胡書(shū)鵬，尚業(yè)華，劉 卉，李 由，趙春江，付衛(wèi)強(qiáng)

?

拖拉機(jī)轉(zhuǎn)向輪轉(zhuǎn)角位移式和四連桿式間接測(cè)量方法對(duì)比試驗(yàn)

胡書(shū)鵬1,2，尚業(yè)華2,3，劉 卉1，李 由2,3，趙春江2,3，付衛(wèi)強(qiáng)2,3※

（1. 首都師范大學(xué)信息工程學(xué)院，北京 100048； 2. 北京農(nóng)業(yè)信息技術(shù)研究中心，北京 100097； 3. 國(guó)家農(nóng)業(yè)信息化工程技術(shù)研究中心，北京 100097）

針對(duì)車(chē)輪轉(zhuǎn)角直接測(cè)量法在工程實(shí)踐中角度傳感器安裝困難且轉(zhuǎn)軸易斷裂的現(xiàn)象，結(jié)合車(chē)輪轉(zhuǎn)向過(guò)程，提出了位移式間接轉(zhuǎn)角測(cè)量法和四連桿式間接轉(zhuǎn)角測(cè)量法。依據(jù)位移式和四連桿式2種間接測(cè)量方法原理，分別建立轉(zhuǎn)角測(cè)量模型，以雷沃M800型拖拉機(jī)為基礎(chǔ)，構(gòu)建自動(dòng)導(dǎo)航試驗(yàn)平臺(tái)，通過(guò)轉(zhuǎn)角測(cè)量試驗(yàn)、瀝青路面與農(nóng)田環(huán)境下的導(dǎo)航精度對(duì)比試驗(yàn)，分析四連桿式間接測(cè)量法、位移式間接測(cè)量法和直接測(cè)量法3種方法的應(yīng)用效果。轉(zhuǎn)角測(cè)量對(duì)比試驗(yàn)結(jié)果表明，3種方法的角度值最大誤差為0.081°，平均誤差分別為0.061°、0.014°和0.017°，小于傳感器的測(cè)量精度0.088°，3種測(cè)量方法測(cè)量的測(cè)量精度一致。通過(guò)瀝青路面與農(nóng)田環(huán)境2種地況試驗(yàn)測(cè)試，瀝青路面上和農(nóng)田環(huán)境下，3種方法的橫向偏差平均值的最大值分別為0.235 9、0.364 5、0.498 4 cm，試驗(yàn)表明3種測(cè)量方法的導(dǎo)航精度一致。相對(duì)于位移式間接轉(zhuǎn)角測(cè)量法和直接測(cè)量法，在瀝青路面上和農(nóng)田環(huán)境下，四連桿式間接測(cè)量法導(dǎo)航精度標(biāo)準(zhǔn)差最小，分別為0.890 4和1.297 5 cm。四連桿式間接轉(zhuǎn)角測(cè)量法所采用的四連桿式角度傳感器安裝簡(jiǎn)便、易于防護(hù)，無(wú)摩擦損耗，可代替直接轉(zhuǎn)角測(cè)量法，應(yīng)用于實(shí)踐中。

農(nóng)業(yè)機(jī)械；轉(zhuǎn)向；模型；自動(dòng)導(dǎo)航；轉(zhuǎn)角測(cè)量；位移；四連桿；導(dǎo)航精度

0 引 言

隨著精準(zhǔn)農(nóng)業(yè)的發(fā)展，拖拉機(jī)自動(dòng)導(dǎo)航系統(tǒng)作為農(nóng)業(yè)智能裝備的重點(diǎn)，應(yīng)用越來(lái)越廣泛[1-2]。拖拉機(jī)自動(dòng)導(dǎo)航系統(tǒng)是通過(guò)控制轉(zhuǎn)向油缸活塞桿的位置，實(shí)現(xiàn)拖拉機(jī)運(yùn)動(dòng)軌跡控制。通常車(chē)輪對(duì)中時(shí)，車(chē)輪軸線與車(chē)身中軸線平行。當(dāng)車(chē)輪轉(zhuǎn)動(dòng)后，車(chē)輪軸線與車(chē)身中軸線的夾角即為車(chē)輪轉(zhuǎn)角。車(chē)輪轉(zhuǎn)角測(cè)量作為自動(dòng)導(dǎo)航系統(tǒng)自動(dòng)轉(zhuǎn)向單元的一部分，是影響自動(dòng)導(dǎo)航精度的重要因素之一[3-4]。

國(guó)內(nèi)外研究人員采用了不同的技術(shù)手段進(jìn)行拖拉機(jī)自動(dòng)導(dǎo)航系統(tǒng)車(chē)輪轉(zhuǎn)角的測(cè)量。Xiang等[5-8]通過(guò)電位計(jì)測(cè)量轉(zhuǎn)向節(jié)旋轉(zhuǎn)角度，獲取車(chē)輪轉(zhuǎn)角，Lee等[9-11]采用絕對(duì)式編碼器測(cè)量車(chē)輪轉(zhuǎn)角，Hu等[12-13]通過(guò)位移式傳感器測(cè)量轉(zhuǎn)向油缸行程，推算車(chē)輪轉(zhuǎn)角。馮朝印等[14-17]采用電阻式角度傳感器，黎永鍵等[18-19]采用KMA199型磁敏電阻式角度傳感器測(cè)量車(chē)輪轉(zhuǎn)角，尤文寬等[20-21]采用霍爾角位移傳感器測(cè)量轉(zhuǎn)向輪轉(zhuǎn)角值，任文濤等[22-24]采用位移式傳感器測(cè)量車(chē)輪轉(zhuǎn)角，王鶴等[25-27]采用將GAS60型角度傳感器安裝在前橋上，并通過(guò)連桿與轉(zhuǎn)向節(jié)連接，實(shí)現(xiàn)車(chē)輪轉(zhuǎn)角測(cè)量。據(jù)此，常用的車(chē)輪轉(zhuǎn)角測(cè)量方法有角度傳感器直接測(cè)量法、位移式間接轉(zhuǎn)角測(cè)量法和四連桿式間接轉(zhuǎn)角測(cè)量法等3種。但在科研試驗(yàn)與工程實(shí)踐中發(fā)現(xiàn)，角度傳感器安裝困難且轉(zhuǎn)軸易斷裂,編碼器的分辨率較低，磁阻式角度傳感器受氣隙磁場(chǎng)不均勻影響很大[15]。

本文以雷沃M800型拖拉機(jī)為研究平臺(tái)，選擇霍爾角度傳感器作為角度傳感器直接法的轉(zhuǎn)角測(cè)量設(shè)備；選擇直線位移傳感器和四連桿式角度傳感器作為間接轉(zhuǎn)角測(cè)量設(shè)備，根據(jù)2種傳感器測(cè)量轉(zhuǎn)角的原理，分別建立轉(zhuǎn)角測(cè)量模型，設(shè)計(jì)對(duì)比試驗(yàn)比較直接測(cè)量法和2種間接測(cè)量法時(shí)的測(cè)量精度，并通過(guò)田間試驗(yàn)對(duì)比其用于拖拉機(jī)自動(dòng)導(dǎo)航系統(tǒng)對(duì)導(dǎo)航精度的影響。

1 車(chē)輪轉(zhuǎn)角測(cè)量法

1.1 角度傳感器直接測(cè)量法

將角度傳感器與轉(zhuǎn)向節(jié)立軸同軸安裝，使角度傳感器轉(zhuǎn)軸與轉(zhuǎn)向節(jié)同步旋轉(zhuǎn)。由于轉(zhuǎn)向節(jié)相對(duì)于車(chē)輪有一定傾斜（圖1），從車(chē)輛前方看車(chē)輪，轉(zhuǎn)向節(jié)與車(chē)輪中軸線有一個(gè)夾角，即為轉(zhuǎn)向節(jié)側(cè)傾角；從車(chē)輛側(cè)面看車(chē)輪，轉(zhuǎn)向節(jié)與車(chē)輪軸線有一個(gè)夾角，即為轉(zhuǎn)向節(jié)后傾角。

轉(zhuǎn)向節(jié)傾斜使得轉(zhuǎn)向節(jié)旋轉(zhuǎn)角度與車(chē)輪實(shí)際轉(zhuǎn)角值不相等，其車(chē)輪-轉(zhuǎn)向節(jié)轉(zhuǎn)角的關(guān)系模型如下[26-27]

式（2）即為角度傳感器直接測(cè)量法的角位移量與車(chē)輪轉(zhuǎn)角關(guān)系式，其中和值可從拖拉機(jī)手冊(cè)中查到，值由角度傳感器測(cè)量得到。

1.轉(zhuǎn)向節(jié) 2.導(dǎo)向輪

1.Knuckle 2.Guide wheel

注：為內(nèi)傾角，(°)；為后傾角，(°)。

Note:represents camber, (°)；represents caster angle, (°)。

圖1 車(chē)輪轉(zhuǎn)向節(jié)內(nèi)傾角和后傾角

Fig.1 Wheel knuckle caster angle and inclination angle

1.2 位移式間接轉(zhuǎn)角測(cè)量法

直線位移傳感器與轉(zhuǎn)向油缸并列安裝，其安裝示意圖如圖2a所示。

1.轉(zhuǎn)向節(jié)臂 2.轉(zhuǎn)向節(jié) 3.前橋 4.轉(zhuǎn)向油缸 5.直線位移傳感器

1.Knuckle arm 2.Kunckle 3.Front axle 4.Steering cylinder 5.Displacement sensor

注：1為轉(zhuǎn)向節(jié)中心點(diǎn)到轉(zhuǎn)向油缸活塞桿固定點(diǎn)長(zhǎng)度，mm；2為轉(zhuǎn)向節(jié)中心點(diǎn)到轉(zhuǎn)向油缸固定點(diǎn)的長(zhǎng)度，mm；3為車(chē)輪對(duì)中時(shí)的轉(zhuǎn)向油缸長(zhǎng)度，mm；為轉(zhuǎn)向油缸活塞桿位移量，mm；為車(chē)輪對(duì)中時(shí)，轉(zhuǎn)向節(jié)臂與轉(zhuǎn)向節(jié)中心點(diǎn)到轉(zhuǎn)向油缸固定點(diǎn)連線之間的夾角，(°)；為轉(zhuǎn)向節(jié)旋轉(zhuǎn)角度，(°)。

Note:1represents length of knuckle center point to steering cylinder piston rod fixed point, mm;2represents length of knuckle center point to steering cylinder fixed point, mm;3represents steering cylinder when wheel is centered, mm;represents displacement of steering cylinder piston rod, mm;represents angle between knuckle arm and connection from knuckle pivot center point to steering cylinder fixed point, (°);represents knuckle rotation angle, (°)。

圖2 直線位移傳感器安裝示意圖和數(shù)學(xué)模型

Fig.2 Displacement sensor fix and mathematical model

通過(guò)其幾何關(guān)系建立的轉(zhuǎn)向油缸行程到轉(zhuǎn)向節(jié)轉(zhuǎn)角模型（圖2b）。在?0和?1中，分別得到

式中1為轉(zhuǎn)向節(jié)中心點(diǎn)到轉(zhuǎn)向油缸活塞桿固定點(diǎn)長(zhǎng)度，mm；2為轉(zhuǎn)向節(jié)中心點(diǎn)到轉(zhuǎn)向油缸固定點(diǎn)的長(zhǎng)度，mm；3為車(chē)輪對(duì)中時(shí)的轉(zhuǎn)向油缸長(zhǎng)度，mm；為轉(zhuǎn)向油缸活塞桿位移量，mm；為車(chē)輪對(duì)中時(shí)，轉(zhuǎn)向節(jié)臂與轉(zhuǎn)向節(jié)到轉(zhuǎn)向油缸固定點(diǎn)連線之間的夾角，(°)。

由式（1）～式（4）得到，車(chē)輪轉(zhuǎn)角與轉(zhuǎn)向油缸活塞桿位移量的關(guān)系式如下

1.3 四連桿式間接轉(zhuǎn)角測(cè)量法

四連桿式角度傳感器的安裝示意圖如圖3a所示。在實(shí)際安裝時(shí)，采用鉛垂線測(cè)量、、3點(diǎn)對(duì)地高度，通過(guò)添加墊片調(diào)節(jié)固定點(diǎn)與前橋間的高度，確保3個(gè)點(diǎn)對(duì)地高度一致，以保證四連桿機(jī)構(gòu)在同一平面內(nèi)運(yùn)動(dòng)。

1.轉(zhuǎn)向節(jié)臂 2.轉(zhuǎn)向節(jié) 3.前橋 4.連桿 5.擺桿

1. Knuckle arm 2. Knuckle 3.Forward axle 4.Connecting rod 5.Pendulum rod

注：4為轉(zhuǎn)向節(jié)中心點(diǎn)到四連桿角度傳感器在前橋上的固定點(diǎn)長(zhǎng)度，mm；5為擺桿長(zhǎng)度，mm；6為連桿長(zhǎng)度，mm；7為轉(zhuǎn)向節(jié)中心點(diǎn)到連桿在轉(zhuǎn)向節(jié)臂上固定點(diǎn)的長(zhǎng)度，mm；8為車(chē)輪對(duì)中時(shí)，轉(zhuǎn)向節(jié)中心點(diǎn)到連桿與擺桿連接點(diǎn)長(zhǎng)度，mm；9為車(chē)輪轉(zhuǎn)動(dòng)后，轉(zhuǎn)向節(jié)中心點(diǎn)到連桿與擺桿連接點(diǎn)長(zhǎng)度，mm；0為車(chē)輪對(duì)中時(shí)，擺桿與前橋夾角，(°)；1為車(chē)輪轉(zhuǎn)動(dòng)后，擺桿與前橋夾角，(°)；為車(chē)輪對(duì)中時(shí)，轉(zhuǎn)向節(jié)臂與前橋夾角，(°)；為車(chē)輪轉(zhuǎn)動(dòng)后轉(zhuǎn)向節(jié)臂與前橋夾角，(°)。

Note:4represents length of fixed point of knuckle center point to four-bar angle sensor on front axle, mm;5represents Pendulum rod length，mm；6represents connecting rod length, mm;7represents length of knuckle center point to fixed point of bar on knuckle arm, mm;8represents length of knuckle center point to connecting point of bar and swing bar when wheel is centered, mm;9represents length from center point of steering knuckle to connecting point of bar and swing bar when wheel is centered, mm;0represents angle between connecting rod and pendulum rod when wheel is centered, (°);1represents angle between connecting rod and pendulum rod when wheel turned, (°);represents angle between knuckle arm and forward axle when wheel is centered, (°);represents angle between knuckle arm and forward axle when wheel is turned, (°).

圖3 四連桿式角度傳感器安裝示意圖和數(shù)學(xué)模型

Fig.3 Four-bar angle sensor fix and mathematical model

建立如圖3b所示的四連桿式轉(zhuǎn)角測(cè)量模型。在?0和?00中，得到

在?1和?11中，得到

如圖3b所示，則

式中為四連桿式角度傳感器測(cè)量值變化量，4為轉(zhuǎn)向節(jié)中心點(diǎn)到四連桿角度傳感器在前橋上的固定點(diǎn)長(zhǎng)度，mm；5為擺桿長(zhǎng)度，mm；6為連桿長(zhǎng)度，mm；7為轉(zhuǎn)向節(jié)中心點(diǎn)到連桿在轉(zhuǎn)向節(jié)臂上固定點(diǎn)的長(zhǎng)度，mm；8為車(chē)輪對(duì)中時(shí)，轉(zhuǎn)向節(jié)中心點(diǎn)到連桿與擺桿連接點(diǎn)長(zhǎng)度，mm；9為車(chē)輪轉(zhuǎn)動(dòng)后，轉(zhuǎn)向節(jié)中心點(diǎn)到連桿與擺桿連接點(diǎn)長(zhǎng)度，mm；0為車(chē)輪對(duì)中時(shí)，擺桿與前橋夾角，(°)；1為車(chē)輪轉(zhuǎn)動(dòng)后，擺桿與前橋夾角，(°)；為車(chē)輪對(duì)中時(shí)，轉(zhuǎn)向節(jié)臂與前橋夾角，(°)；為車(chē)輪轉(zhuǎn)動(dòng)后轉(zhuǎn)向節(jié)臂與前橋夾角，(°)。

由式（1）、式（2）、式（6）、式（7）、式（9）、式（10）、式（11）得

2 轉(zhuǎn)角測(cè)量對(duì)比試驗(yàn)

2.1 構(gòu)建試驗(yàn)平臺(tái)

為檢驗(yàn)和對(duì)比位移式間接轉(zhuǎn)角測(cè)量法、四連桿式間接轉(zhuǎn)角測(cè)量法和直接轉(zhuǎn)角測(cè)量法對(duì)導(dǎo)向輪轉(zhuǎn)角測(cè)量精度的影響，構(gòu)建試驗(yàn)測(cè)試平臺(tái)。試驗(yàn)平臺(tái)包括：雷沃M800型拖拉機(jī)；北京農(nóng)業(yè)智能裝備技術(shù)研究中心的AMG-1102型自動(dòng)導(dǎo)航系統(tǒng)，直線作業(yè)橫向偏差小于2.5 cm；米朗公司的KPC-250型直線位移傳感器，量程為0～250 mm，線性精度±0.05%FS；四連桿式角度傳感器為通磁偉業(yè)公司的WYT-AT-3型霍爾角度傳感器，擺桿長(zhǎng)度為145 mm，連桿長(zhǎng)度為234 mm，量程為0～90°，線性度1.0%FS；便攜式計(jì)算機(jī)。其中，AMG-1102型自動(dòng)導(dǎo)航系統(tǒng)采用角度傳感器直接測(cè)量法，使用通磁偉業(yè)公司的WYT-AT-3型霍爾角度傳感器?；魻柦嵌葌鞲衅髋c轉(zhuǎn)向節(jié)同軸安裝，四連桿式角度傳感器固定在前橋上，連桿與轉(zhuǎn)向節(jié)臂連接，直線位移傳感器與轉(zhuǎn)向油缸并列安裝。圖4為傳感器的安裝位置。

2.2 2種間接轉(zhuǎn)角測(cè)量法的傳感器標(biāo)定

2種間接轉(zhuǎn)角測(cè)量法是通過(guò)建立測(cè)量模型，將測(cè)量值轉(zhuǎn)換為目標(biāo)值，轉(zhuǎn)換關(guān)系式復(fù)雜，計(jì)算量大，影響轉(zhuǎn)向控制器的控制性能，因此采用最小二乘法線性擬合測(cè)量模型，便于轉(zhuǎn)向控制器完成傳感器測(cè)量值到轉(zhuǎn)角值的轉(zhuǎn)換處理。

2.2.1 直線位移傳感器的標(biāo)定

直線位移傳感器安裝完成后，測(cè)量參數(shù)1為142 mm，2為561 mm，3為543 mm，雷沃M800型拖拉機(jī)的轉(zhuǎn)向節(jié)內(nèi)傾角=9°，轉(zhuǎn)向節(jié)后傾角=1°，對(duì)式（5）中位移量與車(chē)輪轉(zhuǎn)角的變化關(guān)系進(jìn)行最小二乘法線性擬合。擬合方程為

拖拉機(jī)的工作環(huán)境使得拖拉機(jī)的振動(dòng)較大，在實(shí)際的控制中，振動(dòng)對(duì)AD采樣易造成振動(dòng)干擾。本文選擇遞推平均濾波，該濾波算法對(duì)周期性干擾有良好的抑制作用，適用于振蕩系統(tǒng)[28-30]，濾波后信號(hào)平滑度高。

2.2.2 四連桿式角度傳感器標(biāo)定

四連桿式角度傳感器安裝后，測(cè)量參數(shù)4為210 mm，5為145 mm，6為234 mm，7為149 mm，8為286 mm，對(duì)式（12）中與轉(zhuǎn)角的變化關(guān)系進(jìn)行最小二乘法線性擬合。擬合方程為

2.3 轉(zhuǎn)角靜態(tài)測(cè)量對(duì)比

為了分析直接測(cè)量法與2種間接測(cè)量法對(duì)角度測(cè)量值的差異性，設(shè)計(jì)了轉(zhuǎn)角靜態(tài)測(cè)量試驗(yàn)。試驗(yàn)在平整路面上進(jìn)行，轉(zhuǎn)動(dòng)方向盤(pán)到不同位置，采用直接測(cè)量法、位移式間接測(cè)量法和四連桿式間接測(cè)量法3種方法分別測(cè)量當(dāng)前轉(zhuǎn)角值，由于車(chē)輪轉(zhuǎn)角真值不能直接測(cè)量，故以直接測(cè)量法20次測(cè)量值的平均值為對(duì)比參考值，對(duì)比3種測(cè)量方法的測(cè)量結(jié)果。考慮到拖拉機(jī)自動(dòng)導(dǎo)航直線行駛時(shí)，角度主要在車(chē)輪對(duì)中位置附近變化，表1中列舉了直接測(cè)量法測(cè)量值、四連桿式間接測(cè)量法測(cè)量值和位移式間接測(cè)量法測(cè)量值的部分?jǐn)?shù)據(jù)。

表1 轉(zhuǎn)角值測(cè)量結(jié)果

注：對(duì)直接測(cè)量法測(cè)量20次的結(jié)果取平均值，作為參考值。

Note: Results of direct measurement method 20 times average, as a reference value.

由表1可知，3種測(cè)量方法測(cè)量的角度值最大誤差為0.081°，平均誤差分別為0.017°、0.014°和0.061°，小于傳感器的測(cè)量精度0.088°，3種測(cè)量方法測(cè)量的測(cè)量精度一致。

在二輪車(chē)運(yùn)動(dòng)學(xué)模型中[1-2]，車(chē)輪轉(zhuǎn)角為虛擬中位輪與車(chē)身軸線的夾角，這是不可直接測(cè)量的，雖然可以通過(guò)阿克曼轉(zhuǎn)角模型轉(zhuǎn)換為測(cè)量左右車(chē)輪的轉(zhuǎn)角，但阿克曼轉(zhuǎn)角模型是建立在理想條件下，有一定的誤差[25-26]，中國(guó)科學(xué)院沈陽(yáng)自動(dòng)化研究所采用SPZJ-1型汽車(chē)轉(zhuǎn)向角檢測(cè)儀（分辨率0.1°）進(jìn)行轉(zhuǎn)角測(cè)量獲得車(chē)輪轉(zhuǎn)角值，但是測(cè)量精度不高[27]。本研究下一步擬借鑒北京理工大學(xué)在汽車(chē)領(lǐng)域轉(zhuǎn)角測(cè)量方法，通過(guò)計(jì)算拖拉機(jī)運(yùn)動(dòng)軌跡切向矢量的方向變化率，結(jié)合轉(zhuǎn)向輪側(cè)偏剛度，推算出轉(zhuǎn)向輪轉(zhuǎn)角值[31]。

3 導(dǎo)航效果對(duì)比試驗(yàn)

試驗(yàn)在北京市昌平區(qū)小湯山國(guó)家精準(zhǔn)農(nóng)業(yè)研究示范基地進(jìn)行，選擇了瀝青平整路面和農(nóng)田地塊2種地況，其中瀝青路面長(zhǎng)度約400 m，農(nóng)田地塊南北長(zhǎng)度約200 m。分別采用霍爾角度傳感器、直線位移傳感器和四連桿式角度傳感器作為測(cè)量單元，在2種地況下檢驗(yàn)自動(dòng)導(dǎo)航系統(tǒng)的導(dǎo)航精度。在瀝青路面上測(cè)試時(shí)，拖拉機(jī)不掛接農(nóng)具；在田間測(cè)試時(shí)，拖拉機(jī)懸掛農(nóng)具；車(chē)速均保持在4.2 km/h左右。通過(guò)導(dǎo)航控制終端實(shí)時(shí)記錄拖拉機(jī)自動(dòng)導(dǎo)航模式下直線追蹤導(dǎo)航的橫向偏差，以便于分析2種測(cè)量方法下的導(dǎo)航精度。

3.1 試驗(yàn)數(shù)據(jù)處理方法

試驗(yàn)中通過(guò)導(dǎo)航終端實(shí)時(shí)記錄拖拉機(jī)橫向偏差，對(duì)橫向偏差的平均值（單次試驗(yàn)全部數(shù)據(jù)取均值）和標(biāo)準(zhǔn)差進(jìn)行統(tǒng)計(jì)分析，作為評(píng)價(jià)指標(biāo)。其中平均值反映了自動(dòng)導(dǎo)航精度的效果，而標(biāo)準(zhǔn)差反映了自動(dòng)導(dǎo)航時(shí)的穩(wěn)定性[4,32-33]，計(jì)算式如式（15）與式（16），表2為瀝青路面上與農(nóng)田環(huán)境下自動(dòng)導(dǎo)航橫向偏差的統(tǒng)計(jì)分析結(jié)果。

式中e為時(shí)刻的橫向偏差，cm；為橫向偏差平均值，cm；XET為橫向偏差的標(biāo)準(zhǔn)差，表示自動(dòng)導(dǎo)航的穩(wěn)定性，cm。

3.2 導(dǎo)航效果對(duì)比分析

3.2.1 導(dǎo)航精度對(duì)比

瀝青路面上，位移式間接轉(zhuǎn)角測(cè)量法的導(dǎo)航精度最高，橫向偏差均值為0.106 5 cm，小于四連桿式間接測(cè)量法的0.150 6 cm和直接測(cè)量法的0.291 9 cm；在農(nóng)田環(huán)境下，直接測(cè)量法的導(dǎo)航精度最高為0.014 6 cm，小于四連桿式間接測(cè)量法的0.028 2 cm和位移式間接轉(zhuǎn)角測(cè)量法的0.109 0 cm。

通過(guò)瀝青路面與農(nóng)田環(huán)境2種地況試驗(yàn)測(cè)試，瀝青路面上和農(nóng)田環(huán)境下，四連桿式間接測(cè)量法、位移式間接測(cè)量法和直接測(cè)量法的橫向偏差平均值的最大值分別為0.235 9、0.364 5、0.498 4 cm，試驗(yàn)表明3種測(cè)量方法的導(dǎo)航精度一致。

3.2.2 導(dǎo)航穩(wěn)定性對(duì)比

瀝青路面上，四連桿式間接轉(zhuǎn)角測(cè)量法的導(dǎo)航穩(wěn)定性最高，為0.890 4 cm，小于直接測(cè)量法的0.987 7 cm和位移式間接轉(zhuǎn)角測(cè)量法的1.277 8 cm；在農(nóng)田環(huán)境下，四連桿式間接轉(zhuǎn)角測(cè)量法的導(dǎo)航穩(wěn)定性最高，為1.297 5 cm，小于直接測(cè)量法的1.426 8 cm和位移式間接轉(zhuǎn)角測(cè)量法的1.340 0 cm。

綜上所述，四連桿式間接轉(zhuǎn)角測(cè)量法的導(dǎo)航效果是最好的，雖然位移式間接轉(zhuǎn)角測(cè)量法的導(dǎo)航精度在瀝青路面上是最高的，但傳感器內(nèi)部電刷與阻軌長(zhǎng)時(shí)間在小范圍內(nèi)摩擦，使得直線位移傳感器線性度變差。在農(nóng)田環(huán)境下使用大約50 h后，導(dǎo)航系統(tǒng)的橫向偏差均值為0.456 1 cm，標(biāo)準(zhǔn)差為2.683 4 cm，導(dǎo)航精度下降顯著。

表2 瀝青路面與農(nóng)田環(huán)境橫向偏差統(tǒng)計(jì)分析表

4 結(jié) 論

1）在不考慮車(chē)輪變形、機(jī)械結(jié)構(gòu)精度等因素下，建立了位移式間接轉(zhuǎn)角測(cè)量模型與四連桿式間接轉(zhuǎn)角測(cè)量模型，并進(jìn)行轉(zhuǎn)角測(cè)量對(duì)比試驗(yàn)。四連桿式間接測(cè)量法、位移式間接測(cè)量法和直接測(cè)量法測(cè)量的角度值最大誤差為0.081°，平均誤差分別為0.061°、0.014°和0.017°，小于傳感器的測(cè)量精度0.088°，3種測(cè)量方法測(cè)量的測(cè)量精度一致。

2）通過(guò)瀝青路面與農(nóng)田環(huán)境2種地況試驗(yàn)測(cè)試，瀝青路面上和農(nóng)田環(huán)境下，四連桿式間接測(cè)量法、位移式間接測(cè)量法和直接測(cè)量法的橫向偏差平均值的最大值分別為0.235 9、0.364 5、0.498 4 cm，試驗(yàn)表明3種測(cè)量方法的導(dǎo)航精度一致。

3）相對(duì)于位移式間接轉(zhuǎn)角測(cè)量法和直接測(cè)量法，在瀝青路面上和農(nóng)田環(huán)境下，四連桿式間接測(cè)量法導(dǎo)航精度標(biāo)準(zhǔn)差最小，分別為0.890 4和1.297 5 cm。試驗(yàn)表明，在導(dǎo)航精度一致的情況下，四連桿式角度傳感器有最小的導(dǎo)航精度標(biāo)準(zhǔn)差，并且安裝方便，易于防護(hù)，可以代替直接轉(zhuǎn)角測(cè)量法，應(yīng)用于工程中。

[1] 胡靜濤，高雷，白曉平，等. 農(nóng)業(yè)機(jī)械自動(dòng)導(dǎo)航技術(shù)研究進(jìn)展[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2015，31(10)：1－10.

Hu Jingtao, Gao Lei, Bai Xiaoping, et al. Review of research on automatic guidance of agricultural vehicles[J]. Transactionsof the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2015, 31(10): 1－10. (in Chinese with English abstract)

[2] 姬長(zhǎng)英，周俊. 農(nóng)業(yè)機(jī)械導(dǎo)航技術(shù)發(fā)展分析[J].農(nóng)業(yè)機(jī)械學(xué)報(bào)，2014，45(9)：44－54.

Ji Changying, Zhou Jun. Current situation of navigation technologies for agricultural machinery[J]. Transactions of the Chinese Society for Agricultural Machinery, 2014, 45(9): 44－54. (in Chinese with English abstract)

[3] 楊柳，羅婷婷，程新榮，等. 基于Raspberry Pi 的拖拉機(jī)通用自動(dòng)駕駛系統(tǒng)[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2015，31(21)：109－115.

Yang Liu, Luo Tingting, Cheng Xinrong, et al. Universal autopilot system of tractor based on Raspberry Pi[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2015, 31(21): 109－115. (in Chinese with English abstract)

[4] 籍穎，張漫，劉剛，等. 農(nóng)業(yè)機(jī)械導(dǎo)航系統(tǒng)綜合評(píng)價(jià)方法[J].農(nóng)業(yè)機(jī)械學(xué)報(bào)，2010，41(12)：160—164.

Ji Ying, Zhang man, Liu Gang, et al. Synthetically evaluation of agriculture machine navigation system[J]. Transactions of the Chinese Society for Agricultural Machinery, 2010, 41(12): 160－164. (in Chinese with English abstract)

[5] Xiang Y, Noguchi N. Development and evaluation of a general-purpose electric off-road robot based on agricultural navigation.[J]. International Journal of Agricultural & Biological Engineering, 2014, 7(5): 14－21.

[6] Barbosa R S. New method for railway track quality identification through the safety dynamic performance of instrumented railway vehicle[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2016, 38(8): 2265－2275.

[7] Kraus T. High-speed adaptive nonlinear predictive control for autonomous tractor navigation[C]//Bio-Robotics. 2013: 135－140.

[8] 趙建東. 基于東方紅SG-250拖拉機(jī)電控液壓轉(zhuǎn)向系統(tǒng)研究[D]. 南京：南京農(nóng)業(yè)大學(xué)，2012.

Zhao Jiandong. Research of electronic Hydraulic Steering System Based on the Dong Fang-Hong SG-250 Tractor[D]. Nanjing: Nanjing Agricultural University, 2012. (in Chinese with English abstract)

[9] Lee S Y, Yang Haiwon. Navigation of automated guided vehicles using magnet spot guidance method[J]. Robotics and Computer-Integrated Manufacturing, 2012, 28: 425—436.

[10] Maximov V N, Chernomorsky A I. Distributed navigation system for uniaxial wheeled modules[J]. Journal of Computer and System Sciences International, 2016, 55(5): 807—820.

[11] 羅錫文，張智剛，趙祚喜，等. 東方紅X-804拖拉機(jī)的DGPS自動(dòng)導(dǎo)航控制系統(tǒng)[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2009，25(11)：139－145.

Luo Xiwen, Zhang Zhigang, Zhao Zuoxi, et al. Design of DGPS navigation control system for Dongfanghong X-804 tractor[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2009, 25(11): 139－145. (in Chinese with English abstract)

[12] Hu J T, Li T C. Cascaded navigation control for agricultural vehicles tracking straight paths[J]. International Journal of Agricultural & Biological Engineering, 2014, 7(1): 36－44.

[13] Thanpattranon P, Ahamed T, Takigawa T. Navigation of autonomous tractor for orchards and plantations using a laser range finder: Automatic control of trailer position with tractor[J]. Biosystems Engineering, 2016, 147: 90－103.

[14] 馮朝印，劉亞楠. 拖拉機(jī)轉(zhuǎn)向角檢測(cè)系統(tǒng)的研究[J]. 農(nóng)機(jī)化研究，2013，12(12)：207－209.

Feng Chaoyin, Liu Ya’nan. Vehicles ceflection angle examination system’s research[J]. Journal of Agricultural Mechanization Research, 2013, 12(12): 207－209. (in Chinese with English abstract)

[15] 劉金波，遲德霞，金宏亮. 國(guó)內(nèi)的農(nóng)用車(chē)輛自動(dòng)轉(zhuǎn)向系統(tǒng)研究進(jìn)展[J]. 農(nóng)業(yè)科技與裝備，2011(4)：67－72.

Liu Jinbo, Chi Dexia, Jin Hongliang. Research progress on automatic steering system in domestic farm vehicles[J]. Agricultural Science & Technology and Equipment, 2011(4): 67－72. (in Chinese with English abstract)

[16] 陳文良，謝斌，宋正河，等. 拖拉機(jī)電控液壓動(dòng)力轉(zhuǎn)向系統(tǒng)的研究[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2006，22(10)：122－125.

Chen Wenliang, Xie Bin, Song Zhenghe, et al. Electro-hydraulic power steering system for tractors[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2006, 22(10): 122－125. (in Chinese with English abstract)

[17] 謝明，馬蓉，任玲，等.拖拉機(jī)自動(dòng)轉(zhuǎn)向系統(tǒng)設(shè)計(jì)及仿真[J].農(nóng)機(jī)化研究，2015(11)：108－112.

Xie Ming, Ma Rong, Ren Ling, et al. Design and simulation on tractor automatic steering system[J]. Journal of Agricultural Mechanization Research, 2015(11): 108－112. (in Chinese with English abstract)

[18] 黎永鍵，趙祚喜，黃培奎，等.東方紅拖拉機(jī)自動(dòng)轉(zhuǎn)向控制器設(shè)計(jì)及試驗(yàn)[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2015，31(增刊2)：93－99.

Li Yongjian, Zhao Zuoxi, Huang Peikui, et al. Design and experiment of automatic steering control system based on dongfanghong tractor[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2015, 31(Supp.2): 93－99. (in Chinese with English abstract)

[19] 吳曉鵬，趙祚喜，張智剛，等. 東方紅拖拉機(jī)自動(dòng)轉(zhuǎn)向控制系統(tǒng)設(shè)計(jì)[J]. 農(nóng)業(yè)機(jī)械學(xué)報(bào)，2009，40(增刊)：1－5.

Wu Xiaopeng, Zhao Zuoxi, Zhang Zhigang, et al. Development of automatic steering control system based on Dongfanghong tractor[J]. Transactions of the Chinese Society for Agricultural Machinery, 2009, 40(Supp.): 1－5. (in Chinese with English abstract)

[20] 尤文寬. 拖拉機(jī)播種作業(yè)自動(dòng)轉(zhuǎn)向控制系統(tǒng)的設(shè)計(jì)與研究[D]. 石河子：石河子大學(xué)，2014.

You Wenkuan. Design and Research on Automatic Steering Control System of Tractor seeding operation[D]. Shihezi: Shihezi University, 2014. (in Chinese with English abstract)

[21] 劉沛，陳軍，張明穎. 基于激光導(dǎo)航的果園拖拉機(jī)自動(dòng)控制系統(tǒng)[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2011，27(3)：196－199.

Liu Pei, Chen Jun, Zhang Mingying. Automatic control system of orchard tractor based on laser navigation[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2011, 27(3): 196－199. (in Chinese with English abstract)

[22] 任文濤，遲德霞，劉金波，等. 遙控插秧機(jī)自動(dòng)轉(zhuǎn)向系統(tǒng)設(shè)計(jì)與試驗(yàn)[J]. 農(nóng)業(yè)機(jī)械學(xué)報(bào)，2012，43(1)：175－179.

Ren Wentao, Chi Dexia, Liu Jinbo, et al. Design and test on remote rice transplanter automatic steering system[J]. Transactions of the Chinese Society for Agricultural Machinery, 2012, 43(1): 175－179. (in Chinese with English abstract)

[23] 劉軍，袁俊，蔡駿宇，等. 基于GPS/INS 和線控轉(zhuǎn)向的農(nóng)業(yè)機(jī)械自動(dòng)駕駛系統(tǒng)[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2016，32(1)：46－53.

Liu Jun, Yuan Jun, Cai Junyu, et al. Autopilot system of agricultural vehicles based on GPS/INS and steer-by-wire[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2016, 32(1): 46－53. (in Chinese with English abstract)

[24] 張義華，高公如，韓斌，等. 裝載機(jī)線控轉(zhuǎn)向角度測(cè)量控制研究[J]. 設(shè)計(jì)與研究，2013(4)：19－21.

Zhang Yihua, Gao Gongru, Han Bin, et al. Loaders steer-by-wire angle measurement control[J]. Journal of Design And Research, 2013(4): 19－21. (in Chinese with English abstract)

[25] 王鶴，胡靜濤，高雷. 農(nóng)業(yè)機(jī)械自動(dòng)導(dǎo)航車(chē)輪轉(zhuǎn)角測(cè)量誤差補(bǔ)償模型[J]. 農(nóng)業(yè)機(jī)械學(xué)報(bào)，2014，45(8)：33－37.

Wang He, Hu Jingtao, Gao Lei. Compensation model for measurement error of wheel truning angle in agricultural vehicle guidance[J]. Transactions of the Chinese Society for Agricultural Machinery, 2014, 45(8): 33－37. (in Chinese with English abstract)

[26] 王霄鋒，胡濤，金曉輝，等. 汽車(chē)內(nèi)、外前輪轉(zhuǎn)角關(guān)系的實(shí)驗(yàn)研究[J]. 拖拉機(jī)與農(nóng)用運(yùn)輸車(chē)，2010，37(4)：13－15.

Wang Xiaofeng, Hu Tao, Jin Xiaohui, et al. Experimental study on relationship between inside and outside steered wheels of motor vehicle[J]. Tractor & Farm Transporter, 2010, 37(4): 13－15. (in Chinese with English abstract)

[27] 郭孔輝，李寧，景立新. 基于轉(zhuǎn)向試驗(yàn)的車(chē)輛主銷(xiāo)定位參數(shù)完整解算[J]. 農(nóng)業(yè)機(jī)械學(xué)報(bào)，2011，42(10)：1－5.

Guo Konghui, Li Ning, Jing Lixin. Calculation of vehicle kingpin positional parameters based on steering test[J]. Transactions of the Chinese Society for Agricultural Machinery, 2011, 42(10): 1－5. (in Chinese with English abstract)

[28] 楊德，鄧國(guó)強(qiáng)，暢福善. 整車(chē)式不停車(chē)稱(chēng)重系統(tǒng)設(shè)計(jì)[J].控制工程，2015，22(6)：1114－1117.

Yang De, Deng Guoqiang, Chang Fushan. Design of non-stop and whole vehicle weighing system[J]. Control Engineering of China, 2015, 22(6): 1114－1117. (in Chinese with English abstract)

[29] 文常保，高麗紅，方吉善，等. 基于改進(jìn)型限幅平均濾波法的高精度稱(chēng)重系統(tǒng)研究[J]. 傳感技術(shù)學(xué)報(bào)，2014，27(5)：649－653.

Wen Changbao, Gao Lihong, Fang Jishan，et al. The high-precision weighing system based on the improved amplitude-limiting and average filtering algorithm[J]. Chinese Journal of Sensors and Actuators, 2014, 27(5): 649－653. (in Chinese with English abstract)

[30] 熊連松，卓放，劉小康. 增強(qiáng)型滑動(dòng)平均濾波算法及其在畸變電網(wǎng)相位同步控制中的應(yīng)用[J]. 電工技術(shù)學(xué)報(bào)，2015，30(21)：13－23.

Xiong Liansong, Zhuo Fang, Liu Xiaokang. Enhanced moving average filter and its applications in phase locking control of distorted power system[J]. Transactions of China Electrotechnical Society, 2015, 30(21): 13－23. (in Chinese

with English abstract)

[31] 劉啟佳. 四輪轉(zhuǎn)向汽車(chē)側(cè)向動(dòng)力學(xué)最優(yōu)控制和內(nèi)外環(huán)聯(lián)合控制研究[D]. 北京：北京理工大學(xué)，2014.

Liu Qijia. The Lateral Dynamic Optimal Control of Four Wheel Steering Vehicle and the Research of Inner Loop Controller and Outer Loop Controller Cooperate Simulation[D]. Beijing: Beijing Institute of Technology, 2014. (in Chinese with English abstract)

[32] 吉輝利，王熙. 拖拉機(jī)衛(wèi)星導(dǎo)航精度評(píng)估方法研究[J]. 農(nóng)機(jī)化研究，2016(11)：242－262.

Ji Huili, Wang Xi. The research of agricultural machinery is about satellite navigation accuracy of the evaluation method[J]. Journal of Agricultural Mechanization Research, 2016(11): 242－262. (in Chinese with English abstract)

[33] 朱永興，馮來(lái)平，賈小林，等. 北斗區(qū)域系統(tǒng)的PPP精度分析[J]. 測(cè)繪學(xué)報(bào)，2015，44(4)：377－383.

Zhu Yongxing, Feng Laiping, Jia Xiaolin, et al. The PPP precision analysis based on bds regional navigation system[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(4): 377－383. (in Chinese with English abstract)

Comparative test between displacement and four-bar indirect measurement methods for tractor guide wheel angle

Hu Shupeng1,2, Shang Yehua2,3, Liu Hui1, Li You2,3, Zhao Chunjiang2,3, Fu Weiqiang2,3※

(1.100048; 2.100097,; 3.100097,)

Wheel swivel angle is regarded as a critical parameter in agriculture automatic navigation system, and it can always be measured by using angle sensor. In engineering practice, angle sensor is difficult to fix, and the shaft is easily broken. In order to solve the problem, displacement indirect measurement method and four-bar indirect measurement method are proposed in this paper. Wheel rotation depends on steering cylinder piston movement, and the movement of steering cylinder piston causes the movement of steering trapezoidal mechanism. Therefore it is available to apply displacement sensor in measuring the position of the steering cylinder piston rod, and the displacement sensor is parallel fixed with the steering cylinder. Referring to the motion of steering trapezoidal mechanism, it is proposed to use the front axle, knuckle arm, connecting rod and pendulum rod to form a four-bar linkage. According to the fixed location of the displacement sensor and four-bar angle sensor, it is available to establish measurement models for those 2 indirect measurement methods, and calibrate the relation between sensor measurement and wheel swivel angle, but those 3 measurement methods are incapable to measure the real wheel swivel angle. In the 2 kinematic models of wheel vehicle, wheel swivel angle is the angle between wheel axis and vehicle body axis, and thus Ackerman transformation must be used for converting the test angle into wheel swivel angle. However, different vehicles are different in the transformation of Ackerman, and the ideal Ackerman transformation cannot be used. In fact, the rotation angles of left and right wheels have little bias with the wheel swivel angle when the wheel swivel angle is being in a small range in the middle of the pair. Therefore it is supposed that the measurement angle is the wheel swivel angle. Through automatic navigation precision comparison experiment, the advantages and disadvantages of different measurement methods are compared. The experiment is performed on basis of the LOVOL tractor M800, in which the self developed automatic navigation system was used, and an experiment platform was built. The experiment is completed on the asphalt pavement and the field, and the platform can be utilized to compare the accuracy of 3 measurement methods of wheel swivel angle and compare the accuracy of navigation through statistical analysis. The result shows that the four-bar angle sensor can provide the highest angle measurement accuracy and navigation accuracy. When the vehicle keeps the speed of about 4.2 km/h, the mean value of lateral deviation is -0.028 2 cm by using the four-bar angle sensor in the field, and the mean value of lateral deviation is -0.014 6 cm by using the hall angle sensor and 0.109 0 cm by using the displacement sensor in the same experiment environment. Therefore the four-bar indirect measurement method offers almost a navigation accuracy equal with the direct angle measurement, but the standard deviation of lateral deviation for automatic navigation of the four-bar indirect measurement method is 1.297 5 cm, which is less than the direct measurement method.But considering the displacement sensor wear, when the sensor has been used for about 50 h in the same environment, the mean value of lateral deviation is -0.456 1 cm. Thus the displacement angle measurement is incapable of replacing the direct angle measurement,while the four-bar angle sensor is capable to replace direct angle measurement method and can be further applied in practice, which is easily fixed and protected.

agricultural machinery; steering; models; automatic navigation; wheel swivel angle measure; displacement; four-bar; navigation accuracy

10.11975/j.issn.1002-6819.2017.04.011

S237; U463.42

A

1002-6819(2017)-04-0076-07

2016-05-20

2016-12-12

國(guó)家“863”高技術(shù)研究發(fā)展計(jì)劃項(xiàng)目（2013AA102308）；國(guó)家自然科學(xué)基金資助項(xiàng)目（31571564，31571563）；北京市科技計(jì)劃課題（D161100003216003）

胡書(shū)鵬，男（漢族），河南信陽(yáng)人，主要從事拖拉機(jī)自動(dòng)導(dǎo)航技術(shù)研究。北京 首都師范大學(xué)信息工程學(xué)院，100048。 Email：fengshengppp@163.com

付衛(wèi)強(qiáng)，男（漢族），河北定州人，副研究員，博士生，主要從事農(nóng)業(yè)智能裝備與導(dǎo)航技術(shù)研究。北京 北京農(nóng)業(yè)信息技術(shù)研究中心，100097。Email：fuwq@nercita.org.cn

胡書(shū)鵬，尚業(yè)華，劉 卉，李 由，趙春江，付衛(wèi)強(qiáng). 拖拉機(jī)轉(zhuǎn)向輪轉(zhuǎn)角位移式和四連桿式間接測(cè)量方法對(duì)比試驗(yàn)[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2017，33(4)：76－82. doi：10.11975/j.issn.1002-6819.2017.04.011 http://www.tcsae.org

Hu Shupeng, Shang Yehua, Liu Hui, Li You, Zhao Chunjiang, Fu Weiqiang. Comparative test between displacement and four-bar indirect measurement methods for tractor guide wheel angle[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2017, 33(4): 76－82. (in Chinese with English abstract) doi：10.11975/j.issn.1002-6819.2017.04.011 http://www.tcsae.org