Design and Testing of a Controller for Autonomous Vehicle Path Tracking Using GPS/INS Sensors

Transcription

1 Poceeing o he 7h Wol Conge he nenaional Feeaion o Auoaic Conol Seoul, Koea, July -, Deign an eing o a Conolle o Auonoou Vehicle Pah acking Uing GPS/NS Seno Juyong Kang*. Rai Y. Hiniyeh** Seung-Wuk Moon***, J. Chiian Gee****, Kyongu Yi***** *School o Mechanical an Aeopace Engineeing, Seoul Naional Univeiy, Seoul, Koea **Depaen o Mechanical Engineeing, Sano Univeiy, Sano, CA935 USA(e-ail: [email protected] ***School o Mechanical an Aeopace Engineeing, Seoul Naional Univeiy, Seoul, Koea ****Depaen o Mechanical Engineeing, Sano Univeiy, Sano, CA935 USA(e-ail: [email protected] *****School o Mechanical an Aeopace Engineeing, Seoul Naional Univeiy, Seoul, Koea(e-ail: [email protected] Abac: hi pape ecibe a eeing conolle inegae ih pee conolle o auonoou pah acking uing GPS an NS eno. he eeing conolle o pah acking i evelope bae on he inie pevie opial conol eho. he eeing conol inpu i copue uing he oa inoaion ihin pevie iance. he pee conolle eeine he pee coan neceay o ainain a laeal acceleaion lii an ipove vehicle aey. he vehicle oel o iulaion uy i valiae uing vehicle e aa. Finally, he conolle i ipleene on a by-ie vehicle, P, o valiae he peoance o he eeing conolle inegae ih pee conolle.. NRODUCON nelligen Vehicle an Highay Sye (VHS echnologie have aace going aenion aong eeache houghou he ol in he pa eveal yea. Conol algoih o auonoou vehicle, incluing pope conol o he eeing inpu an pee coan o pah-acking an ae laeal vehicle behavio, ae a ciical coponen o VHS (Peng, 99, He e. al. 99. n hi pape, a eeing conolle o pah-acking an a pee conolle o ipoving he aey o laeal vehicle behavio ae inveigae. he eeing conolle i evelope bae on he inie pevie opial conol eho. he eeing inpu o he eeing conolle coni o a eeback conol inpu uing laeal poiion an ya angle eo a ell a a ee-oa conol inpu copue uing he oa inoaion ihin he pevie iance. he ee-oa pevie conol inpu can ipove no only he acking peoance o he eeing conolle, bu alo he ie qualiy copae ih he non-pevie conolle. (Ki e. al., 7 he pee conolle copue a pee coan o ha he laeal acceleaion o he e vehicle oe no ecee an abiay ciical value in oe o ipove he aey o laeal vehicle behavio. A vehicle iulaion ha inclue laeal vehicle ynaic, longiuinal vehicle ynaic, an acuao ynaic i ue o evelop he conolle. he conolle evelope ae hen ipleene on a ee-by-ie e vehicle, P, an valiae epeienally.. ES PLAFORM he eeing conolle inegae ih pee conolle ha been evelope o P, a uen buil by-ie plao belonging o he Dynaic Deign Lab a Sano Univeiy, hon in Fig.. Fig.. P epeienal by-ie vehicle hi vehicle eaue hole by ie an inepenen le an igh ee-by-ie a he on heel. P poeplan coni o o AC populion oo ha povie inepenen le an igh ea heel ive a ell a egeneaive baking capabiliy. P eno uie inclue a hee anenna GPS ye an ana auooive gae NS eno. Real-ie ae eiaion i accoplihe hough eno uion via eene Kalan ile o heaing, velociy, an poiion (Ryu e. al.,. A GPS bae aion ha been ue o povie ieenial coecion o poiion eaueen. 3. VEHCLE MODEL AND MODEL VALDAON 3. Vehicle Moel he vehicle iulaion a eigne a an alenae oe o he SMULNK oae ha noally un in eal-ie on he e vehicle. eplace haae ive ih a vehicle oel ha ceae eno ignal ha ae pocee in he ae anne a hey oul be in eal ie on he vehicle. hi aciliae eoe evelopen o conolle o he e plao by eeache a Seoul Naional Univeiy //$. FAC 93.3/7-5-KR-.35

2 7h FAC Wol Conge (FAC' Seoul, Koea, July -, he iulaion inclue laeal, longiuinal, an eeing acuao ynaic, a ecibe belo. Laeal Dynaic: P laeal ynaic have been oelle uing a ou heel plana oel (Gaa e. al., 7, a hon in Fig. belo: l F y Fyl l v Fig.. Fou heel plana oel he equaion o he laeal ynaic ae given belo, v y + v ε Fyl + Fy + Fyl + Fy ( ε l ( F + F l ( F + F z yl y yl y hee l an l ae he iance o he on an ea ale o he CG, z i he oen o ineia, i he vehicle a, an F yl, F y, F yl an F y ae he laeal ie oce a he on le, on igh, ea igh, an ea le ie, epecively. he laeal ie oce ae linea uncion o lip angle α an α an coneing inee C an C. F C α ; i, l,, l ( yi i i Uing a all angle appoiaion, he ie lip angle ae a given in he epeion belo, hee i he ack ih o he vehicle. Vehicle paaee ae given in able.. ε v y l F y Fyl vy + l ε vy l ε α j j, αj ; j l, v ε / v ε / Longiuinal Dynaic: he oel o longiuinal ynaic ap a volage coan o oo oque ( τ uing iple oel o P acion baey pack, invee, oo, an geaboe. hee oo oque eve a an inpu ino a iulaion o longiuinal ynaic ha accoun o aniion ineia ( J, heel ineia ( an J, olling eiance, an he ag heel oce ( τ ai acing on P. hi longiuinal oel aue zeo heel lip an no coupling ih laeal ynaic; o he level o laeal acceleaion une conieaion (<.5g, hee aupion ae eaonable. Equaion (3 peen he equaion o he oel o P longiuinal ynaic, ( n τ τai τoll a, a (3 ( J + J + J / heel an chai hee, enoe he ie olling aiu, n he ive aio, Jchai he chai ineia an Seeing Sye Dynaic: a he longiuinal acceleaion. A iple econ oe oel i ue o ecibe he oupu ha angle θ o P le an igh eeing oo an geabo aeblie, ( J / ηθ gn( θ b θ+ (/ n ( τ + τ + k ( aligning jacking M in hee J i he eecive ineia being ace upon by he oo, η he oo eiciency, he icion, b he coeicien o aping, n he eeing ye gea aio, τ aligning he aligning oque ue o ie laeal oce, τ jacking he oque ue o upenion jacking, k M he oo conan, an in he cuen inpu o he oo. τ aligning i copue uing ie laeal oce an he oen a euling o echanical an pneuaic ail, hile τ jacking i copue o an epiically eeine uncion oθ. A PD-conolle ih ee-oa e povie he cuen inpu in o ack a coane ha angle θ e, in K cuen KP ( θe θ + KD ( θe θ + K Bθe + K Jθ (5 e hee K P i he popoional gain, K D i he eivaive gain, K Bθe i he aping ee-oa e, K Jθe i he ineia ee-oa e, an K cuen i a conveion o uni o oque (N- o cuen (A. able Vehicle paaee Sybol Value Sybol Value 3.5E- 7. kg J N /a z 3 kg.53 N l.35 b.3 N/a l.5 M.3N/A C 5 N/a n C 9 N/a.5 3. Vehicle Moel Valiaion Uing e Daa Valiaion o he vehicle oel i accoplihe by copaion o iulaion peicion o P e aa obaine uing P GPS/NS eno uie. he longiuinal velociy aa i ue a he eeence inpu o a cuie conolle ha en volage coan o he acion ye oel. he ean o he le an igh eeing angle o he e aa i ue a he eeence inpu o he eeing ye oel. Fig. 3 ho a copaion o e aa an iulaion eul. Seeing Angle[eg] e Daa Vehicle Moel ie [ec] 9

3 7h FAC Wol Conge (FAC' Seoul, Koea, July -, Vehicle Spee [kph] Ya Rae [eg/] Laeal Accel [/ ] 3 3 e Daa Vehicle Moel e Daa - Vehicle Moel e Daa Vehicle Moel ie [ec] Fig. 3. Copaion o e aa an vehicle iulaion eul he iulaion peicion agee cloely ih he e aa, uggeing ha he oel i eaible a a e plao o evelopen o he eeing an pee conolle in he linea hanling egie o he e vehicle (Ha e. al., 3. DEVELOPMEN OF HE SEERNG CONROLLER FOR PAH-RACKNG. Conol Objecive Fig. ho he ive-vehicle ye. n Fig., laeal poiion eo (y i eine a he laeal iance beeen he vehicle C.G (C an he ceneline o he eie pah (R. Ya angle eo ( ε ε i eine uing he ya angle o he vehicle (ε an he eie ya angle a icae by he eie pah ( ε (Kang e. al.,, 7. ε y ε Fig.. Dive vehicle ye Global X cooinae L p We eek o eliinae laeal an ya angle eo hough a cobinaion o eeback an ee-oa conol. he eeback conol inpu o he eeing conolle o pahacking i copue uing laeal poiion eo an ya angle eo. he ee-oa conol inpu i copue uing he oa inoaion ihin he pevie iance. o evelop he eeing conolle uing inie pevie conol heoy, pevie iance i anoe ino pevie ie ( p a in (. L p p (. Sae Equaion A -DOF bicycle oel i ue o eign he eeing conolle. Equaion (9 ho he ynaic equaion o a - DOF bicycle oel, v y + v ε ( Fy + Fy (9 ε l F l F z y y hee enoe he a o he boy, z he ya oen o ineia, F y an F he on an ea laeal ie oce, y an l an l he iance o he cene o gaviy(cg o he on an ea ale, epecively. Fo he linea ie oel, he laeal ie oce can be epee a hon in (, vy + l ε Fyl Fy C ( ( + l ( ε ε l C { + ( ε ε ε} v v vy l ε Fyl Fy C ( l ( ε ε l C { + ( ε ε + ε} hee C an C enoe he equivalen on an ea coneing inee. Subiuing ( ino (9, he ae equaion can be obaine a in ( (Peng e. al., 99, A + B + F ( [ y ε ε ε ε ] he ae o change o he laeal poiion eo (y an ya angle eo ( ε ε ae eine a in ( an (7 (Peng, 99, y v + v ( ε ε v + v ( ε ε y y y v ε, ε v (7 ρ ρ ( hee A A A A A3 A A3 B B B F hee ρ enoe he cuvaue aiu o he eie pah. 95

4 7h FAC Wol Conge (FAC' Seoul, Koea, July -, ( C + C A ( l C + l C A ( l C + l C A A 3 z ( l C l C + z C B C l B n (, he iubance e ( inoaion ( ε, ε. z A + ε ρ A ε ε i eine o oa.3 Seeing Conolle Uing Finie Pevie Opial Conol heoy he eeing conol inpu( ( i copue o iniize he peoance ine given in ( (Chen, 9. ( Q R li E{ + + } λ ( A + B + F ( he oluion ha iniize he peoance ine i given by he ell-knon Eule Lagange equaion: ( Q R L (, λ, + + (3 λ ( A + B + F ] i L L λ Q A λ ( ii L L R B λ (5 iii L L A BR B λ + F λ λ ( n oe o obain oluion o (, λ ( an (, λ ( i aue o ake he o hon in (7 (Bul, 99. λ ( P( ( + H( (7 hee H ( i a ee-oa conol. he ieenial o o (7 i hon belo: λ P + P A BR B + F + H Q A [ P + H ( ] [ λ ] ( ( Subiuing (7 ino ( an gouping e, he olloing o equaliy coniion ae obaine (Chen, 9 P + PA PBR B P + A P + Q (9 H Ac H P F ( hee Ac A B R B P Equaion (9 i he ana LQ Riccai equaion. A, he oluion P( o (9 en o appoach i eay ae value an i inepenen o he inal coniion P(. hen, equaion (9 becoe he ell-knon Conol Algebaic Riccai Equaion a hon belo: PA PBR BP + AP + Q ( he oa inoaion beyon he pevie ie ( p i e equal o zeo ( (, [ + p, ], equaion ( becoe (Chen, 9: + p Ac ( τ (, p [ ( τ ] H e P F τ ( A a eul, he eeing conol inpu i copue a in (3, ( K ( + M( (3 eie hee op, ( A c F e P F Kop R B P p ( ( ( M R B F ξ + ξ ξ Fo (3, i i clea ha he eeing conol inpu i copue uing he oa inoaion beeen an + p. Fig. 5 ho he block iaga o he eeing conolle. Roa noaion Beeen an +p Vehicle Spee y ε ε ε ε Diubance Copuaion R B F i i p Δ ξ K op N Lp N v ( b N [ ( ξ ( + Δξ Δξ] Fig. 5. Block iaga o eeing conolle ( + i Δξ i eie he eie eeing angle hich i copue by he eeing conolle i applie o he vehicle oel an e vehicle uing Ackeann eeing geoey a in (, eie L ( eie ( / L eie R + ( / L eie hee an L R enoe he le an igh on eeing angle, epecively, an L he heelbae. 5. DEVELOPMEN OF HE SPEED CONROLLER he pee conolle i eigne o ceae ae laeal vehicle behavio by ean o keeping he laeal acceleaion belo a ciical value ( a a ollo, y _ lii VLii i VLii VSe Veie VSe i VLii > VSe V VLii a a _ lii V ρ a ρ ρ y y Lii y_ lii (5 9

5 7h FAC Wol Conge (FAC' Seoul, Koea, July -, hee, V e he vehicle e pee eeine by he ive, an V he vehicle pee equie o no ecee Lii a. y _ lii n oe o ack he eie pee, he pee coan (volage en o he ive oo i copue uing he popoional conolle a hon belo V Lii VSe V Veie Fig.. Block iaga o Spee Conolle V K ( V V ( iving oo cuie eie hee K cuie enoe he cuie conol popoional gain.. SMULAON RESULS Siulaion have been un ih he eeing conolle acive a conan pee an hen he pee conolle i inegae ih he eeing conolle a hon belo. Seeing Angle[eg] Vehicle Spee [kph] Laeal Accel [/ ] Conan Spee Spee Conol Conan Spee Deie Spee Spee Conol Conan Spee Ciical Value Spee Conol ie [ec] Global Y Cooinae[] Deie Pah Vehicle ajecoy Ya Angle Eo [eg] - Conan Spee Spee Conol ie [ec] Fig. 7. Siulaion eul o eeing conolle an inegae conolle he iulaion ue a ap locae a a paking lo a Sano Univeiy. Fig. 7 copae he iulaion eul une he o e cenaio. n boh cenaio, he vehicle ack he ap vey cloely, ih he agniue o laeal an ya angle eo no eceeing. an eg, epecively. he iulaion eul alo ho ha he laeal acceleaion o vehicle oen ecee a uing pah acking ih y _ lii he pee conolle acive. Alo, he laeal acceleaion i loe agniue hen copae o pah acking a he conan (e pee. A a eul, i i oun ha he aey o laeal vehicle behavio i ipove ih he pee conolle acive in conjuncion ih he eeing conolle. 7. EXPERMENAL RESULS 7. Seeing Conolle a Conan Spee he epeienal eul o pah acking a conan pee ae peene in Fig.. he e ee peoe ih he ae ap ue o iulaion uie, an ae copae o iulaion eul. n Fig. an 9, he epeienal eeing angle i he ean o he le an igh eeing angle. Seeing Angle [eg] Vehicle Spee [kph] Laeal Accel [/ ] e Reul Siulaion Reul e Reul Siulaion Reul e Reul Siulaion Reul Laeal Poiion Eo [] Global X Cooinae [] -. Conan Spee Spee Conol ie [ec] Laeal Poiion Eo [] e Reul Siulaion Reul ie [ec] 97

6 7h FAC Wol Conge (FAC' Seoul, Koea, July -, Ya Angle Eo [] - e Reul Siulaion Reul ie [ec] Fig.. Copaion o he iulaion eul an e eul, conan pee e he e eul agee cloely ih he iulaion eul. he eeing conolle pouce aiacoy acking peoance, ih he agniue o laeal an ya angle eo belo.5 an.5 egee, epecively. hee eo ae on he ae oe o agniue a he eo peice in iulaion. 7. Seeing Conolle negae Wih Spee Conolle he e eul o he inegae conolle ae peene in Fig. 9 an copae ih e eul a a conan pee equivalen o he e pee o he pee conolle: Seeing Angle [eg] Vehicle Spee [kph] Laeal Accel [/ ] Laeal Poiion Eo [] Ya Angle Eo [eg] Conan Spee e Deie Spee 3 Spee Conol Conan Spee e Ciical Laeal Acceleaion Spee Conol Conan Spee Spee Conol Conan Spee Spee Conol ie [ec] Fig. 9. Copaion o e eul, conan pee e veu e ih inegae conolle he bulk acceleaion o he vehicle (neglecing high equency vaiaion ue o vibaion, heel hop, ec. i ainaine belo he laeal acceleaion lii o /. A peice in iulaion, ue o he pee conolle in conjuncion ih he eeing conolle igniicanly euce laeal acceleaion hen copae o pah-acking a he conan (e pee.. CONCLUSONS A eeing conolle inegae ih a pee conolle o auonoou vehicle pah acking ha been peene in hi pape. he conolle ee evelope uing a nueical iulaion uy an ipleene on a by-ie e vehicle. Fo he iulaion eul an he e eul, i i oun ha he eeing conolle uing inie pevie opial conol pouce aiacoy pah acking peoance. Fuheoe, he aey o laeal vehicle behaviou i ipove by cobining he eeing conolle ih a pee conolle ha ainain a laeal acceleaion lii. ACKNOWLEDGMENS hi ok ha been uppoe by BK School o Ceaive Engineeing Deign o Ne Geneaion Mechanical an Aeopace Sye, Koea. REFERENCES Bul, Jeey B. (99. Linea Opial Conol, pp.79~. Aion-Weley Longan, Boon, MA. Chen, Long-Chain (9. An acive upenion ye ih pevie conol o paenge auoobile. PhD hei, Maachue niue o echnology. Gaa, Chiophe D., Sha M. La, an J. Chiian Gee (7, Geneaing Diagnoic Reiual o See-by Wie Vehicle. EEE anacion on Conol Sye echnology, Vol. 5, No. 3, pp. 59~5. Ha, Jungoo (3. Valiaion o 3D Vehicle Moel an Dive Seeing Moel ih Vehicle e. Sping Con. Poc. KSAE, Vol., pp. 7-. He, R.A., A. Mojahezaeh (99. A Conol heoeic oel o ive eeing behaviou. EEE conol Sye Magazine, Vol., No. 5, pp. 3~. Peng, Huei (99. Vehicle Laeal Conol o Highay Auoaion. PhD hei, Univeiy o Calionia a Bekeley. Peng, H., oizuka, M. (99, Laeal Conol o Fon-Wheel- Seeing. Rubbe-ie Vehicle, Publicaion o PAH pojec, S, UC Bekeley, UCB-S-PRR-9-5 Ryu, Jihan an J. Chiian Gee (. negaing neial Seno ih GPS o Vehicle Dynaic Conol. Jounal o Dynaic Sye, Meaueen an Conol, Vol., pp Kang, JuYong., Yi, Kyongu. an Noh, Kihan. (, Developen o a Finie Pevie Opial Conolbae Huan Dive Seeing Moel, KSAE Sping Coneence in, KSAE, Vol., pp. 3~37 Kang, JuYong., Yi, Kyongu. an Noh, Kihan. (7, Developen an Valiaion o a Finie Pevie Opial Conol-bae Huan Dive Seeing Moel, KSME Sping Coneence in 7, KSME, pp. 3~35 Ki, Wongun. an Yi, Kyongu. (7, Developen o an nelligen Auonoou Conol Algoih an e Vehicle Peoance Veiicaion, KSME Sping Coneence in 7, KSME, pp. 3~ 9