田光兆，顧寶興，Irshad Ali Mari，周 俊，王海青

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基于三目視覺(jué)的自主導(dǎo)航拖拉機(jī)行駛軌跡預(yù)測(cè)方法及試驗(yàn)

田光兆1，顧寶興1※，Irshad Ali Mari2，周 俊1，王海青1

（1. 南京農(nóng)業(yè)大學(xué)工學(xué)院，南京 210031；2. 巴基斯坦信德農(nóng)業(yè)大學(xué)凱爾布爾工程技術(shù)學(xué)院，凱爾布爾 66020）

為了實(shí)現(xiàn)自主導(dǎo)航拖拉機(jī)離開(kāi)衛(wèi)星定位系統(tǒng)時(shí)能夠持續(xù)可靠工作，該文提出了基于三目視覺(jué)的拖拉機(jī)行駛軌跡預(yù)測(cè)方法。該方法將三目相機(jī)分解為長(zhǎng)短基線2套雙目視覺(jué)系統(tǒng)分時(shí)獨(dú)立工作。通過(guò)檢測(cè)相鄰時(shí)刻農(nóng)業(yè)環(huán)境中同一特征點(diǎn)的坐標(biāo)變化反推拖拉機(jī)在水平方向上的運(yùn)動(dòng)矢量，并通過(guò)灰色模型預(yù)測(cè)未來(lái)時(shí)刻的運(yùn)動(dòng)矢量變化，最終建立不同速度下的前進(jìn)方向誤差模型。試驗(yàn)結(jié)果表明：拖拉機(jī)行駛速度為0.2 m/s時(shí)，46.5 s后前進(jìn)方向誤差超過(guò)0.1 m，對(duì)應(yīng)行駛距離為9.3 m。行駛速度上升到0.5 m/s時(shí)，該時(shí)間和行駛距離分別降低到17.2 s和8.6 m。當(dāng)行駛速度上升到0.8 m/s時(shí)，該時(shí)間和距離分別快速降低至8.5 s和6.8 m。行駛速度越高，前進(jìn)方向誤差增速越高。該方法可用于短時(shí)預(yù)測(cè)拖拉機(jī)的行駛軌跡，為自主導(dǎo)航控制提供依據(jù)。

拖拉機(jī)；自主導(dǎo)航；機(jī)器視覺(jué)；軌跡預(yù)測(cè)；灰色模型

0 引 言

為了降低人工成本、提高作業(yè)效率、改善作業(yè)質(zhì)量，具有自主導(dǎo)航功能的農(nóng)業(yè)機(jī)械越來(lái)越多地應(yīng)用到農(nóng)業(yè)生產(chǎn)中來(lái)。比如，自主導(dǎo)航拖拉機(jī)能夠作為牽引機(jī)械進(jìn)行田間播種、施肥、耕地[1-7]。自主導(dǎo)航聯(lián)合收割機(jī)能夠在無(wú)人干預(yù)的情況下收獲小麥、水稻和玉米[8-14]。自主導(dǎo)航插秧機(jī)能夠在水田里精準(zhǔn)插秧，大幅提高作業(yè)精度，其效率是人工的50倍[15-18]。

視覺(jué)系統(tǒng)是自主導(dǎo)航農(nóng)業(yè)裝備的重要組成部分。視覺(jué)系統(tǒng)主要用來(lái)識(shí)別作物行、溝壟或障礙物，是農(nóng)機(jī)智能化作業(yè)的重要外界環(huán)境和自身姿態(tài)感知工具[19-21]。尤其是當(dāng)GPS或北斗定位系統(tǒng)受到干擾無(wú)法正常工作時(shí)，視覺(jué)系統(tǒng)能夠進(jìn)行輔助相對(duì)定位，保證導(dǎo)航工作能夠繼續(xù)進(jìn)行[22-27]。同時(shí)，通過(guò)視覺(jué)系統(tǒng)也能夠?qū)ξ磥?lái)進(jìn)行預(yù)測(cè)，其預(yù)測(cè)結(jié)果為導(dǎo)航?jīng)Q策與控制提供數(shù)據(jù)基礎(chǔ)。由于農(nóng)業(yè)機(jī)械導(dǎo)航控制具有嚴(yán)重時(shí)滯性，為了提高常規(guī)PID控制效果，文獻(xiàn)[28]和[29]都提到通過(guò)預(yù)測(cè)數(shù)據(jù)能夠顯著改善PID控制效果，具有很強(qiáng)的工程實(shí)際意義。

現(xiàn)有研究中，大多是在GPS或北斗可靠工作的前提下討論導(dǎo)航控制方法問(wèn)題。而本文探討的問(wèn)題是當(dāng)GPS或北斗失效時(shí)，如何單獨(dú)利用視覺(jué)系統(tǒng)為自主導(dǎo)航拖拉機(jī)進(jìn)行行駛軌跡預(yù)測(cè)，并提出一種基于灰色理論的軌跡預(yù)測(cè)方法。

1 視覺(jué)系統(tǒng)硬件組成

本研究中視覺(jué)系統(tǒng)由Point Gray公司BBX3三目相機(jī)、1394B采集卡和工控機(jī)組成。

三目相機(jī)由右、中、左3個(gè)子相機(jī)構(gòu)成。其中右、中2個(gè)子相機(jī)構(gòu)成短基線雙目視覺(jué)系統(tǒng)，右、左2個(gè)子相機(jī)構(gòu)成長(zhǎng)基線雙目視覺(jué)系統(tǒng)。三目視覺(jué)系統(tǒng)由長(zhǎng)短基線2套雙目視覺(jué)系統(tǒng)疊加而成。2套雙目視覺(jué)系統(tǒng)空間坐標(biāo)系原點(diǎn)和各軸正方向相同，原點(diǎn)在右相機(jī)光心，水平向右為軸正方向，垂直向下為軸正方向，水平向前為軸正方向。為了提高開(kāi)發(fā)效率，Point Gray公司已經(jīng)直接將雙目系統(tǒng)的另外一個(gè)相機(jī)的抓圖和系統(tǒng)的視覺(jué)測(cè)量功能固化到API[30]。使用者無(wú)需采用傳統(tǒng)的雙目抓圖、圖像特征點(diǎn)檢測(cè)與匹配、視差法測(cè)距等一系列過(guò)程，只需根據(jù)單幅右相機(jī)圖像即可獲取環(huán)境深度信息。

圖1 三目相機(jī)結(jié)構(gòu)

1394B采集卡用于高速接收相機(jī)回傳的數(shù)字圖像。工控機(jī)是圖像處理的核心部件，用于程序控制相機(jī)采集圖像，執(zhí)行圖像處理程序，輸出解算結(jié)果。

2 拖拉機(jī)運(yùn)動(dòng)矢量檢測(cè)與預(yù)測(cè)方法

2.1 拖拉機(jī)運(yùn)動(dòng)矢量檢測(cè)

拖拉機(jī)運(yùn)動(dòng)矢量檢測(cè)的基本原理是：利用同一組靜止的特征點(diǎn)相鄰時(shí)刻在相機(jī)坐標(biāo)系中的坐標(biāo)變化，反推拖拉機(jī)的運(yùn)動(dòng)矢量，其具體檢測(cè)流程如圖2所示。

圖2 拖拉機(jī)運(yùn)動(dòng)矢量檢測(cè)流程

由于2套視覺(jué)系統(tǒng)空間坐標(biāo)原點(diǎn)重合，所以同一個(gè)實(shí)際物理點(diǎn)在2套視覺(jué)系統(tǒng)中的坐標(biāo)理論上也是完全吻合的。但是由于2套系統(tǒng)的基線長(zhǎng)度不一樣，就會(huì)導(dǎo)致測(cè)量結(jié)果略有偏差。為了得到精確的測(cè)量結(jié)果，長(zhǎng)短基線2套視覺(jué)系統(tǒng)執(zhí)行相同的運(yùn)動(dòng)檢測(cè)方法，然后求取均值。

其步驟包括：

1）在復(fù)雜背景農(nóng)業(yè)環(huán)境中，右相機(jī)采集圖像，圖像編號(hào)自增1，并將圖像存儲(chǔ)。

2）對(duì)右相機(jī)采集到的圖像進(jìn)行SIFT特征點(diǎn)檢測(cè)，計(jì)算環(huán)境中所有特征點(diǎn)圖像坐標(biāo)[31]。由于相機(jī)的圖像將不可避免地發(fā)生畸變，所以還需要對(duì)每個(gè)特征點(diǎn)的近似權(quán)值進(jìn)行估算。圖3為某一特征點(diǎn)的近似權(quán)值估算方法如式（1）所示。

3）根據(jù)特征點(diǎn)的圖像坐標(biāo)和步驟1）采集到的深度圖像，利用相機(jī)提供的API函數(shù)進(jìn)行圖像坐標(biāo)到相機(jī)坐標(biāo)的轉(zhuǎn)換。

4）判斷當(dāng)前處理的是否為第1幅圖像。若是，將每個(gè)有效特征點(diǎn)的圖像坐標(biāo)、相機(jī)坐標(biāo)以及權(quán)值存儲(chǔ)到數(shù)組中，然后重復(fù)步驟1）～4）。若不是第1幅圖像，則將以上數(shù)據(jù)存儲(chǔ)到數(shù)組中。

5）與前1幅圖像進(jìn)行SIFT特征點(diǎn)匹配。將匹配成功的特征點(diǎn)對(duì)的圖像坐標(biāo)保存到數(shù)組中。

圖3 特征點(diǎn)近似權(quán)值計(jì)算

6）遍歷數(shù)組，分別從數(shù)組和中找出匹配成功的特征點(diǎn)對(duì)所對(duì)應(yīng)的相機(jī)坐標(biāo)和近似權(quán)值，保存到數(shù)組。

式中表示有效特征點(diǎn)的總個(gè)數(shù)。

2.2 拖拉機(jī)運(yùn)動(dòng)矢量預(yù)測(cè)

農(nóng)用拖拉機(jī)大多數(shù)都是勻速低速作業(yè)，根據(jù)其作業(yè)特點(diǎn)，本文設(shè)計(jì)了灰色理論的軌跡預(yù)測(cè)方案。

圖4 通過(guò)滑動(dòng)窗口獲取預(yù)測(cè)數(shù)據(jù)

假設(shè)時(shí)刻滑窗內(nèi)個(gè)運(yùn)動(dòng)矢量組成樣本(0)，其中(0)形式為式（4）。

為了降低干擾數(shù)據(jù)對(duì)有效數(shù)據(jù)的影響，對(duì)(0)進(jìn)行一次累加，得到(0)的1-AGO序列為(1)，如式（5）所示。

其中

則GM(1,1)模型的表達(dá)式為一階微分方程，如式（6）所示。

其中

對(duì)式（8）離散化后，可得出一次累加后+1時(shí)刻的預(yù)測(cè)模型，如式（9）所示。

3 拖拉機(jī)行駛軌跡預(yù)測(cè)試驗(yàn)與結(jié)果分析

3.1 試驗(yàn)設(shè)計(jì)

以東方紅SG250型拖拉機(jī)為試驗(yàn)平臺(tái)，將BBX3型三目相機(jī)以水平姿態(tài)安裝在拖拉機(jī)頭部的配重梁前端，距離地面0.6 m，如圖5所示。同時(shí)拖拉機(jī)頂部安裝精度為厘米級(jí)的RTK-GPS系統(tǒng)。在光線條件良好的晴天上午，在具有大量砂石的硬路面開(kāi)展試驗(yàn)。視覺(jué)檢測(cè)和RTK-GPS檢測(cè)同步，頻率都是10 Hz。拖拉機(jī)分別以0.2、0.5、0.8 m/s的低速直線行駛。通過(guò)工控機(jī)采集GPS數(shù)據(jù)和視覺(jué)預(yù)測(cè)數(shù)據(jù)，繪制實(shí)測(cè)軌跡和預(yù)測(cè)軌跡，提取相同行駛距離內(nèi)的有效數(shù)據(jù)，分析預(yù)測(cè)精度。所用工控機(jī)型號(hào)為研華ARK3500P，CPU型號(hào)為i7-3610，內(nèi)存4 GB。由于GPS采用了載波相位實(shí)時(shí)差分技術(shù)，定位精度可達(dá)厘米級(jí)，因此可將GPS定位數(shù)據(jù)作為參考標(biāo)準(zhǔn)，以此驗(yàn)證三目視覺(jué)系統(tǒng)的運(yùn)動(dòng)檢測(cè)與預(yù)測(cè)精度。

圖5 三目相機(jī)安裝位置

試驗(yàn)過(guò)程中，GPS初始時(shí)刻的全局定位數(shù)據(jù)作為基準(zhǔn)。按照文中方法，通過(guò)視覺(jué)系統(tǒng)獲得的下一時(shí)刻的增量數(shù)據(jù)加上GPS基準(zhǔn)數(shù)據(jù)，就形成了視覺(jué)系統(tǒng)的測(cè)量數(shù)據(jù)（也是絕對(duì)坐標(biāo)）。由多個(gè)視覺(jué)系統(tǒng)測(cè)量數(shù)據(jù)可以形成視覺(jué)系統(tǒng)預(yù)測(cè)數(shù)據(jù)。在某時(shí)刻的視覺(jué)系統(tǒng)預(yù)測(cè)數(shù)據(jù)和該時(shí)刻的GPS的定位數(shù)據(jù)之間必然存在一定的誤差。本文得到這個(gè)誤差后再向前進(jìn)方向（方向）和側(cè)向（方向）進(jìn)行分解，得到2個(gè)方向上的誤差分量。

3.2 結(jié)果與分析

拖拉機(jī)分別在0.2、0.5、0.8 m/s的恒定速度下直線行駛，軌跡預(yù)測(cè)試驗(yàn)結(jié)果分別如圖6～圖7和表1所示。

圖6a、6c、6e中，實(shí)線是根據(jù)GPS數(shù)據(jù)繪制的拖拉機(jī)行駛軌跡。虛線是根據(jù)前文所述三目視覺(jué)預(yù)測(cè)方法得到的預(yù)測(cè)軌跡。視覺(jué)預(yù)測(cè)軌跡基本與GPS實(shí)測(cè)軌跡一致。但是隨著行駛距離的增大，預(yù)測(cè)的累積誤差越來(lái)越明顯。

圖6b、6d、6f表明，方向的誤差是導(dǎo)致預(yù)測(cè)軌跡和實(shí)測(cè)軌跡偏差越來(lái)越大的主要原因。方向誤差在震蕩中不斷增大。根據(jù)試驗(yàn)數(shù)據(jù)，分別建立了不同速度下方向累積誤差的2次多項(xiàng)式模型。當(dāng)拖拉機(jī)行駛速度為分別0.2、0.5、0.8 m/s時(shí)，該模型分別如式（11）～（13）所示，對(duì)應(yīng)2分別為0.93、0.97、0.98。式（11）～（13）中，對(duì)的一階導(dǎo)數(shù)反映出方向累計(jì)誤差的變化。由于二次項(xiàng)系數(shù)均大于0，故一階導(dǎo)數(shù)均為遞增函數(shù)，即方向誤差的變化呈線性遞增。通過(guò)計(jì)算，線性遞增的斜率分別為0.000 2、0.002 6、0.005 0，表明拖拉機(jī)行駛速度越高，方向誤差增速越高。該模型可以用來(lái)估計(jì)當(dāng)前時(shí)刻誤差狀態(tài)。

式中表示行駛時(shí)間，表示方向累積誤差。

圖7反映出不同速度下方向的誤差變化很小。主要原因是試驗(yàn)過(guò)程中拖拉機(jī)直線行駛，在方向上位移很小，因此累積誤差也很小，在±5 cm以內(nèi)。

圖7 不同恒定速度下x方向累積誤差

表1 x和z方向累積誤差數(shù)據(jù)

表1定量分析了不同速度下，、方向累積誤差變化。行駛速度越快，方向累積誤差上升越快。速度為0.2 m/s時(shí)，需要46.5 s的時(shí)間方向累積誤差超過(guò)0.1 m，當(dāng)速度上升到0.8 m/s時(shí)，這個(gè)時(shí)間縮短到8.5 s。方向誤差變化沒(méi)有明顯規(guī)律性。通過(guò)對(duì)表1的數(shù)據(jù)進(jìn)行非線性擬合，得到方向累積誤差變化速率（單位m/s）與行駛速度之間的關(guān)系

據(jù)式（14）可以直接計(jì)算不同速度下的方向累積誤差變化速率。

在國(guó)內(nèi)外近期類似研究中，文獻(xiàn)[32]中提到采用粒子濾波方式對(duì)改裝的農(nóng)業(yè)機(jī)器人進(jìn)行了60 m的直線跟蹤，橫向偏差為4±0.7 cm。文獻(xiàn)[33]中提到改裝后的茂源250拖拉機(jī)以0.58 m/s速度視覺(jué)導(dǎo)航，最大誤差18 cm，平均誤差4.8 cm。這些關(guān)于機(jī)器視覺(jué)在農(nóng)機(jī)導(dǎo)航上的最新研究成果與本文研究最大的區(qū)別在于研究?jī)?nèi)容的不同。上述研究均是以機(jī)器視覺(jué)和其他傳感器聯(lián)合，進(jìn)行直線跟蹤研究。而本文是研究預(yù)測(cè)軌跡與實(shí)際軌跡的偏差。由于本文是單獨(dú)通過(guò)視覺(jué)傳感器對(duì)運(yùn)動(dòng)軌跡進(jìn)行檢測(cè)，并在此基礎(chǔ)上再次預(yù)測(cè)，那么累積誤差將不可避免。

誤差產(chǎn)生的原因主要包括：自然光線影響和圖像處理的時(shí)間延遲造成。為了減小累積誤差，得到更好的試驗(yàn)效果，建議使用更高性能工控機(jī)和高速快門相機(jī)。

4 結(jié) 論

1）通過(guò)長(zhǎng)短基線2套雙目視覺(jué)系統(tǒng)疊加構(gòu)建三目視覺(jué)系統(tǒng)，并通過(guò)灰色預(yù)測(cè)算法，確實(shí)能夠預(yù)測(cè)拖拉機(jī)在平面上的運(yùn)動(dòng)軌跡。

2）通過(guò)視覺(jué)系統(tǒng)得到的預(yù)測(cè)軌跡與真實(shí)軌跡之間存在累積誤差。該誤差主要由前進(jìn)方向的測(cè)量誤差引起。

3）拖拉機(jī)行駛速度越高，前進(jìn)方向累積誤差增速越高。速度為0.2 m/s時(shí)，前進(jìn)方向累積誤差超過(guò)0.1 m的時(shí)間和行駛距離分別為46.5 s和9.3 m。速度上升到0.5 m/s時(shí)，該時(shí)間和行駛距離分別降低到17.2 s和8.6 m。當(dāng)速度上升到0.8 m/s時(shí)，該時(shí)間和距離分別快速降低至8.5 s和6.8 m。

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Traveling trajectory prediction method and experiment of autonomous navigation tractor based on trinocular vision

Tian Guangzhao1, Gu Baoxing1※, Irshad Ali Mari2, Zhou Jun1, Wang Haiqing1

(1.210031,; 2.66020,)

In order to make the autonomous navigation tractors work steadily and continuously without the satellite positioning system, a traveling trajectory prediction system and method based on trinocular vision were designed in this paper. The system was composed of a trinocular vision camera, an IEEE 1394 acquisition card and an embedded industrial personal computer (IPC). The right and left sub cameras constituted a binocular vision system with a long base line. The right and middle sub cameras constituted another binocular vision system with a narrow base line. To obtain more precise measurement results, the two binocular vision systems worked independently and in time-sharing. Then the motion vectors of tractor, which were in presentation of horizontal direction data, were calculated by the feature point coordinate changing in the working environment of the tractor. Finally, the error models which were in the direction of heading were established at different velocities, and the motion vectors of tractor were predicted by the models based on grey method. The contrast experiments were completed with a modified tractor of Dongfanghong SG250 at the speed of 0.2, 0.5 and 0.8m/s. During the experiments, the IPC was used to collect RTK-GPS data and predict movement tracks. The RTK-GPS used in the experiments was a kind of high-precision measuring device, and the measuring precision can reach 1-2 cm. Therefore, the location data of RTK-GPS were supposed as the standard which was used to compare with the data from trinocular vision system. The experimental results showed that the method mentioned above could accurately predict the trajectory of the tractor on the plane with an inevitable error which was mainly caused by the visual measurement error of the forward direction (direction). When the tractor travelled at the speed of 0.2 m/s, the time and the distance that the error in forward direction exceeded 0.1 m equaled 46.5 s and 9.3 m, respectively. When the speed increased to 0.5 m/s, the time and the distance decreased to 17.2 s and 8.6 m, respectively. When the driving speed increased to 0.8 m/s, the time and distance quickly decreased to 8.5 s and 6.8 m, respectively. It showed that the higher the tractor traveling speed, the faster the error in forward direction increased. After that, the relationship between errors in forward direction and traveling time was acquired and analyzed by the way of nonlinear data fitting. In addition, the experimental results showed that the trend of lateral error (direction) which was perpendicular to forward direction was not regular. When the speed was 0.2 m/s, the average error was 0.002 5 m with a standard deviation (STD) of 0.003 9. When the speed increased to 0.5 m/s and 0.8 m/s, the average error in lateral direction was 0.008 2 m with an STD of 0.012 4 and 0.003 6 m with an STD of 0.006 4. The result showed that the lateral error was very small and almost invariable. Therefore, the errors of trinocular vision were mainly caused by the errors of the forward direction. The root causes of the error were the natural light and time-delay during the image processing. According to the experimental data and results, the system and method proposed in this paper could be used to measure and predict the traveling trajectory of a tractor in the dry agricultural environment with the sudden loss of the satellite signal in a short period of time. The measured and predicted data could provide temporary help for the operations of autonomous tractors.

tractor; automatic guidance; machine vision; trajectory prediction; gray model

10.11975/j.issn.1002-6819.2018.19.005

S219.1

A

1002-6819(2018)-19-0040-06

2018-06-13

2018-08-27

中央高?；緲I(yè)務(wù)費(fèi)資助項(xiàng)目（KYGX201701）；國(guó)家自然科學(xué)基金資助項(xiàng)目（31401291）；江蘇省自然科學(xué)基金資助項(xiàng)目（BK20140729）

田光兆，講師，博士，主要從事農(nóng)業(yè)機(jī)械導(dǎo)航與控制研究。 Email：tgz@njau.edu.cn

顧寶興，講師，博士，主要從事智能化農(nóng)業(yè)裝備研究。 Email：gbx@njau.edu.cn

田光兆，顧寶興，Irshad Ali Mari，周 俊，王海青. 基于三目視覺(jué)的自主導(dǎo)航拖拉機(jī)行駛軌跡預(yù)測(cè)方法及試驗(yàn)[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2018，34(19)：40－45. doi：10.11975/j.issn.1002-6819.2018.19.005 http://www.tcsae.org

Tian Guangzhao, Gu Baoxing, Irshad Ali Mari, Zhou Jun, Wang Haiqing. Traveling trajectory prediction method and experiment of autonomous navigation tractor based on trinocular vision [J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2018, 34(19): 40－45. (in Chinese with English abstract) doi：10.11975/j.issn.1002-6819.2018.19.005 http://www.tcsae.org