包建華,喬 曦,李道亮
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雙矢量定姿算法提高海參捕撈裝置捷聯(lián)慣導系統(tǒng)粗對準精度
包建華1,2,3,喬 曦1,3,李道亮1,3※
(1. 中國農(nóng)業(yè)大學信息與電氣工程學院,北京 100083;2. 江蘇師范大學電氣工程及自動化學院,徐州 221116;3. 北京農(nóng)業(yè)物聯(lián)網(wǎng)工程技術(shù)研究中心,北京 100083)
針對傳統(tǒng)解析粗對準算法中水平對準精度同時受陀螺儀和加速度計測量誤差影響的問題,提出一種雙矢量定姿粗對準算法,該算法在選定重力矢量為主參考矢量的前提下,預(yù)先對參與姿態(tài)解算的矢量作單位正交化處理。理論分析表明,所述算法使得水平對準精度只受加速度計水平測量誤差影響,提高了捷聯(lián)慣導系統(tǒng)粗對準精度;實測數(shù)據(jù)的試驗結(jié)果表明,所述粗對準算法的水平誤差角的大小不超過1°,方位誤差角的大小不超過3°,在粗對準所要求的誤差范圍之內(nèi),為后續(xù)利用濾波方法進行精對準提供了有效的初始條件。
漁業(yè);導航;算法;捷聯(lián)慣導;粗對準;雙矢量定姿;靜基座;海參捕撈
用信息技術(shù)提升農(nóng)業(yè)機械化水平是建設(shè)現(xiàn)代農(nóng)業(yè)的戰(zhàn)略選擇,為加強農(nóng)機裝備的信息技術(shù)創(chuàng)新,需要突破智能農(nóng)業(yè)裝備數(shù)字化設(shè)計、自動導航協(xié)調(diào)控制等關(guān)鍵技術(shù)[1]。農(nóng)業(yè)機械自動導航是精準農(nóng)業(yè)的重要技術(shù)支撐,已廣泛應(yīng)用于現(xiàn)代農(nóng)業(yè)生產(chǎn)各過程[2-5]。中國是海參生產(chǎn)和消費大國,目前,海參捕撈方式主要是拖網(wǎng)和人工捕撈,對潛水員的生命健康和海洋生態(tài)都有潛在危害[6]。為減輕潛水員的勞動強度,人們已開發(fā)了一些機械式捕撈裝置來代替人工進行海參捕撈[7-9],但自動化程度低,作業(yè)效率不高。因此,在當前海參養(yǎng)殖規(guī)模不斷擴大的背景下,開發(fā)一種自主式海參捕撈裝置顯得尤其迫切。自主式海參捕撈裝置關(guān)鍵要解決海參柔性抓捕和載體的自主導航定位問題。捷聯(lián)慣性導航系統(tǒng)(SINS,strapdown inertial navigation system)具有自主性和無源性的特點,已被廣泛用于飛機、艦艇、船舶等的導航[10-12],隨著低成本MEMS(micro-electro- mechanical system)慣性傳感器技術(shù)的進步,捷聯(lián)慣性導航系統(tǒng)被越來越多地應(yīng)用于民用領(lǐng)域[13]。為解決海參捕撈裝置的自主導航定位問題,課題組開展了以捷聯(lián)慣導為主的組合導航研究。
初始對準是捷聯(lián)慣導系統(tǒng)關(guān)鍵技術(shù)之一,其目的就是在執(zhí)行導航任務(wù)之前,事先確定出載體坐標系相對導航坐標系的初始位置關(guān)系,即確定姿態(tài)矩陣的初始值,為后續(xù)捷聯(lián)解算提供必要的初始條件[14-15],因此,初始對準的好壞將直接影響導航系統(tǒng)的性能。為了既快又準地實現(xiàn)對準,捷聯(lián)慣導系統(tǒng)的初始對準過程通常分為粗對準和精對準兩個階段[16-17]。粗對準著重解決對準的快速性問題,盡快將姿態(tài)角誤差縮小到一定的范圍內(nèi),為下一步精對準提供有效的初始條件,因此,研究一種算法簡單且具有較高精度的粗對準方案有其實際的應(yīng)用價值[18-19]。傳統(tǒng)解析粗對準是直接利用重力矢量和地球自轉(zhuǎn)角速度矢量估算姿態(tài)矩陣[20],由于其水平對準精度同時受陀螺儀和加速度計測量誤差的影響,使得粗對準效果不佳。為改善水平對準精度,本文提出一種雙矢量定姿粗對準方案,并用MEMS慣性測量單元與三維電子羅盤的實測數(shù)據(jù)進行了試驗驗證。
1.1 坐標系規(guī)定
1)導航坐標系文中選地理坐標系為導航坐標系,其原點位于載體重心,軸指向東,軸指向北,軸指向天。
1.2 解析粗對準算法
1.2.1 傳統(tǒng)解析粗對準
傳統(tǒng)解析粗對準是借助空間兩個“不共線”的地球自轉(zhuǎn)角速度矢量和地球重力矢量,直接估算從載體坐標系到導航坐標系的初始姿態(tài)矩陣[21-22]。重力矢量、地球自轉(zhuǎn)角速度矢量在導航坐標系和載體坐標系上的投影關(guān)系可分別表示為:
(2)
為了求解從系到系的變換矩陣,再利用和的叉乘運算構(gòu)造一個新的矢量:
(4)
聯(lián)立(1)、(2)、(4)式,寫成矩陣形式:
(6)
(8)
受慣性傳感器本身測量偏差和外界干擾的影響,使得按(6)式求解的姿態(tài)矩陣不能嚴格滿足正交化要求[23],可以按下式進行正交化處理:
1.2.2 雙矢量定姿粗對準
1)雙矢量定姿原理
雙矢量定姿是利用兩個不共線的矢量在直角坐標系系和系下的投影坐標,從而確定兩坐標系之間的方位關(guān)系[24-25]。不妨假設(shè)兩個不共線的矢量為和,它們在系和系下的投影坐標依次記為、、、,則系和系間方位關(guān)系可用方向余弦矩陣(姿態(tài)矩陣)來描述,通過引入輔助矢量并利用矢量坐標變換關(guān)系,不難得到:
針對(10)式的一種改進思路是預(yù)先對參與解算的所有矢量作單位正交化處理。圖1給出了由測量矢量和構(gòu)造3個單位正交矢量、和的空間方位示意圖。圖1中,被選為主矢量,選擇主矢量的一般原則是選擇兩個矢量中的測量誤差較小者。
2)雙矢量定姿粗對準
(13)
(15)
于是式(12)、(13)分別改寫為:
(17)
進一步寫成:
(19)
(21)
考慮到加速度計的測量誤差一般小于陀螺儀的測量誤差,文中選擇作為主參考矢量,參照式(11)可得姿態(tài)矩陣估計算法表達式:
(22)
將式(7)、(8)代入式(22),經(jīng)化簡后得到:
實際對準過程中,為降低慣性傳感器高頻噪聲的影響,可以采集一段時間內(nèi)的傳感器數(shù)據(jù)求平均,然后用該時間段內(nèi)的平均角速度及平均加速度分別代替式(23)中的和,從而估算出初始姿態(tài)矩陣。
估算出姿態(tài)矩陣后,不難解算出載體的姿態(tài)角。假設(shè)海參捕撈裝置的俯仰角、橫滾角和航向角分別用(°)、(°)和(°)表示,則姿態(tài)矩陣可寫成[26]:
(24)
由式(24),得:
1.3 誤差分析
從理論上分析不同對準方法的誤差特性,對于工程實踐中選擇更好的對準方案具有指導意義。傳統(tǒng)解析粗對準中,正交化后的姿態(tài)矩陣估計值消除了刻度系數(shù)誤差和歪斜誤差,但仍然含有漂移誤差,文獻[27]導出的漂移誤差失準角的估算式為:
(27)
(28)
將式(29)按向量叉乘運算規(guī)則展開,忽略二階及以上小量,并記慣性傳感器的測量誤差和,得:
為簡化書寫,式(30)中與誤差分析結(jié)果不相關(guān)的元素用“*”表示。
(32)
即有:
可見,雙矢量定姿粗對準的水平失準角只受加速度計水平測量誤差、的影響,而傳統(tǒng)解析粗對準的水平失準角除跟加速度計測量誤差有關(guān)外,還和天向陀螺漂移誤差有關(guān),一般情況下,由于陀螺測量誤差遠大于加速度計測量誤差,因此,雙矢量定姿粗對準算法提高了水平對準精度。對比式(28)、(33)可知,兩者方位對準精度相當,且方位失準角主要取決于陀螺的東向漂移誤差。
為驗證上述2種粗對準算法的優(yōu)劣,試驗中使用瑞芬科技有限公司的AH106B型MEMS慣性測量單元和DCM260型三維電子羅盤的實測值進行對比試驗,實物如圖2所示。試驗條件:當?shù)鼐暥?40.004 9°;所用慣性測量單元的陀螺儀常值漂移20°/h,陀螺儀隨機游走系數(shù),加速度計零偏,陀螺儀和加速度計的最大數(shù)據(jù)輸出頻率300 Hz,試驗中陀螺儀和加速度計的數(shù)據(jù)采集周期均設(shè)置為20 ms;三維電子羅盤的傾角分辨率0.1°,數(shù)據(jù)輸出頻率20 Hz。海參捕撈裝置主要由導航模塊、推進器模塊、水下攝像機、捕撈機構(gòu)等構(gòu)成;其中,導航模塊安裝于海參捕撈裝置載體中部的封閉式平臺上。試驗地點選擇山東海陽某海參養(yǎng)殖場水域,與本試驗相關(guān)場景圖如圖3所示。數(shù)據(jù)采集試驗步驟如下:1)將慣性測量單元、三維電子羅盤固定于減振平臺上,并保證兩模塊的向軸線分別平行,然后將減振平臺靜置于海參捕撈裝置的載體上;2)同時采集并存儲慣性測量單元中陀螺儀和加速度計輸出的原始數(shù)據(jù)以及三維電子羅盤輸出的姿態(tài)角數(shù)據(jù);3)保持試驗系統(tǒng)靜止30 min后停止數(shù)據(jù)采集與記錄。
選取慣性測量單元采集的同一原始試驗數(shù)據(jù),在Matlab平臺上,應(yīng)用前述的兩種粗對準算法分別進行粗對準解算,每次對準時間為1 min,共進行了30次對準試驗。圖4為傳統(tǒng)解析粗對準算法得到的捷聯(lián)慣導系統(tǒng)俯仰角、橫滾角和航向角的估算值,而雙矢量定姿粗對準算法得到的俯仰角、橫滾角和航向角的估算值如圖5所示。圖4、5的俯仰角和橫滾角代表載體的水平姿態(tài),而航向角代表載體的方位姿態(tài)。圖4的水平姿態(tài)角變化幅度大且呈現(xiàn)出明顯的振蕩特性,而圖5的水平姿態(tài)角變化幅度小且變化平穩(wěn);圖4和5的方位姿態(tài)角變化規(guī)律一致。
圖4 傳統(tǒng)解析粗對準算法估算的姿態(tài)角
圖5 雙矢量定姿粗對準算法估算的姿態(tài)角
為進一步驗證粗對準算法效果,文中使用三維電子羅盤實測值作為算法評估的參考基準,試驗中所用三維電子羅盤的俯仰和橫滾精度為0.1°、航向精度為0.5°。為使數(shù)據(jù)比較有意義,安裝時,該電子羅盤的3個軸向與慣性測量單元模塊的對應(yīng)軸向平行且一致。在進行靜態(tài)數(shù)據(jù)采集的30 min內(nèi),三維電子羅盤輸出的俯仰角和橫滾角的數(shù)值穩(wěn)定,分別為–0.8°和–0.2°,而航向角做低頻小幅度變化,取其平均值為143.5°,將這3個實測值在圖4、5中標示成水平直線,以便與30次粗對準試驗的估算值作對比。將粗對準算法所得的姿態(tài)估算值減去對應(yīng)時刻三維電子羅盤實測的姿態(tài)值得到姿態(tài)誤差。表1給出30次粗對準試驗中2種粗對準算法對應(yīng)姿態(tài)誤差的試驗結(jié)果,其中“算法1”代表傳統(tǒng)解析粗對準算法,“算法2”代表雙矢量定姿粗對準算法,由于2種算法的方位對準的精度相當,表1中合并列出了航向角誤差??紤]到電子羅盤提供的參考基準精度僅為0.1°,表1中數(shù)值只保留一位有效數(shù)字。
表1 粗對準姿態(tài)估算值與電子羅盤姿態(tài)測量值間的誤差
從表1所列粗對準結(jié)果可見,傳統(tǒng)解析粗對準算法的俯仰角誤差和橫滾角誤差偏大且變化比較劇烈,而雙矢量定姿粗對準算法的水平誤差角的大小不超過1°,方位誤差角的大小不超過3°,方位誤差大于水平誤差,與前述誤差特性的理論分析結(jié)果相吻合。
1)所提出的雙矢量定姿粗對準算法預(yù)先對參與姿態(tài)解算的矢量作單位正交化處理,使得姿態(tài)矩陣估計值自然滿足正交化條件,有效降低了慣性傳感器測量誤差和外界干擾對粗對準精度的影響。
2)理論分析和試驗結(jié)果都表明,所述算法提高了海參捕撈裝置捷聯(lián)慣導系統(tǒng)的水平對準精度。以三維電子羅盤實測值作為基準,所述粗對準算法的水平誤差角小于1°,方位誤差角小于3°,在粗對準所要求的誤差范圍之內(nèi),為后續(xù)利用濾波方法進行精對準提供了有效的初始條件。
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Double-vector attitude determination algorithm improving coarse alignment accuracy of strapdown inertial navigation system for sea cucumber fishing device
Bao Jianhua1,2,3, Qiao Xi1,3, Li Daoliang1,3※
(1.100083,; 2.221116,; 3.100083,)
Autonomous navigation is one of the key technologies for an intelligent agricultural equipment, which has been widely used in modern agricultural production. Sea cucumber production and consumption are very large in China. At present, the sea cucumber harvest mainly relies on trawl or artificial fishing, which will cause a potential hazard to the health of divers and the marine ecology. Therefore, in order to overcome the shortcomings of traditional sea cucumber fishing methods, it is necessary to develop a sea cucumber fishing device with autonomous navigation and positioning functions. Strapdown inertial navigation system (SINS) is suitable for the navigation of the autonomous sea cucumber fishing device because of its autonomy, passivity and complete navigation parameters. For the SINS, initial alignment must be completed before starting a navigation mission. The purpose of the initial alignment is to determine the initial position of the carrier coordinate system relative to the navigation coordinate system, that is, to determine the initial value of the attitude matrix. Initial alignment is one of the key technologies of SINS, which is divided into coarse alignment and fine alignment, and the coarse alignment accuracy will directly determine the performance of the initial alignment. Therefore, it is of practical value to study a coarse alignment scheme with simple algorithm and high alignment precision. The traditional analytical coarse alignment algorithm directly utilizes the earth gravity vector and the earth rotation angular velocity vector to estimate the initial attitude matrix. In view of the problem that the horizontal alignment accuracy of SINS is affected by the measurement errors of gyroscope and accelerometer in the traditional analytical coarse alignment algorithm, a novel coarse alignment algorithm based on double-vector attitude determination is proposed. In general, the measurement error of the accelerometer is much smaller than that of the gyroscope, so the earth gravity vector in the proposed algorithm is chosen as the main reference vector. Then, 3 unit orthogonal vectors are constructed based on the earth gravity vector and the earth rotation angular velocity vector, and the resulting attitude matrix is a unit orthogonal matrix. The theoretical analysis shows that horizontal misalignment angles of SINS are only related to the accelerometer level measurement errors in the case of using the proposed algorithm, however, using the conventional algorithm, the horizontal misalignment angles are related to the accelerometer measurement errors and the gyroscope drift error. Therefore, the coarse alignment accuracy of SINS using the aforementioned algorithm is significantly improved.Based on the same measured data from an inertial measurement unit, the simulation experiment was carried out for 30 times using the conventional coarse alignment algorithm and the proposed algorithm, respectively. Simulation curves demonstrated that the variation of the horizontal attitude angles using the algorithm proposed was smoother. To further verify the effectiveness of the algorithm, the attitude angles calculated from the measured values of the inertial measurement unit were compared with the measured value of a high-precision three-dimensional electronic compass, and the experimental results showed that the horizontal error angles of the aforementioned coarse alignment algorithm did not exceed 1° and the azimuth error angle did not exceed 3°. The results can meet the accuracy requirement of coarse alignment and will provide an effective initial condition for the subsequent fine alignment using filtering methods.
fisheries; navigation; algorithms; strapdown inertial navigation; coarse alignment; double-vector attitude determination; stationary base; sea cucumber fishing
10.11975/j.issn.1002-6819.2017.12.037
TN966; TP391.9
A
1002-6819(2017)-12-0286-07
2016-12-29
2017-03-27
國家國際科技合作專項項目(2013DFA11320);中央高校基本科研業(yè)務(wù)費專項資金資助項目(2016XD001)
包建華,男,安徽肥東人,副教授,博士生,主要從事慣性導航及組合導航研究。北京 中國農(nóng)業(yè)大學信息與電氣工程學院,100083。 Email:baojhxz@cau.edu.cn
李道亮,男,山東墾利人,教授,博士生導師,主要從事農(nóng)業(yè)信息先進感知與智能處理研究。北京 中國農(nóng)業(yè)大學信息與電氣工程學院,100083。Email:dliangl@cau.edu.cn
包建華,喬 曦,李道亮. 雙矢量定姿算法提高海參捕撈裝置捷聯(lián)慣導系統(tǒng)粗對準精度[J]. 農(nóng)業(yè)工程學報,2017,33(12):286-292. doi:10.11975/j.issn.1002-6819.2017.12.037 http://www.tcsae.org
Bao Jianhua,Qiao Xi,Li Daoliang. Double-vector attitude determination algorithm improving coarse alignment accuracy of strapdown inertial navigation system for sea cucumber fishing device[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2017, 33(12): 286-292. (in Chinese with English abstract) doi:10.11975/j.issn.1002-6819.2017.12.037 http://www.tcsae.org