12] ZHANG Mingjun, LI Shupeng, LI Xuan. Research on technologies of underwater feature extraction and target location based on binocular vision[C]//Proceedings of the 27th Chinese Control and Decision Conference (CCDC). Qingdao, China: IEEE, 2015: 15341469. (0) [13] 杨超, 郭佳, 张铭钧. 基于RBF神经网络的作业型AUV自适应终端滑模控制方法及实验研究[J]. 机器人, 2018, 40(3): 336-345. YANG Chao, GUO Jia, ZHANG Mingjun. Adaptive terminal sliding mode control method based on RBF neural network for operational AUV and its experimental research[J]. Robot, 2018, 40(3): 336-345. (0) [14] 杨超, 张铭钧, 秦洪德, 等. 水下机器人-机械手姿态调节系统研究[J]. 哈尔滨工程大学学报, 2018, 39(2): 377-383. YANG Chao, ZHANG Mingjun, QIN Hongde, et al. Attitude control system for autonomous underwater vehicle-manipulator system[J]. Journal of Harbin Engineering University, 2018, 39(2): 377-383. (0) [15] LIU Weixin, WANG Yujia, LIU Xing, et al. Weak thruster fault detection for AUV based on stochastic resonance and wavelet reconstruction[J]. Journal of central south university, 2016, 23(11): 2883-2895. DOI:10.1007/s11771-016-3352-1 (0)