拖拉機轉(zhuǎn)向輪轉(zhuǎn)角位移式和四連桿式間接測量方法對比試驗

胡書鵬，尚業(yè)華，劉 卉，李 由，趙春江，付衛(wèi)強

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拖拉機轉(zhuǎn)向輪轉(zhuǎn)角位移式和四連桿式間接測量方法對比試驗

胡書鵬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. 國家農(nóng)業(yè)信息化工程技術(shù)研究中心，北京 100097）

針對車輪轉(zhuǎn)角直接測量法在工程實踐中角度傳感器安裝困難且轉(zhuǎn)軸易斷裂的現(xiàn)象，結(jié)合車輪轉(zhuǎn)向過程，提出了位移式間接轉(zhuǎn)角測量法和四連桿式間接轉(zhuǎn)角測量法。依據(jù)位移式和四連桿式2種間接測量方法原理，分別建立轉(zhuǎn)角測量模型，以雷沃M800型拖拉機為基礎(chǔ)，構(gòu)建自動導(dǎo)航試驗平臺，通過轉(zhuǎn)角測量試驗、瀝青路面與農(nóng)田環(huán)境下的導(dǎo)航精度對比試驗，分析四連桿式間接測量法、位移式間接測量法和直接測量法3種方法的應(yīng)用效果。轉(zhuǎn)角測量對比試驗結(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°，小于傳感器的測量精度0.088°，3種測量方法測量的測量精度一致。通過瀝青路面與農(nóng)田環(huán)境2種地況試驗測試，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，試驗表明3種測量方法的導(dǎo)航精度一致。相對于位移式間接轉(zhuǎn)角測量法和直接測量法，在瀝青路面上和農(nóng)田環(huán)境下，四連桿式間接測量法導(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)角測量法所采用的四連桿式角度傳感器安裝簡便、易于防護，無摩擦損耗，可代替直接轉(zhuǎn)角測量法，應(yīng)用于實踐中。

農(nóng)業(yè)機械；轉(zhuǎn)向；模型；自動導(dǎo)航；轉(zhuǎn)角測量；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，拖拉機自動導(dǎo)航系統(tǒng)作為農(nóng)業(yè)智能裝備的重點，應(yīng)用越來越廣泛[1-2]。拖拉機自動導(dǎo)航系統(tǒng)是通過控制轉(zhuǎn)向油缸活塞桿的位置，實現(xiàn)拖拉機運動軌跡控制。通常車輪對中時，車輪軸線與車身中軸線平行。當(dāng)車輪轉(zhuǎn)動后，車輪軸線與車身中軸線的夾角即為車輪轉(zhuǎn)角。車輪轉(zhuǎn)角測量作為自動導(dǎo)航系統(tǒng)自動轉(zhuǎn)向單元的一部分，是影響自動導(dǎo)航精度的重要因素之一[3-4]。

國內(nèi)外研究人員采用了不同的技術(shù)手段進行拖拉機自動導(dǎo)航系統(tǒng)車輪轉(zhuǎn)角的測量。Xiang等[5-8]通過電位計測量轉(zhuǎn)向節(jié)旋轉(zhuǎn)角度，獲取車輪轉(zhuǎn)角，Lee等[9-11]采用絕對式編碼器測量車輪轉(zhuǎn)角，Hu等[12-13]通過位移式傳感器測量轉(zhuǎn)向油缸行程，推算車輪轉(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量車輪轉(zhuǎn)角，尤文寬等[20-21]采用霍爾角位移傳感器測量轉(zhuǎn)向輪轉(zhuǎn)角值，任文濤等[22-24]采用位移式傳感器測量車輪轉(zhuǎn)角，王鶴等[25-27]采用將GAS60型角度傳感器安裝在前橋上，并通過連桿與轉(zhuǎn)向節(jié)連接，實現(xiàn)車輪轉(zhuǎn)角測量。據(jù)此，常用的車輪轉(zhuǎn)角測量方法有角度傳感器直接測量法、位移式間接轉(zhuǎn)角測量法和四連桿式間接轉(zhuǎn)角測量法等3種。但在科研試驗與工程實踐中發(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不均勻影響很大[15]。

本文以雷沃M800型拖拉機為研究平臺，選擇霍爾角度傳感器作為角度傳感器直接法的轉(zhuǎn)角測量設(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)角測量設(shè)備，根據(jù)2種傳感器測量轉(zhuǎn)角的原理，分別建立轉(zhuǎn)角測量模型，設(shè)計對比試驗比較直接測量法和2種間接測量法時的測量精度，并通過田間試驗對比其用于拖拉機自動導(dǎo)航系統(tǒng)對導(dǎo)航精度的影響。

1 車輪轉(zhuǎn)角測量法

1.1 角度傳感器直接測量法

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)相對于車輪有一定傾斜（圖1），從車輛前方看車輪，轉(zhuǎn)向節(jié)與車輪中軸線有一個夾角，即為轉(zhuǎn)向節(jié)側(cè)傾角；從車輛側(cè)面看車輪，轉(zhuǎn)向節(jié)與車輪軸線有一個夾角，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)角度與車輪實際轉(zhuǎn)角值不相等，其車輪-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量法的角位移量與車輪轉(zhuǎn)角關(guān)系式，其中和值可從拖拉機手冊中查到，值由角度傳感器測量得到。

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)中心點到轉(zhuǎn)向油缸活塞桿固定點長度，mm；2為轉(zhuǎn)向節(jié)中心點到轉(zhuǎn)向油缸固定點的長度，mm；3為車輪對中時的轉(zhuǎn)向油缸長度，mm；為轉(zhuǎn)向油缸活塞桿位移量，mm；為車輪對中時，轉(zhuǎn)向節(jié)臂與轉(zhuǎn)向節(jié)中心點到轉(zhuǎn)向油缸固定點連線之間的夾角，(°)；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)中心點到轉(zhuǎn)向油缸活塞桿固定點長度，mm；2為轉(zhuǎn)向節(jié)中心點到轉(zhuǎn)向油缸固定點的長度，mm；3為車輪對中時的轉(zhuǎn)向油缸長度，mm；為轉(zhuǎn)向油缸活塞桿位移量，mm；為車輪對中時，轉(zhuǎn)向節(jié)臂與轉(zhuǎn)向節(jié)到轉(zhuǎn)向油缸固定點連線之間的夾角，(°)。

由式（1）～式（4）得到，車輪轉(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)角測量法

四連桿式角度傳感器的安裝示意圖如圖3a所示。在實際安裝時，采用鉛垂線測量、、3點對地高度，通過添加墊片調(diào)節(jié)固定點與前橋間的高度，確保3個點對地高度一致，以保證四連桿機構(gòu)在同一平面內(nèi)運動。

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)中心點到四連桿角度傳感器在前橋上的固定點長度，mm；5為擺桿長度，mm；6為連桿長度，mm；7為轉(zhuǎn)向節(jié)中心點到連桿在轉(zhuǎn)向節(jié)臂上固定點的長度，mm；8為車輪對中時，轉(zhuǎn)向節(jié)中心點到連桿與擺桿連接點長度，mm；9為車輪轉(zhuǎn)動后，轉(zhuǎn)向節(jié)中心點到連桿與擺桿連接點長度，mm；0為車輪對中時，擺桿與前橋夾角，(°)；1為車輪轉(zhuǎn)動后，擺桿與前橋夾角，(°)；為車輪對中時，轉(zhuǎn)向節(jié)臂與前橋夾角，(°)；為車輪轉(zhuǎn)動后轉(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量值變化量，4為轉(zhuǎn)向節(jié)中心點到四連桿角度傳感器在前橋上的固定點長度，mm；5為擺桿長度，mm；6為連桿長度，mm；7為轉(zhuǎn)向節(jié)中心點到連桿在轉(zhuǎn)向節(jié)臂上固定點的長度，mm；8為車輪對中時，轉(zhuǎn)向節(jié)中心點到連桿與擺桿連接點長度，mm；9為車輪轉(zhuǎn)動后，轉(zhuǎn)向節(jié)中心點到連桿與擺桿連接點長度，mm；0為車輪對中時，擺桿與前橋夾角，(°)；1為車輪轉(zhuǎn)動后，擺桿與前橋夾角，(°)；為車輪對中時，轉(zhuǎn)向節(jié)臂與前橋夾角，(°)；為車輪轉(zhuǎn)動后轉(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)角測量對比試驗

2.1 構(gòu)建試驗平臺

為檢驗和對比位移式間接轉(zhuǎn)角測量法、四連桿式間接轉(zhuǎn)角測量法和直接轉(zhuǎn)角測量法對導(dǎo)向輪轉(zhuǎn)角測量精度的影響，構(gòu)建試驗測試平臺。試驗平臺包括：雷沃M800型拖拉機；北京農(nóng)業(yè)智能裝備技術(shù)研究中心的AMG-1102型自動導(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，擺桿長度為145 mm，連桿長度為234 mm，量程為0～90°，線性度1.0%FS；便攜式計算機。其中，AMG-1102型自動導(dǎo)航系統(tǒng)采用角度傳感器直接測量法，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)角測量法的傳感器標(biāo)定

2種間接轉(zhuǎn)角測量法是通過建立測量模型，將測量值轉(zhuǎn)換為目標(biāo)值，轉(zhuǎn)換關(guān)系式復(fù)雜，計算量大，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量模型，便于轉(zhuǎn)向控制器完成傳感器測量值到轉(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，測量參數(shù)1為142 mm，2為561 mm，3為543 mm，雷沃M800型拖拉機的轉(zhuǎn)向節(jié)內(nèi)傾角=9°，轉(zhuǎn)向節(jié)后傾角=1°，對式（5）中位移量與車輪轉(zhuǎn)角的變化關(guān)系進行最小二乘法線性擬合。擬合方程為

拖拉機的工作環(huán)境使得拖拉機的振動較大，在實際的控制中，振動對AD采樣易造成振動干擾。本文選擇遞推平均濾波，該濾波算法對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，對式（12）中與轉(zhuǎn)角的變化關(guān)系進行最小二乘法線性擬合。擬合方程為

2.3 轉(zhuǎn)角靜態(tài)測量對比

為了分析直接測量法與2種間接測量法對角度測量值的差異性，設(shè)計了轉(zhuǎn)角靜態(tài)測量試驗。試驗在平整路面上進行，轉(zhuǎn)動方向盤到不同位置，采用直接測量法、位移式間接測量法和四連桿式間接測量法3種方法分別測量當(dāng)前轉(zhuǎn)角值，由于車輪轉(zhuǎn)角真值不能直接測量，故以直接測量法20次測量值的平均值為對比參考值，對比3種測量方法的測量結(jié)果?？紤]到拖拉機自動導(dǎo)航直線行駛時，角度主要在車輪對中位置附近變化，表1中列舉了直接測量法測量值、四連桿式間接測量法測量值和位移式間接測量法測量值的部分?jǐn)?shù)據(jù)。

表1 轉(zhuǎn)角值測量結(jié)果

注：對直接測量法測量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種測量方法測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°，小于傳感器的測量精度0.088°，3種測量方法測量的測量精度一致。

在二輪車運動學(xué)模型中[1-2]，車輪轉(zhuǎn)角為虛擬中位輪與車身軸線的夾角，這是不可直接測量的，雖然可以通過阿克曼轉(zhuǎn)角模型轉(zhuǎn)換為測量左右車輪的轉(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]，中國科學(xué)院沈陽自動化研究所采用SPZJ-1型汽車轉(zhuǎn)向角檢測儀（分辨率0.1°）進行轉(zhuǎn)角測量獲得車輪轉(zhuǎn)角值，但是測量精度不高[27]。本研究下一步擬借鑒北京理工大學(xué)在汽車領(lǐng)域轉(zhuǎn)角測量方法，通過計算拖拉機運動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)航效果對比試驗

試驗在北京市昌平區(qū)小湯山國家精準(zhǔn)農(nóng)業(yè)研究示范基地進行，選擇了瀝青平整路面和農(nóng)田地塊2種地況，其中瀝青路面長度約400 m，農(nóng)田地塊南北長度約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量單元，在2種地況下檢驗自動導(dǎo)航系統(tǒng)的導(dǎo)航精度。在瀝青路面上測試時，拖拉機不掛接農(nóng)具；在田間測試時，拖拉機懸掛農(nóng)具；車速均保持在4.2 km/h左右。通過導(dǎo)航控制終端實時記錄拖拉機自動導(dǎo)航模式下直線追蹤導(dǎo)航的橫向偏差，以便于分析2種測量方法下的導(dǎo)航精度。

3.1 試驗數(shù)據(jù)處理方法

試驗中通過導(dǎo)航終端實時記錄拖拉機橫向偏差，對橫向偏差的平均值（單次試驗全部數(shù)據(jù)取均值）和標(biāo)準(zhǔn)差進行統(tǒng)計分析，作為評價指標(biāo)。其中平均值反映了自動導(dǎo)航精度的效果，而標(biāo)準(zhǔn)差反映了自動導(dǎo)航時的穩(wěn)定性[4,32-33]，計算式如式（15）與式（16），表2為瀝青路面上與農(nóng)田環(huán)境下自動導(dǎo)航橫向偏差的統(tǒng)計分析結(jié)果。

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

3.2 導(dǎo)航效果對比分析

3.2.1 導(dǎo)航精度對比

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

通過瀝青路面與農(nóng)田環(huán)境2種地況試驗測試，瀝青路面上和農(nóng)田環(huán)境下，四連桿式間接測量法、位移式間接測量法和直接測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，試驗表明3種測量方法的導(dǎo)航精度一致。

3.2.2 導(dǎo)航穩(wěn)定性對比

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

綜上所述，四連桿式間接轉(zhuǎn)角測量法的導(dǎo)航效果是最好的，雖然位移式間接轉(zhuǎn)角測量法的導(dǎo)航精度在瀝青路面上是最高的，但傳感器內(nèi)部電刷與阻軌長時間在小范圍內(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)計分析表

4 結(jié) 論

1）在不考慮車輪變形、機械結(jié)構(gòu)精度等因素下，建立了位移式間接轉(zhuǎn)角測量模型與四連桿式間接轉(zhuǎn)角測量模型，并進行轉(zhuǎn)角測量對比試驗。四連桿式間接測量法、位移式間接測量法和直接測量法測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°，小于傳感器的測量精度0.088°，3種測量方法測量的測量精度一致。

2）通過瀝青路面與農(nóng)田環(huán)境2種地況試驗測試，瀝青路面上和農(nóng)田環(huán)境下，四連桿式間接測量法、位移式間接測量法和直接測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，試驗表明3種測量方法的導(dǎo)航精度一致。

3）相對于位移式間接轉(zhuǎn)角測量法和直接測量法，在瀝青路面上和農(nóng)田環(huán)境下，四連桿式間接測量法導(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，可以代替直接轉(zhuǎn)角測量法，應(yīng)用于工程中。

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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

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

胡書鵬，男（漢族），河南信陽人，主要從事拖拉機自動導(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，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

胡書鵬，尚業(yè)華，劉 卉，李 由，趙春江，付衛(wèi)強. 拖拉機轉(zhuǎn)向輪轉(zhuǎn)角位移式和四連桿式間接測量方法對比試驗[J]. 農(nóng)業(yè)工程學(xué)報，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