Heavy vehicle path stability control for collision avoidance applications

Transcription

1 Heavy vehicle path stability cotrol for collisio avoidace applicatios Master s Thesis i the Automotive Egieerig program ARMAN NOZAD Departmet of Applied Mechaics Divisio of Automotive Egieerig ad Autoomous Systems CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Swede 211 Master s Thesis 211 :45

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3 MASTER S THESIS 211 Heavy vehicle path stability cotrol for collisio avoidace applicatios Master s Thesis i the Automotive Egieerig program ARMAN NOZAD Departmet of Applied Mechaics Divisio of Automotive Egieerig ad Autoomous Systems CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Swede 211

4 Heavy vehicle path stability cotrol for collisio avoidace applicatios Master s Thesis i the Automotive Egieerig program ARMAN NOZAD ARMAN NOZAD, 211 Master s Thesis 211 ISSN Departmet of Applied Mechaics Divisio of Automotive Egieerig ad Autoomous Systems Chalmers Uiversity of Techology SE Göteborg Swede Telephoe: + 46 () Cover: VOLVO PH12 truck which is close to the vehicle modelled i this study. Departmet of Applied Mechaics Göteborg, Swede 211

5 Heavy vehicle path stability cotrol for collisio avoidace applicatios Master s Thesis i Automotive Egieerig program ARMAN NOZAD Departmet of Applied Mechaics Divisio of Automotive Egieerig ad Autoomous Systems Chalmers Uiversity of Techology Abstract The curret state of the art for Advaced Driver Assistat System (ADAS) i heavy trucks is based o pure brakig itervetios for rear-ed collisios o highways ad rural roads. I order to expad the scope to more geeral target scearios, it is ecessary to itegrate brakig ad steerig for more advaced itervetios. The ivestigated target scearios, which will cover ot oly rear-ed collisio, but also lateral coflicts ad head-o collisios, are developed ad prioritized based o accidet statistics. For advaced itervetios ot oly the speed of the truck but also the path should be uder cotrol. I fact the appropriate path cotroller should be applicable to various target scearios ad robust to variatios i loadig coditios. The overall goal of this work is to develop a path cotroller for a heavy vehicle based o itegrated brakig ad steerig, for collisio avoidace applicatio i the prioritized target scearios. To determie the potetial of various actuator cofiguratios to avoid the collisio, a optimal cotrol problem is formulated ad solved for each sceario. The solutio provides the requiremets for the actuators ad a bech mark for the developed optimal path cotroller. For vehicle implemetatio a robust cotroller which is capable of dealig with disturbaces ad ucertaities is eeded. The performace of the path cotroller i each target sceario ad the sesitivity to key parameters is studied by performig the simulatio o a detailed vehicle model. The target scearios will be further prioritized based o the performace ad robustess of the itegrated brakig ad steerig path cotroller. As a result of this work, a path stability cotroller which is capable of itegratig the steerig ad brakig actuators durig the maoeuvre will be provided. Therefore a robust path cotroller for Advaced Driver Assistat System ca be provided which ca hadle ot oly rear ed collisio scearios but also head-o ad lateral coflicts for heavy trucks. This work ca be a ew costructive step i Heavy truck active safety ad autoomous collisio avoidace maoeuvre that exteds the area i which active safety system participate to reduce the amout of accidets as much as possible. Key words: Path stability cotrol, Collisio Avoidace, Active safety, Itegrated steerig brakig. I

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7 Cotets ABSTRACT CONTENTS PREFACE NOTATIONS I III VI VII 1 INTRODUCTION Problem descriptio Limitatios ad simplificatios Vehicle chassis ad tyre model Cotrol system dyamics Literature review Approach 5 2 USE-CASES Defiitio Prioritizatio 6 3 COLLISION AVOIDANCE OPTIMAL CONTROL Particle model Optimal cotrol problem 1 4 PATH AND SPEED CONTROL Decisio algorithm Path plaig Path plaig requiremets Piecewise polyomial Usig a fifth order polyomial Path stability cotrol desig Feed-forward Feedback Yaw cotrol Tur i brakig Brakig stability cotrol Speed cotrol Collisio avoidace path ad speed cotrol system Performace evaluatio 19 CHALMERS, Applied Mechaics, Master s Thesis 211 III

8 5 REAR-END COLLISION AVOIDANCE (RECA) - SINGLE LANE CHANGE Optimal cotrol results for various actuator cofiguratios Optimal cotrol sesitivity study Fial coarse agle Maoeuvre severity Variable brakig versus costat brakig Path cotrol simulatio RECA maoeuvre Path cotrol results for RECA maoeuvre Path plaig Simulatio results Path ad speed cotrol for RECA maoeuvre Path cotrol results Path ad yaw cotrol for RECA maoeuvre Tur i brakig Brakig stability cotrol Path cotrol sesitivity study Compariso of optimal ad path stability cotrol 41 6 RUN-OFF-ROAD PREVENTION (RORP) Path cotrol simulatio RORP maoeuvre o straight road Path cotrol results for RORP o straight road Path plaig Simulatio results Path cotrol simulatio RORP maoeuvre o curved road Path cotrol results for RORP o curved road Path plaig Simulatio results 51 7 DISCUSSION 54 8 FUTURE WORKS 55 APPENDIX A: HEAVY VEHICLE SYSTEM DYNAMICS 57 A1. Vehicle model ad relevat assumptios 57 A1.1 Plaar free body diagram of the truck 57 A2.1 Plaar equatios of motio for the truck 57 A3.1 Roll of the sprug mass 58 A4.1 Lateral ad logitudial load trasfer 59 A5.1 Slip ad et steerig agles 6 A2. Tyre model ad relevat assumptios 62 A6.1 Adhesio coefficiet ad its alteratio with the vertical load 62 A7.1 Corerig stiffess ad its alteratio with the vertical load 62 CHALMERS, Applied Mechaics, Master s Thesis 211 IV

9 A8.1 Magic Formula parameters 62 A9.1 Trasiet force geeratio 64 A3. Liear steady state corerig 65 A4. Rollover 66 APPENDIX B: VEHICLE DATA 67 REFERENCES 7 CHALMERS, Applied Mechaics, Master s Thesis 211 V

10 Preface This study deals with the desig of a path stability cotroller for heavy vehicles i collisio avoidace applicatios. The study has bee carried out from Jauary 211 to July 211. The work is a part of Iteractive project which is fiaced by Europea Uio. The work is maily performed at Vehicle dyamics group, Applied mechaics departmet, Chalmers Uiversity of Techology, Göteborg, Swede. This part of the project (INCA) has bee carried out with Mathias Lidberg as supervisor ad VOLVO Techology Corporatio as the project leader. I would like to appreciate Mathias Lidberg because of his help ad edless support all alog the project. I would also like to thak Lars Bjelkeflo ad Masour Keshavarz for their cooperatio ad ivolvemet. Göteborg July 21 Arma Nozad CHALMERS, Applied Mechaics, Master s Thesis 211 VI

11 Notatios Uppercase Letters C φ C φ,1 C φ,2 C φ,3 F x, F y, F dy F z,i,stat F z,,stat I xx I xx,s I zz K φ K φ,1 K φ,2 K φ,3 K φ,2+3 L L 1 Roll dampig of the Roll dampig of first axle Roll dampig of secod axle Roll dampig of third axle Logitudial force o th wheel Lateral force o th wheel The force correspodig to dyamical coditio Static load o i th axle Static load o th wheel Vehicle momet of iertia aroud x axis Sprug mass momet of iertia aroud x axis Vehicle momet of iertia aroud z axis Roll stiffess Roll stiffess of first axle Roll stiffess of secod axle Roll stiffess of third axle Roll stiffess of tadem axle Distace betwee the first ad the secod axle Distace betwee CG ad the first axle L 2 L 3 L e Distace betwee CG ad the secod axle (L L 1 ) Distace betwee CG ad the third axle (L + L bs L 1 ) Equivalet wheel base; CHALMERS, Applied Mechaics, Master s Thesis 211 VII

12 L fo L max Frot overhag Total legth of the truck L ro Rear overhag (L max L L bs L fo ) L t M z W W max X Y F z,i Theoretical wheel base Vehicle yaw momet Track width of the truck Total width of the truck Logitudial positio i global coordiate system Lateral positio i global coordiate system Load trasfer o i th axle Lowercase Letters a x a y c δ g i i s l m Logitudial acceleratio Lateral acceleratio Steerig compliace Gravitatioal acceleratio Height of cetre of gravity (CG) from groud Roll cetre height of first axle Roll cetre height of secod axle Roll cetre height of third axle Height of cetre of gravity (CG) from roll cetre (RC) Idex umber of axles startig from frot to rear Steerig gear ratio Logitudial positio of th wheel i the coordiate system fixed to the vehicle Vehicle mass CHALMERS, Applied Mechaics, Master s Thesis 211 VIII

13 m s m u v x v y Sprug mass Usprug mass Idex umber of wheels startig from frot ad left (1) to rear ad right (6) Logitudial speed of the vehicle Lateral speed of the vehicle w Lateral positio of th wheel i the coordiate system fixed to the vehicle Greek Letters α α m δ ε Slip agle Slip agle for which maximum lateral force is geerated Wheel agle of th wheel Roll steer coefficiet of th wheel μ 1 The first coefficiet i adhesio calculatios μ 2 The secod coefficiet i adhesio calculatios σ x σ y φ ψ Logitudial relaxatio legth Lateral relaxatio legth Roll agle Yaw agle CHALMERS, Applied Mechaics, Master s Thesis 211 IX

14 1 Itroductio Traffic safety is a major problem for today s trasportatio. A lot of work has bee doe i the passive safety area where millisecods after the iitiatio of crash are of importace. Nowadays, collisio avoidace i the field of active safety is more prioritised. This study focuses o autoomous path ad path stability cotrol of passeger cars ad heavy vehicles which may serve as a basis for active itervetios, particularly iteded for helpig the driver i critical collisio avoidace maoeuvres. I oe had, pure applicatio of the service brakes to avoid a accidet (by stoppig the vehicle before collidig with the obstacle i frot) is isufficiet at relative high speeds. O the other had, usig oly differetial brakig to steer the vehicle away from the obstacle i frot is ot feasible for a collisio avoidace maoeuvre o the limits, sice if this system is used, the sufficiet amout of lateral forces will be built up whe the vehicle yaw rate icreases up to certai level thus makig it a very slow respose. Therefore the steerig itervetio comes ito play i order to avoid accidets where the hadlig limits of the vehicle should be utilised as much as possible. 1.1 Problem descriptio A very geeral defiitio of the problem treated here is the questio of how to keep a three-axle-truck autoomously o a desired escape path (o the limits). However, this is too geeral especially the umber of solutios ad/or combiatio of them is cocered; therefore the problem has to be arrowed dow. I this study, mai focuses are o: o o o Path plaig The type of actuatio (steerig, brakig or their itegratio) The cotrol algorithm which will make the path followig o the limits to be realised. Possible ad feasible actuatio solutios for this study ca be listed as follows: o o o o Pure frot axle steerig Pure brakig Frot axle steerig + brakig (differetial brakig ad/or service brakig) Frot axle steerig + brakig (differetial brakig ad/or service brakig) + tag axle steerig. The evaluatio criteria for various settigs of the cotroller are give as follows accordig to the priority: o o All wheels must remai i cotact with the road: This is importat to be able to carry out the simulatio from the begiig util the ed. The lateral deviatio from the referece path at the poit where the obstacle is located should be as small as possible: this is importat i order ot to impact the obstacle as the desired path is desiged so that the vehicle will follow it with small lateral deviatios ad avoid the obstacle. CHALMERS, Applied Mechaics, Master s Thesis 211 1

15 o o The maximum path deviatio should be as small as possible: This is especially importat, for istace, i order for the vehicle ot to depart from the road after the obstacle i frot has bee avoided. The steerig cotrol iput should be as smooth (i.e. free of vibratios) as possible i order to had over the cotrol to the driver without a problem. 1.2 Limitatios ad simplificatios As i all studies, there are also simplificatios, limitatios ad assumptios i this study as well. Some of them are related to the cotrol system dyamics which are used to simulate the behaviour of the cotrolled vehicle, whereas the rest is about the vehicle chassis ad tyre properties Vehicle chassis ad tyre model o Pitch dyamics is ot modelled. I fact, yaw ad roll motio together ifluece the pitch dyamics due to the gyroscopic effect. Logitudial load trasfer is calculated by assumig a rigid (i.e. suspesio locked for pitch motio) vehicle ad cross terms cosistig of roll, yaw ad their rates are ot cosidered. o Aerodyamic drag ad the effect of possible side wids are ot modelled. o Suspesio sprigs ad dampers are assumed to behave liearly for the whole rage of roll agles ad roll rates. o Elastokiematical features (e.g. lateral force steer ad aligig momet steer) of the suspesio are ot cosidered whe modellig the axles. For all the axles, oly the roll steer (i.e. kiematical feature) is take ito cosideratio with a simple liear expressio. The camber chage i rigid axles due to roll of sprug mass (lateral load trasfer) is relatively small, that is also eglected. o I a tadem axle group, logitudial force ad torque o oe axle (located o the tadem axle) actually ifluece the vertical load o the other axle due to the measures take to distribute the load o each axle of the tadem group i a predefied ratio o ueve surfaces. Here, it is assumed that the torque reactio rods used to couteract additioal vertical load trasfer due to torques ad logitudial forces are desiged properly so that they (almost) cacel that effect. o The steerig agles of the left ad right frot wheels (o the first axle) are assumed to be the same. The steerig ratio is assumed to be costat. The lumped elasticity i the steerig system is assumed to be liear. o Ladder chassis is assumed to be rigid. I reality, truck chassis is made of socalled profiles with ope cross-sectios. Sice those profiles are torsioally flexible ad relatively rigid for bedig, the overall chassis structure is easily twisted. This is sometimes desired for trucks to better suit the road profile. However, as ca be expected, torsioally flexible ladder chassis affects the lateral load trasfer, but its affect o load trasfer is ot cosidered. o Tyre rollig resistace is eglected. CHALMERS, Applied Mechaics, Master s Thesis 211 2

16 o A liear reductio is assumed for the adhesio coefficiet betwee the tyre ad the groud with respect to the icreasig ormal load. Moreover, the horizotal asymptote for tyre lateral force vs. slip agle characteristic is assumed to be 75% of the peak force. o A liear chage is assumed for the horizotal positio of the tyre peak force vs. slip agle poit. o A first order differetial equatio with costat relaxatio legth is used to model tyre force build-up. o Rotatig wheels are ot simulated i order ot to take the combied slip ito accout. A frictio circle is used to determie the lateral force geerated by a tire i presece of a kow logitudial force Cotrol system dyamics o The etire desired path is estimated at the poit of itervetio. o Oly high μ eviromet: Simulatios o a low μ surface requires a differet tyre model. o Steerig actuator delays ad dyamics are ot modelled. o The delays due to slack i brake system are igored. Istead, brake system is assumed to be pre-charged so that the effect of slack i brake performace is miute. o Aalogue brake ad steerig actuators are assumed i the simulatio (i.e. ifiite resolutio, ifiite update frequecy). CHALMERS, Applied Mechaics, Master s Thesis 211 3

17 1.3 Literature review A approach based o artificial potetial fields is itroduced by Gerdes ad Rossetter [1] to assist the driver with lae keepig issue. They use superposed brake ad steer itervetios o the driver's iput ad achieve both safety ad drivability usig such a system. Hiraoka et.al. [2] propose a path-trackig cotroller for a four wheel steerig (4WS) vehicle based o the slidig mode cotrol theory. By decouplig the frot- ad rearwheel steerig, a advatage is made i cotrollig the vehicle thus achievig more stability ad more precisio i path-trackig i compariso with 2WS. There are more robustess i stability agaist system ucertaities ad perturbatios. A adaptive liear optimal cotrol is employed by Thommyppillai et.al. [3] to drive the car at certai limits of hadlig. The advatages of usig gai-scheduled adaptive cotrol over a fixed-cotrol scheme are show i simulatios of a virtual drivercotrolled car. Kritayakiraa ad Gerdes [4] describes the developmet of a race path-cotroller usig itegrated steerig brakig system desiged to drive a vehicle autoomously to its limits o a ueve dirt surface. I order to mimic the driver s ability i usig the frictio estimatio for cotrollig the vehicle o the limits while trackig the racig lie, the cotroller is divided ito sesig ad cotrol-liig parts. The sesig part imitates the driver, learig the track profile ad sesig the eviromet durig practice. Afterward the cotrollig part calculates the feed forward commad like a driver plaig ahead. While drivig, the feedback cotroller imitates the driver s car cotrol abilities, makig adjustmets based o chagig coditios. Therefore the cotroller ca be divided ito four importat parts, a path descriptio, frictio estimatio, steerig cotroller ad slip circle logitudial cotroller. a clothoid path is used to costruct a desired path. I this paper a pre-kowledge of frictio distributio obtaied from a ramp steer is used. from kowig the curvature, the feedforward steerig iput ca be calculated ad the steerig feedback based o lae-keepig adds the robustess to the cotroller. Kowig the curvature of the track the logitudial feedforward cotroller calculates the amout of throttle ad brake for a desired trajectory. Logitudial feedback cotroller based o slip circle fulfils two purposes. First, it provides a logitudial iput that cotrols tire slip ad secodly the slip circle cotroller esures that the tires are operatig at their limits. This approach ca maximize the tire forces while effectively cotrollig the tire slip. Kharrazi, S. [5] ivestigates the truck accidet statistics due to lateral istability of the truck ad also studies differet combiatio of truck ad trailer cosiderig their effect o lateral stability of the truck. Yag, D. [6] describes the method for beefit predictio of usig specific brake system cofiguratio o vehicle post impact stability cotrol. The iformatio about the beefit study is foud useful for this thesis. Bile, Ö. [7] deals with the heavy truck modelig ad simulatio. Early stage of usecase prioritizatio is also available i this literature. CHALMERS, Applied Mechaics, Master s Thesis 211 4

18 1.4 Approach Autoomous path ad path stability cotrol is a challegig o-liear cotrol problem with costraits. The performace is evaluated with respect to several aspects as idicated above for several use cases described i the ext chapter. There are also several feasible actuatio solutios. Therefore a optimal cotrol based methodology is used to ivestigate the potetials of the actuators to perform the maoeuvre ad also beefits of the collisio avoidace i each maoeuvre. These maoeuvres are defied based o the use cases itroduced i earlier parts of work where the ivestigatio o various target scearios is made. For each maoeuvre there might be cases that are the variats of the mai maoeuvre. Cosequetly, Path stability cotrol simulatio is performed for three differet maoeuvres. These simulatios show how efficiet the cotroller is for each Use-Case. The cotroller will be the implemeted o the demostratio vehicle which is a passeger car from FFA ad a truck from VOLVO 3P usig rapid cotrol prototypig. CHALMERS, Applied Mechaics, Master s Thesis 211 5

19 2 Use-Cases 2.1 Defiitio The truck target scearios covered i deliverable 1.5 [8] represet approximately 4% of all accidets i the used accidet data base. This meas that there are may accidets which have ot bee icluded i the iteractive target sceario aalysis. The major part of these accidets cosists of accidets with crossig traffic. Other large accidet groups are (i) accidets where the truck is hit from behid ad (ii) reversig accidets. These accidets are ot icluded i the aalysis, sice there are other projects focusig o accidets i crossigs (IterSafe2) ad the accidets where the crash happes i the rear ed of the truck are ot cosidered to be i the scope of INCA. Use-Case template i IteractIVe project is based o: (1) the arrative, (2) the sketch ad (3) the sequece diagram. A use case may iclude several alterative flows of evets, which represet differet possible solutios to a similar problem. Alterative flows may iclude differet possible iteractios for similar use cases or a escalatig sequece of evets. Separate use cases should be defied whe the correspodig target scearios differ fudametally. 2.2 Prioritizatio Use-Case prioritizatio is doe based o accidet statistics, Use-Case complexity, optimal cotrol results ad path stability simulatio results. The accidet scearios ca provide us with some iformatio about how frequetly each type of accidet happes or how much ijury or cost. Based o this a early prioritizatio is doe o accidet scearios from previous stages of work. Use-Case complexity is cosiderig the possibility of modellig the maoeuvre ad its eviromet as well as ivestigatig the required complexity of the model ad the cotroller to fulfil the requiremets. The prioritized Use Cases based o accidet statistics ad Use-Case complexity are as follow: o o o Rear-Ed Collisio Avoidace (RECA) : This use case deals with the situatio i which the truck have a higher velocity tha the car i frot. The velocity of iterest based o statistics is 4-8 km/h Ru-off-road prevetio o a straight road (RORP): This use case deals with uwated departure of the vehicle from the lae due to e.g. drowsiess of the driver. The speed of iterest is 8-9 km/h. Ru-off-road prevetio o a curved road (RORP): This use case deals with the vehicle drivig o a curved road with a rather large radius. The lack of actio from the driver departs the truck from the road. The speed of iterest is 8-9 km/h. CHALMERS, Applied Mechaics, Master s Thesis 211 6

20 Based o the prioritizatio of the use-cases above it follows that it is of iterest to study brakig, steerig, ad itegrated brakig ad steerig for collisio avoidace maoeuvres defied by the use cases above. The optimal cotrol results i this report are used to ivestigate the performace of the various actuator cofiguratios for collisio avoidace applicatio i order to fid out whether a specific cofiguratio ca work for this maoeuvre or ot. The use cases will be further prioritized based o the path stability cotroller results i this report to ivestigate the efficiecy of the path cotroller i each maoeuvre. CHALMERS, Applied Mechaics, Master s Thesis 211 7

21 3 Collisio avoidace optimal cotrol The heavy vehicle system dyamics model developed i Appedix A is a oliear multi iput-output dyamic system. The cotrol of the vehicle i collisio avoidace maoeuvres for various actuator cofiguratios such as brakig, steerig ad itegrated brakig-steerig is otrivial. I order to determie the potetial of various actuator cofiguratios ad to bechmark the collisio avoidace path ad speed cotroller, a optimal cotrol problem is formulated ad solved for a simplified vehicle model. For this purpose the dyamics of the vehicle is modelled as a poit mass (particle model). 3.1 Particle model The particle vehicle model depicted i Figure 3.1 has two degrees of freedom i horizotal plae OXY. F y Y F x a Fy Fx Figure 3.1 Schematic sketch of problem defiitio for particle model. ψ b X The driver ad steerig ad brakig actuators cotrol the vehicle motio by demadig frictio forces (steerig F y D ad brakig F x D ). The tire force geeratio i ot istataeous i real tires (see Appedix A), therefore tire relaxatio legths (σ x, σ y ) are take ito accout to model the force geeratio delay. The actual forces o tires are the F x ad F y. x D F F F x x x v x y D F F F y y y v x The frictio forces are defied i local coordiate system Oxy while the particle motio is defied i global coordiate system OXY where the X axis is cosidered as the origial track directio ad Y axis is perpedicular to origial track directio. The logitudial ad lateral distace durig the collisio avoidace maoeuvre are a ad b, respectively. The equatios of plaar motio for the vehicle particle model are: mx F x cos F si 3.3 y CHALMERS, Applied Mechaics, Master s Thesis 211 8

22 my F x si F cos I order to satisfy the force limitatio o the tires the steerig ad brakig forces should stay withi the frictio circle. ( F ) mg x y ( F ) ( ) y 3.4 The collisio avoidace maoeuvre is defied by the iitial ad fial coditios give bellow. V ( X ) V, V () V, X () X, Y() Y, X Y Y 3.5 V ( T) V, V ( T) V, X ( T) X, Y( T) Y 3.6 x xt y The iitial ad fial coditios metioed above are used to defie the boudary coditios for the collisio avoidace maoeuvre. I rear ed collisio avoidace sceario for istace, the fial global lateral velocity ca be zero for the case whe the coarse agle is cosidered as zero or a small value for the case cosiderig o-zero coarse agle. yt T T I order to geerate a particle model which is capable of resemblig the full vehicle model characteristics cosiderig the tire limitatios ad rollover risk, some costraits should be applied to the particle model. Cosiderig the rollover risk, the lateral acceleratio should stay below a certai limit. The logitudial acceleratio ca be limited i a similar way. a F y a y y,max 3.7 m CHALMERS, Applied Mechaics, Master s Thesis 211 9

23 3.2 Optimal cotrol problem Itroducig the state variables as z = [X Y V x V y F x F y ] T, the plaar equatios of motio (Equatios ) ca be trasformed to first order differetial equatios i state space form X Vx Y Vy V ( F cos F si ) / m x x y z V ( F cos F si ) / m 3.8 y y x D F ( v )( F F ) x x x x x D F ( v )( F F ) y x y y y The geeral optimal cotrol formulatio i state space will be as follow: Fid the states z t ad cotrols u t that miimize the objective fuctio: Subjected to equatios of motio from Equatio 3.8 where u = [F x D, F y D ] T ad boudary coditios T T J( z, u) c z() ct z( T) z Qzdt 3.9 J z ( t) f ( z, u) 3.1 z( ) z, JT z( T) z T 3.11 together with costraits o states (e.g. positio) ad state derivatives (e.g. velocity ad acceleratio): costraits o cotrols ad quadratic costraits o cotrols a ( a 3.12 a a z t) 1 7 a 8 2 u 3.13 T u Ru a 9 where the matrices J ad J T are determied by Equatio 3.5 ad 3.6. Limitatios o acceleratio ca be satisfied usig Equatio 3.12 ad the frictio circle is implemeted usig Equatio The optimal cotrol problem is also regularized ad augmeted by addig a small eergy term to the objective fuctio. J ~ ( z, u) J( z, u) w T u T u dt 3.15 CHALMERS, Applied Mechaics, Master s Thesis 211 1

24 4 Path ad speed cotrol A schematic sketch of a geeric path ad speed cotrol system is provided i Figure 4.1. The cotrol system icludes blocks for path plaig, decisio algorithm, feedforward ad feedback. Each of these blocks is explaied i followig text.,, ref FF ref,,a FF y V x, a, Y1, Y1, Y1 Path Plaig a a No Decisio Yes algorithm + Vehicle Feed-forward + a: logitudial distace Feedback Figure 4.1 Schematic sketch of a geeric path ad speed cotrol system. 4.1 Decisio algorithm The decisio algorithm provides a feasible path by performig robust referece path optimizatio usig the particle model defied i Sectio 3.1 with restrictios take ito accout o steerig agle, steerig agle rate, lateral acceleratio ad wheel torque profiles. After fidig a feasible path, the feed-forward steerig agle will be provided as the output of the decisio algorithm. Sice the maoeuvrability of a heavy vehicle o a high frictio surface is limited by the roll over threshold rather tha the tire capability to geerate tire side forces, the lateral acceleratio, should be kept bellow a certai limit obtaied from Equatio A 4. ay a y,max 4.1 Moreover, the hadwheel agle ad hadwheel agle rate should be costraied due to mechaical limitatios of actuators o steerig agle ad agular speed as well as driver s safety., FF FF, max FF FF, max 4.2 The required torque to the steerig system should also be limited due to driver s safety ad also the actuator limitatios. T T w w,max 4.3 CHALMERS, Applied Mechaics, Master s Thesis

25 4.2 Path plaig Path plaig requiremets The path plaig should provide a cotiuous ad smooth profile i advace of the itervetio. This meas that the positio, velocity ad acceleratio profile should be cotiuous. Aother importat aspect is simplicity Piecewise polyomial Cosiderig the requiremets o path plaig, a piecewise polyomial has bee chose to satisfy the requiremets. ( X ) C ( X X ref, i ij i j Y ) j, i 1,2,..., m 4.4 which is subject to the iitial ad fial coditio as follows Y m Y1 ( ) Y1, Y 1() Y 1, Y 1() Y 1 X ( T)) Y, Y ( X ( T)) Y, Y ( X ( T)) Y 4.5 ( 4.6 mt m mt m mt The etire path should be cotiuous ad smooth which ca be defied as follows. Y Y, Y Y, Y Y, Y Y, ref, i, T ref, i1, ref, i, ref, i1, T ref, i, T ref, i 1, Y Y Y Y ref, i, ref, i1, T,, ref, i, ref, i1, T ref, i, T ref, i1, i 2,..., m Usig a fifth order polyomial Usig oe fifth order polyomial is appropriate to satisfy the requiremets sice it ca costrait positio, velocity ad acceleratio as iitial ad fial coditio. The fifth order polyomial is defied as follows: Y ref ( X ) ax bx cx dx ex f, m 1, The followig coefficiets ca be metioed as a example for rear ed collisio avoidace escape path. This example is made for logitudial ad lateral displacemet of 5 m ad 3 m respectively. Coefficiets a b c d e f Values 5.76e-8-7.2e-6 2.4e-4 Table 4.1 A example of coefficiets for fifth order polyomial CHALMERS, Applied Mechaics, Master s Thesis

26 lateral displacemet, X[m] Except the three last coefficiets that remai zero for all the cases i lae chage path plaig, all the other three values chage by chagig the logitudial or lateral distace. The fifth order polyomial with these coefficiets is also show i Figure logitudial displacemet, X[m] Figure 4.2 A example of a fifth order polyomial The mai advatage of the fifth order polyomial is that it provides a very smooth, cotiuous path profile. Therefore this path ca be used for calculatig the feedforward steerig as well as lateral acceleratio required by the path. It is show later i Figure 5.1 that the optimal ad feed-forward steerig profiles are comparable. Therefore it is logical to use the feed-forward steerig profile which is based o the polyomial istead of ruig the optimal cotrol olie to obtai the optimal steerig profile. The fifth order polyomial is used for all the simulatios i Chapter 5-6 with the heavy truck vehicle model. However this polyomial is ot iteded to be implemeted real time. It is likely that a multiple lower order polyomials will be used i real time implemetatio. The order of the polyomial depeds o the dyamics (e.g. filterig) of the truck ad the actuators. As the coclusio to this part, it ca be metioed that the frameworks is quite flexible i usig the polyomial ad ca easily chage to ay other polyomials with differet order ad multiple segmets. 4.3 Path stability cotrol desig The path stability cotroller objective is to miimize the path ad headig agle error while maitaiig the maoeuvrability ad roll stability i order to perform the collisio avoidace maoeuvre. Commo actuators for this approach are steerig ad brakig. Optimal cotrol results for differet actuators, shows more beefit i usig the steerig actuator i these cases (Sectio 5.1). For a better efficiecy ad accuracy the path stability cotroller is desiged i two parts, feed-forward steerig which is the output of the path plaig ad decisio algorithm is implemeted i order to icrease the resposiveess of the cotroller ad feedback part that is operatig o headig agle ad headig agle rate error is used to compesate for iaccuracies. Sice the vehicle respose to steerig ad brakig iput is ot istataeous cotrollig the vehicle based o the referece poit that it just passed caot help the vehicle to follow the trajectory ahead especially if the vehicle is movig i high speed. Therefore, a preview time which provides a referece CHALMERS, Applied Mechaics, Master s Thesis

27 poit ahead of the vehicle at the distace depedig o the velocity is implemeted. The cotroller should operate withi the badwidth of steerig actuator otherwise the actuator caot provide what the cotroller requests for performig the maoeuvre. It is also assumed that the absolute positio of the vehicle at each time which is used for brakig stability cotrol after the maoeuvre is kow usig a GPS or similar positioig system. The iformatio about the headig agle, headig agle rate etc. are provided by build i sesors Feed-forward The feed-forward steerig agle is provided i advace based o the path provided by the path plaig. The feed-forward output from path plaig should satisfy the costraits i decisio algorithm before beig supplied to path stability cotroller. This steerig agle is determied based o the path profile ad assumig a two axle vehicle i steady state coditio, defied i Sectio A3. Cosequetly a cotiuous ad smooth steerig profile is provided i advace. The followig equatio is used to calculate the feed-forward steerig iput. L a e y, ref K FF u 4.9 R g where the referece lateral acceleratio a y,ref is based o the referece path,y ref.ad L e is the effective wheelbase based o the static ormal load o the i t axle, F zi,static. L e Fz 1, static L ( l3 l2) 4.1 F F z2, static z3, static Feedback Feedback steerig cotrol is defied as a liear PD cotrol o yaw agle error ad yaw rate error. This part of the cotroller is applied i order to compesate the errors due to simplificatios ad iaccuracies. I order to compesate for the truck ad tire dyamics, a preview time (t p ) is also used to apply the steerig i advace. ( t t ) ( t) K ( ( t t ) ( )) ( t) K t FB p ref p d ref p 4.11 where ψ ref (t + t p ) is the headig agle of the truck at the preview time ahead of the vehicle while ψ is the actual headig agle of the vehicle. The referece headig agle is directly calculated from the path profile. The total steerig iput of the vehicle will the be: dy ref ( X ) ta 1 ref 4.12 dx FF 4.13 FB CHALMERS, Applied Mechaics, Master s Thesis

28 A schematic figure of the path stability cotroller is provided i Figure 4.3 Path cotrol feed-forward FF + + FB Vehicle Path cotrol feedback,, ref ref Figure 4.3 Schematic sketch of path stability cotroller. 4.4 Yaw cotrol I this study, the differetial brakig used for yaw cotrol is divided ito two parts: o o Tur i brakig: Feed forward iitial differetial brakig for compesatig the delays due to dyamics of the steerig system ad vehicle yaw dyamics. Brakig stability cotrol: Differetial brakig as a feedback cotrol o positio after the lae chage to stabilize the vehicle motio Tur i brakig Due to dyamics of the steerig system, tire characteristics ad vehicle yaw dyamics, the vehicle respod to the steerig iput is ot istataeous. I fact these dyamics operate very similar to a first order filter o the steerig agle. Therefore there is a loss i steerig performace while cosiderig this effect i the simulatio. I order to compesate this loss two differet strategies ca be cosidered. o o Icreasig the preview time Usig differetial brakig to icrease the steerig performace of the vehicle i very begiig of the maoeuvre i order to help the vehicle to follow the path with the same preview time that was used for the simulatio without takig the system dyamics ito accout. Sice icreasig the preview time is ot favourable i desigig the cotroller due to the fact that the cotroller is ot supposed to get activated too early, the secod approach is cosidered as the preferred approach. I this method the amout of brakig force FD FF o both wheels o either the left or right side of the truck will be provided as step iput. The brakig force is applied o side that is demaded by the referece curvature determied based o the referece path. CHALMERS, Applied Mechaics, Master s Thesis

29 4.4.2 Brakig stability cotrol The differetial brakig is used as a proportioal cotroller o positio error i order to compesate the offset due to iaccuracies, chages i the coditio ad faults at the ed of the maoeuvre. FD FB ( t) K Y ( t t ) Y( t) 4.14 p ref p FD FD FF FD FB 4.15 The wheels used for differetial brakig are determied based o global lateral positio error as idicated i Figure 4.4. =1st wheel =2d wheel Y ref Y Y = 2, 24, 4 i=1st axle Y ref Y X Y ref Y Y = 2, 1, 43 Y ref Y i=2d axle =3rd wheel =4th wheel X i=3rd axle =5th wheel =6th wheel Figure 4.4 Schematic sketch of the brakig stability cotrol. Schematic figure of the yaw cotroller is provided i Figure 4.5. FD FB Yaw-cotrol Brakig Stability cotrol Y ref Y Yaw-cotrol Tur i brakig FD FF + FD + Vehicle Figure 4.5 Schematic sketch of yaw cotroller. CHALMERS, Applied Mechaics, Master s Thesis

30 4.5 Speed cotrol Very similar to referece path geeratio, a speed profile V ref is geerated by the path plaig algorithm. The differece betwee the actual velocity of the vehicle ad the referece velocity is defied as the velocity error. The speed cotrol is the a feedback proportioal cotroller actig o the velocity error which determies the amout of brakig force that should be applied to the wheels i order to keep the referece speed. The total brakig force is distributed o axles proportioal to the static load. The speed profile is tryig to mimic the optimal cotrol solutio i a simplified way ad it is ot exactly the optimal cotrol results. Therefore it is expected that the performace of this actuator is ot as good as the optimal cotrol. The speed cotrol is the defied as: F FB ( t) K V ( t t ) V( t) p ref p F FB Speed-cotrol V ref V + Vehicle Figure 4.6Schematic sketch of speed cotroller. CHALMERS, Applied Mechaics, Master s Thesis

31 4.6 Collisio avoidace path ad speed cotrol system The complete path ad speed cotrol system for collisio avoidace applicatio is provided i Figure 4.7.,, ref FF ref,,a FF y, Y V x a, Y1, Y1, Path Plaig 1 FD FB Yaw-cotrol Brakig Stability cotrol Y ref Y a a No Decisio Yes algorithm a: logitudial distace Yaw-cotrol Tur i brakig Path cotrol feed-forward FD FF + FF + + F FB FB Speed-cotrol Vehicle Path cotrol feedback V ref V,, ref ref Figure 4.7 Schematic sketch of path ad speed cotrol system. CHALMERS, Applied Mechaics, Master s Thesis

32 4.7 Performace evaluatio I order to evaluate the performace of the path cotroller, some parameters are defied as performace criteria. These parameters are defied as follow. Path error which shows the performace of the path cotroller is defied as e Y Y ref 4.17 where the Y is the actual positio of the vehicle, Y ref is the desired (referece) positio. Headig agle error is defied as ref 4.18 where ψ is the actual headig agle of the vehicle, ψ ref is the desired (referece) headig agle. The required amout of the torque o the wheel (T) i order to perform the maoeuvre ad also the rate of chage i this torque (T ) are also take ito cosideratio. These parameters are basically the requiremets for the steerig motor ad therefore are limited by the motor limitatios i torque geeratio as well as the torque rate. The lateral jerk i is defied as the derivative of lateral acceleratio a y. Safety margi for the distace betwee the host ad target vehicle is defied as the miimum allowed distace betwee the vehicles durig the maoeuvre. Target value ca be set for some parameters as follow. Due to roll over limit, the target value for maximum lateral acceleratio is set to 3.6 m/s^2 ad due to the driver iteractio ad comfort, the maximum torque o the wheels are set to 115Nm. By takig ito accout the driver iteractio ad safety o oe had ad the actuator limitatios o the other had the target value for maximum hadwheel agle ad agular speed is set to 6 deg ad 5deg/s respectively. These target values may be refied later by collectig more iformatio about the actuator ad also receivig more data from SP3 i the field of driver iteractio. CHALMERS, Applied Mechaics, Master s Thesis

33 5 Rear-Ed Collisio Avoidace (RECA) - Sigle lae chage 5.1 Optimal cotrol results for various actuator cofiguratios The optimal cotrol results are provided i this part for differet actuator cofiguratios usig the simplified truck model itroduced i Sectio 3.1. Ivestigatios are made to fid out the advatages ad disadvatages of various actuator solutios for variats of maoeuvre specificatios e.g. iitial speed of the collisio avoidace maoeuvre ad also bechmark the path stability cotroller. The objective is to fid F y ad F x over [, T] to miimize the followig fuctio: T 2 2 J X ( T) w ( F F ) dt 5.1 The particle model is also subjected to the equatios of motio, frictio circle as well as the lateral acceleratio costrait. Maximum allowed lateral acceleratio to avoid rollover risk is a y,max = 3.6 m/s^2 for all cofiguratios. Iitial ad fial coditio is defied as follow: y x X, Y, V x 8 km/h, V 5.2 y Y 3m, V. 5.3 T Note that the delays due to tire relaxatio legths are eglected i.e. it is assumed that the force geeratio is istataeous o the wheels (σ x,y = ). The problem is solved usig the software PROPT [9] with 5 odes ad the weightig factor w = 5E 4. The followig three differet actuator cofiguratios are studied: o Usig steerig actuator for avoidig the collisio Two differet cases are cosidered for steerig actuator, for the first case, the rollover limit is the active costraits. This case is represetig the high frictio surfaces (max (a y ) = 3.6 m s2, μ >.37). Secod case is represetig the low frictio surface where the frictio of the road is ot eough for reachig the rollover limit ( max(a y ) < 3.6 m s2, μ <.37). The Brakig force is set to zero i this cofiguratio ( F D x = ). o Usig brakig actuator for avoidig the collisio Two differet cases for differet road coditios are cosidered for brakig maoeuvre. Note that the Steerig force is set to zero i this cofiguratio ( F y D = ). o Usig itegrated steerig-brakig actuator for avoidig the collisio Two differet cases with differet brakig force ad the same steerig force metioed above is cosidered for this case. yt CHALMERS, Applied Mechaics, Master s Thesis 211 2

34 Required logitudial distace, a * [m] Figure 5.1 shows the required logitudial distace, a, to perform the rear-ed collisio avoidace maoeuvre versus the iitial velocity of the truck for various actuator cofiguratios. The performace of these cofiguratios is measured by the amout of required logitudial distace for each velocity. Therefore the cofiguratio which requires less logitudial displacemet is cosidered to be more beeficial for that speed. Note that the lateral displacemet is oly made i presece of the steerig actuator. I pure brakig actuator cofiguratio simulatio the lateral displacemet is set to zero. 7 Particle collisio avoidace/ Sigle lae chage lateral displacemet, b=3 m Brakig a x, max = 6 m/s 2 (high frictio surface) 6 Brakig a x, max Steerig a y, max = 7 m/s 2 (extra-high frictio surface) = 3.6 m/s 2 (high frictio surface) 5 Steerig a y, max = 2 m/s 2 (low frictio surface) Brakig a x, max = 7 m/s 2, Steerig a y, max = 3.6 m/s 2 Brakig a x, max = 6 m/s 2, Steerig a y, max = 3.6 m/s Iitial logitudial velocity, V x [kph] Figure 5.1 Required logitudial distace versus iitial logitudial velocity. These results show the break poit velocity where the brakig actuator cofiguratio is ot aymore the best optio for avoidig the rear-ed collisio. Cosiderig the curve for steerig actuator cofiguratio o high frictio road with maximum logitudial deceleratio of a x,max = 6 m/s 2, it is observed that steerig becomes better tha brakig at 78 km/h. It is also show i Figure 5.1, that the itegrated steerig-brakig actuator cofiguratio moves this poit dow to 68 km/h. This meas that the itegrated steerig-brakig actuator cofiguratio gives a wider velocity rage where the performace is better tha pure brakig. Actually, the brake poit velocity for pure steerig occurs at a very high velocity for a truck which results i a quite arrow velocity widow. Therefore the coclusios ca be made that the CHALMERS, Applied Mechaics, Master s Thesis

35 itegrated steerig-brakig actuator cofiguratio has the potetial to improve the performace of the rear-ed collisio avoidace maoeuvre i wide rage of velocities compared to pure brakig. It also covers lower velocities compared to pure steerig. As expected for pure steerig results, the maoeuvre o high frictio surface requires less logitudial distace sice the tires are operatig o the rollover limit ad the required logitudial distace icreases almost liearly with the iitial logitudial velocity. Usig pure brakig, the results show that for differet brakig deceleratios the gai i performace is small for low velocities but icreases sigificatly with velocity. Therefore, it ca be cocluded that the effect of harsh brakig is sigificat for high speeds. 5.2 Optimal cotrol sesitivity study The objective of optimal cotrol sesitivity study is to ivestigate the effect of chage i key parameters o the results of the rear ed collisio avoidace. The goal of study i each case is explaied i details. Simplified truck model itroduced i Sectio 3.1 is used for all these cases. Lateral displacemet Optimal cotrol problem is solved for a particle model to ivestigate the sesitivity of required logitudial distace with respect to lateral distace. The lateral distace i RECA maoeuvre is oe of the mai parameters. Larger logitudial distace provides more opportuity to prevet the collisio with mild maoeuvres while large lateral displacemet causes more lateral acceleratio, steerig agle ad steerig agle rate ad therefore a more aggressive maoeuvre. The driver comfort is also affected by harsh maoeuvre. This study shows how much ca be gaied by decreasig the lateral distace i the maoeuvre for example if the car i frot is positioed with a offset regardig to the referece vehicle or if the vehicle is passig a motorcycle. As a result kowig the advatage of decreasig lateral displacemet ad cosiderig the safety margi, defied i Performace evaluatio, a desired lateral displacemet ca be decided. Usig pure steerig actuator cofiguratio, the objective is to fid F y over [, T] to miimize the followig fuctio: J T 2 X ( T) w F dt 5.4 y The particle model is also subjected to the equatios of motio, frictio circle as well as the lateral acceleratio costrait. Maximum allowed lateral acceleratio to avoid rollover risk is 3.6 m/s^2 i this case. Iitial ad fial coditio is defied as follow: X, Y, V 8 km/h, x V y 5.5 Y b, V, b.5,3 m 5.6 T The problem is solved usig 5 odes ad weightig factor of w = 5E 4. yt CHALMERS, Applied Mechaics, Master s Thesis

36 a* [m] Required logitudial distace, a* [m] km/h 5 km/h 2 km/h Lateral distace, b [m] Figure 5.2 Required logitudial distace versus lateral distace for give speed. 2 Chage of required logitudial distace regardig iitial velocity Iitial logitudial velocity, V x [km/h] Figure 5.3 The amout of chage i logitudial distace( a*) by reducig the lateral distace b from 3 to 1. As illustrated i Figure 5.2 the required logitudial distace for the particle to avoid the obstacle by oly steerig is icreasig almost liearly with lateral distace for all speeds. CHALMERS, Applied Mechaics, Master s Thesis

37 Global lateral displacemet Y [m] Required logitudial distace, a* [m] Fial coarse agle Optimal cotrol problem is solved for the particle model to ivestigate the sesitivity of required logitudial distace regardig the fial coarse agle which is defied as: V 1 yt ta T 5.7 VxT Fial lateral velocity of the vehicle i RECA maoeuvre is a parameter which plays a importat role i stabilizig ad cotrollig the vehicle after makig the maoeuvre. I geeral zero course agle (zero lateral velocity) i fial coditio is preferred. This study ivestigates the effect of very small course agle o efficiecy of the maoeuvre. The desired result will be to fid small course agles givig remarkable improvemets i maoeuvre efficiecy. Usig the pure steerig actuator cofiguratio, the objective is to fid F y over [, T] to miimize the followig fuctio: J T 2 X ( T) w F dt 5.8 y The particle model is also subjected to the equatios of motio, frictio circle as well as the lateral acceleratio costrait. Maximum allowed lateral acceleratio to avoid rollover risk is 3.6 m/s^2 i this case. Iitial ad fial coditio is defied as follow: (The fial lateral velocity of km/h correspods to coarse agle of -1 degree usig Equatio 5.7) X, Y, V 8 km/h, x V y 5.9 Y 3, V,14.4 km/h 5.1 T The problem is solved usig 5 odes ad weightig factor of w = 5E 4. yt km/h 5 km/h 2 km/h Global logitudial displacemet X [m] Course agle, [rad] Figure 5.4 Required logitudial distace versus fial course agle. CHALMERS, Applied Mechaics, Master s Thesis

38 The chage i required logitudial distace is oliear to course agle variatio after 4 degree. Ad it is also observed that after 1 degree the required logitudial distace will ot chage sigificatly with the coarse agle variatio. This meas that by makig a small coarse agle (less tha 1 degree) at the ed of maoeuvre, a deg of coarse agle -6 deg of coarse agle -9 deg of coarse agle 8 a* [m] Iitial logitudial velocity, V x [m] sigificat decrease i required logitudial distace ca be achieved. Figure 5.5 The amout of chage i logitudial distace( a*) by icreasig the course agle. CHALMERS, Applied Mechaics, Master s Thesis

39 5.2.2 Maoeuvre severity Optimal cotrol problem is solved for a particle model to ivestigate the optimal itegratio of steerig-brakig fuctios with respect to the severity of the maoeuvre. The objective of this study is to show the optimal itegratio of steerig-brakig fuctios i RECA cosiderig the severity of the maoeuvre. The results of this study ca be used for bechmarkig the path stability cotrol i terms of combiig steerig-brakig fuctio. Usig the kiematic relatios, required logitudial distace to stop the particle with the iitial velocity of V x ad road frictio coefficiet μ is calculated as 2 Vx c 5.11 g ad the maximum lateral distace feasible with the speed of V x ad frictio of μ o the road is obtaied from a auxiliary optimal cotrol problem ( b max ). The severity factor is defied as α = a which is the ratio of available to required logitudial c distace. Less available logitudial distace icreases the severity of maoeuvre which meas lower values of alpha. Schematic sketch of the problem is provided i Figure 3.1. Usig the itegrated steerig-brakig actuator, the objective is to fid F y ad F x over [, T] to miimize the followig fuctio: J V x T 2 2 ( T) w ( F F ) dt x y 5.12 This objective fuctio miimizes the fial velocity which is oe of the solutios for RECA ad may be a useful method e.g. for givig the cotrol back to driver i a lower speed which is easier to cotrol. Moreover the forces by the actuators which is the secod term of objective fuctio ca be cotrolled i this method e.g. performig a less aggressive maoeuvre. The particle model is also subjected to the equatios of motio, frictio circle as well as the lateral acceleratio costrait. Maximum allowed lateral acceleratio to avoid rollover risk is 73.6 m/s^2 i this case. Usig itegrated steerig-brakig actuator Iitial ad fial coditio is defied as follow: ga X, Y, V, V x y 5.13 Y.75 b, V max 5.14 T The problem is solved usig 5 odes ad weightig factor of w = 5E 4. yt CHALMERS, Applied Mechaics, Master s Thesis

40 Normalized brakig force, Fx/mg [ - ] Normalized steerig force, Fy/mg [ - ] =.4 =.6.2 =.8 = Normalized Time, t [sec].5 = =.6 =.8 = Normalized Time, t [sec] Figure 5.6 Steerig-brakig itegratio regardig the maeuver severity It is observed from the results that for more severe maoeuvres (lower alpha values), the optimal way of itegratig steerig ad brakig is to steer more at the begiig. This is because of gettig closer to last poit of steer which is defied as the last poit where pure steerig ca be applied to avoid the collisio. The last poit of steer ca be determied from Figure 5.1 as α =.24 Therefore the closer the itervetio gets to this poit the more steerig will be eeded at the begiig of the maoeuvre. It ca also be cocluded from these results that if the path ad speed cotrol system is hesitatig about how to combie the path ad speed cotrol due to iaccuracies, sesor problems, lack of data etc. it is the beeficial to brake at the begiig util more iformatio is available ad the severity of the maoeuvre is kow. Cosequetly, if the maoeuvre is ot severe the vehicle has ot lost ay opportuity by reducig the speed ad goig ito a higher α value which meas deceased maoeuvre severity. O the other had, if the maoeuvre is severe there will be two possible scearios. Firstly, assumig that the vehicle has ot passed the last poit of steer, where brakig had bee helpful sice last poit of steer is postpoed by reducig the speed. Secodly, if the vehicle has passed the last poit of steer, pure steerig cofiguratio will ot be helpful to avoid the accidet ad brakig or itegrated steerig-brakig are the oly available optios. Cosequetly, it may be possible to stop the vehicle before the obstacle depedig o velocity of the vehicle or avoidig the vehicle with itegrated steerig-brakig itervetio. Figure 5.1 shows whe brakig is better tha steerig. I the velocities where brakig is worse there is o chace to stop the vehicle before the obstacle sice the steerig caot perform the maoeuvre either. Nevertheless the accidet is mitigated by brakig ad reducig the speed. It ca be cocluded brakig is very ofte a good iitial actio if the required iformatio to take the optimal actio is ot available. CHALMERS, Applied Mechaics, Master s Thesis

41 Required logitudial distace, a* [m] Variable brakig versus costat brakig This sectio ivestigates the beefit of usig variable brakig compared to costat brakig. I costat brakig the amout of brakig does ot chage durig the maoeuvre while implemetig the variable brakig, the brakig force ca freely chage to obtai the optimal results. The same problem formulatio i Sectio 5.1 is also used here. The plots bellow shows the results of this sesitivity study. 39 Variable brakig vs Costat brakig 38.5 variable brakig costat brakig Severity factor, Figure 5.7 Comparig the required logitudial distace versus the maeuver severity for costat ad variable brakig This meas that usig variable brakig, the amout of required logitudial distace is decreased which meas that the variable brakig system is more efficiet. It ca also be observed that for more severe maeuver with higher iitial speed (lower severity factor), there is small differece betwee costat ad variable brakig. However, the variable brakig becomes more efficiet compared to costat brakig i less severe maoeuvres. CHALMERS, Applied Mechaics, Master s Thesis

42 5.3 Path cotrol simulatio RECA maoeuvre I this sceario the host vehicle is movig with the speed of V=8 km/h while the vehicle i frot is stadig still. The amout of lateral distace is set to 3 m ad the feasible logitudial distace will be give by path plaig ad decisio algorithm. Figure 5.8 shows schematic sketch of the maoeuvre. Lateral distace Log distace Figure 5.8 RECA simulatio maoeuvre setup. Table 5.1 shows the parameters for settig up the simulatio as well as the costraits which are used i decisio algorithm. Parameters Values Iput Values: Frictio, µ.7 Lateral distace, b 3 m HV iitial velocity, V1 8 km/h LV iitial velocity, V2 km/h Logitudial distace, a 4 m (from path plaig) Preview time, t p.4 s Target values: Maximum lateral acceleratio, a x 3.6 m/s^2 Maximum had wheel Agle, δ 6 deg Maximum had wheel Agle rate, ω 5 deg/s Maximum torque o the wheel, T 115 Nm Table 5.1 RECA maoeuvre parameter settig. CHALMERS, Applied Mechaics, Master s Thesis

43 i [m/s 3 ] d/dt [deg/s] a y [m/s 2 ] Lateral distace Y [m] 5.4 Path cotrol results for RECA maoeuvre The results of the path cotrol are divided ito two parts. First the path plaig results will be show ad later the path cotrol simulatio results will be illustrated. Note that pure steerig actuator cofiguratio is used for this simulatio. The simulatio is doe o high μ surface Path plaig 4 Referece path optimizatio procedure Logitudial distace X [m] 4 Lateral acceleratio 1 Steerig wheel agle Logitudial distace X [m] Lateral jerk 2 [deg] Logitudial Distace X [m] Steerig wheel agle rate Logitudial distace X [m] Logitudial Distace X [m] Figure 5.9 Path plaig results for RECA sceario. Followig plots show the path plaig outputs which are cofirmed by the decisio algorithm. As it ca be observed, the logitudial distace is icreased i steps to meet the costraits at the decisio algorithm. It is observed i Figure 5.1 that the optimal steerig agle for this maoeuvre is close to the feed-forward steerig. Therefore the feed-forward steerig is assumed to be good eough to be used istead of the optimal cotrol results. CHALMERS, Applied Mechaics, Master s Thesis 211 3

44 Yaw agle [deg] Lateral Distace Y [m] Steerig Wheel agle [deg] 1 Steerig Wheel agle Feed-forward Optimal Logitudial Distace X [m] Figure 5.1 Optimal cotrol versus feed-forward steerig agle Comparig the optimal ad feed-forward steerig agle which is the output of path plaig algorithm i Figure 5.1, it is observed that these results are close eough to justify usig the feed-forward agle as the iput to the model. Therefore solvig the optimal cotrol olie does ot seem to be ecessary i this case. These results are made for the same logitudial ad lateral distace ad as expected the optimal results are obtaied i higher velocity compared to path cotrol results Simulatio results Followig plots show the simulatio results. 5 Truck Path Logitudial Distace X [m] 8 Yaw agle Logitudial Distace X [m] Truck right frot corer Truck right rear corer Obstacle Preview Referece Actual Cotroller Active Figure 5.11 Path stability cotrol results for RECA sceario positio ad headig agle It is observed that the cotroller tries to cut the corers which results i lower peak for lateral acceleratio i simulatio results comparig with the steerig agle profile provided by the path plaig algorithm. The udersteerig behaviour of the truck is also observed cosiderig the lies showig the positio of the corers of the vehicle. CHALMERS, Applied Mechaics, Master s Thesis

45 a y [m/s 2 ] 4 d/dt[deg/s] Lateral acceleratio 2 Steerig Wheel agle 2 1 [deg] Logitudial Distace X [m] Lateral Jerk Logitudial Distace X [m] Wheel Steerig agle rate 1 i [m/s 3 ] Logitudial Distace X [m] Logitudial Distace X [m] Figure 5.12 Path cotrol results for RECA sceario steerig wheel agle ad torque ad steerig wheel rate. As expected Couter steerig is observed i presece of the feed-back cotrol. Tire capacity is ot used sigificatly i this case. The reaso is the low gais for the PD cotroller to keep the maoeuvre mild ad easy to hadle for the driver. It is decided that path error is ot the first priority of the cotroller sice that is avoidig the obstacle. Therefore as log as the obstacle is avoided, the gais o the cotroller do ot eed to be icreased more sice that will oly result i harsher maoeuvre without ay improvemet. CHALMERS, Applied Mechaics, Master s Thesis

46 dt/dx [Nm/s] Tire Capacity [ % ] T [Nm] Tire forces o wheel i,j; i=axle umber j=side First axle, Left First axle, Right Secod axle, Left Secod axle, Right Third axle, Left Third axle, Right Torque o the wheel Logitudial Distace X [m] 1 x 14 Torque rate o the wheel Logitudial Distace X [m] Logitudial Distace X [m] Figure 5.13 Path cotrol results for RECA sceario - tire capacity ad the torque profile Table 5.2 shows the results of the simulatio for some parameters of iterest. Maximum value for each parameter, the positio of the maximum value as well as the target value ad the value of the parameter at the obstacle is metioed bellow. Table 5.2 RECA path cotrol simulatio results. CHALMERS, Applied Mechaics, Master s Thesis

47 Yaw agle [deg] Lateral Distace Y [m] 5.5 Path ad speed cotrol for RECA maoeuvre This sectio maily deals with the itegrated steerig-brakig actuator i collisio avoidace maoeuvre. The optimal cotrol results are used i order to improve the uderstadig of a proper itegratio of steerig ad brakig actuators. The cotroller is tured to a path-speed cotroller i this case where a proportioal cotroller is active o the speed i this case. The speed profile is also give i advace from the path plaig algorithm. Note that itegrated steerig-brakig cotrol is used i these simulatios Path cotrol results The results of simulatio for steerig-brakig itegratio are as follow. Note that the simulatio is doe o high μ surface. 5 Truck Path Logitudial Distace X [m] 8 Yaw agle Logitudial Distace X [m] Truck right frot corer Truck right rear corer Obstacle Preview Referece Actual Cotroller Active Figure 5.14 Path ad headig agle profile for itegrated steerig brakig actuator for RECA sceario It ca be observed that the headig agle profile is followed more accurately usig the brakig. The reaso for this behaviour ca be that the brake force is distributes more force o frot wheel therefore, the frot corerig stiffess decreases more tha o other axles. As a result, the vehicle becomes more udersteered ad ca easier follow the path. It is also observed that there is more offset at the ed of the maoeuvre usig brakig. This is due to the decrease i corerig stiffess ad therefore the loss i lateral force. CHALMERS, Applied Mechaics, Master s Thesis

48 dt/dt[nm/s] Tire Capacity [ % ] T [Nm] i [m/s 3 ] d/dt [deg/s] a y [m/s 2 ] Lateral acceleratio Logitudial Distace X [m] Lateral Jerk 1 [deg] Steerig Wheel agle Logitudial Distace X [m] Wheel Steerig agle rate Logitudial Distace X [m] Logitudial Distace X [m] Figure 5.15 Path stability cotrol results for itegrated steerig-brakig actuatorcofiguratios for RECA. lateral acceleratio, steerig wheel agle ad the torque ad steerig agle rate. Comparig these results with pure steerig, It ca be observed that the steerig wheel agle ad also steerig wheel rate is decreased. A decrease i lateral acceleratio as well as the torque o the wheel ad their time derivatives is also observed. Tire forces o wheel i,j; i=axle umber j=side First axle, Left First axle, Right Secod axle, Left Secod axle, Right Third axle, Left Third axle, Right Torque o the wheel Logitudial Distace X [m] Torque rate o the wheel Logitudial Distace X [m] Logitudial Distace X [m] Figure 5.16 Path cotrol results for itegrated steerig brakig actuator for Rear Ed collisio avoidace sceario - tire capacity ad the torque profile o the wheel. CHALMERS, Applied Mechaics, Master s Thesis

49 Velocity, V [ m/s ] It is see that more of tire capacity is used usig the brakig which is expected compared with the oly steerig case Actual velocity Referece velocity profile Logitudial displacemet, X [m] Figure 5.17 Path cotrol results for itegrated steerig brakig actuator for RECA sceario. Speed profile Ivestigatig the results of the path cotrol sesitivity study, it is observed that the results of the itegrated steerig-brakig actuator cofiguratio are ot sigificatly better tha the pure steerig. Comparig these results with optimal cotrol results that showed a reductio i required logitudial distace, it ca be cocluded that the sophisticated itegratio of steerig brakig actuators i optimal cotrol solutio caot be easily implemeted i the path cotroller. CHALMERS, Applied Mechaics, Master s Thesis

50 Tire Capacity [ % ] Tire Capacity [ % ] 5.6 Path ad yaw cotrol for RECA maoeuvre The itetio of implemetig the tur i brakig actuator cofiguratio is to icrease the maoeuvrability of the truck by makig it respod faster to steerig demad. This system ca be basically applied as assistace for steerig actuator. The other usage of the differetial brakig is to assist the steerig for stabilizig the vehicle. The algorithm of differetial brakig implemeted i this study is described i details i Sectio 4.4. The simulatio is doe o high μ surface. Note that the tur i brakig actuator cofiguratio is combied with pure steerig cofiguratio i this simulatio Tur i brakig To ivestigate the performace of the iitial differetial brakig, the simulatio is doe for the case with ad without the iitial differetial brakig (tur i brakig). The problem with this approach is that whe the shorter preview time is applied, the over shoot after the lae chage is ot avoidable if the path is followed with a high accuracy. This pheomeo, which is due to truck yaw dyamics will be discussed later i this part. The steerig cotrol is the same for the previous cases with oly steerig. The followig plots are the results of these simulatios. Tire forces o wheel i,j; i=axle umber j=side First axle, Left First axle, Right Secod axle, Left Secod axle, Right Third axle, Left Third axle, Right Tire forces o wheel i,j; i=axle umber j=side First axle, Left First axle, Right Secod axle, Left Secod axle, Right Third axle, Left Third axle, Right Logitudial Distace X [m] Figure 5.18 Tire force capacity witout tur i brakig Logitudial Distace X [m] Figure 5.19 Tire force capacity with tur i brakig. The shape of the first axle left wheel force curve shows a superpositio of the steerig ad differetial brakig at the begiig of the maoeuvre. It is observed that the curve almost goes back to pure steerig whe the differetial brakig eds. Figure 5.2 shows that the differetial brakig makes the vehicle faster i followig the CHALMERS, Applied Mechaics, Master s Thesis

51 Yaw agle [deg] Lateral Distace Y [m] headig agle profile. O the other had both overshoot ad fial positio offset is icreased. The reaso for the offset is that the feedback cotroller is correctig the iputs based o the headig agle ad headig agle rate. Therefore if a chage i coditio happes e.g. losig frictio o the road, the cotroller is ot able of takig the vehicle to the right positio. Furthermore it ca be stated that the more precise the vehicle follows the path i short preview times or higher speeds the more fial overshoot will be expected. 5 Truck Path Logitudial Distace X [m] 8 Yaw agle Logitudial Distace X [m] Obstacle Preview Referece Actual-No iitial diff brakig Actual-Iitial diff brakig Cotroller Active Figure 5.2 Path ad headig agle profile for the cases with ad without the tur i brakig respectively. CHALMERS, Applied Mechaics, Master s Thesis

52 Tire Capacity [ % ] Tire Capacity [ % ] Brakig stability cotrol I order to compesate the fial positio offset, caused by Tur i brakig, the fial differetial brakig (brake stability cotrol) is implemeted as the feedback cotrol operatig o the positio error for compesatig ay kid of iaccuracy i estimatig the frictio or eve the chage i maoeuvre coditio. This method is applied to the previous case with the offset to ivestigate the performace of the system. Note that the brakig stability actuator cofiguratio is combied with the pure steerig cofiguratio for this simulatio. The results are as follow: Lateral forces o wheel i,j; i=axle umber j=side First axle, Left First axle, Right Secod axle, Left Secod axle, Right Third axle, Left Third axle, Right Lateral forces o wheel i,j; i=axle umber j=side First axle, Left First axle, Right Secod axle, Left Secod axle, Right Third axle, Left Third axle, Right Logitudial Distace X [m] Logitudial Distace X [m] Figure 5.21 Tire force capacity with tur i brakig. Figure 5.22 Tire force capacity with tur i brakig ad brake stability cotrol. CHALMERS, Applied Mechaics, Master s Thesis

53 Yaw agle [deg] Lateral Distace Y [m] 5 Truck Path Logitudial Distace X [m] 8 Yaw agle Logitudial Distace X [m] Obstacle Preview Referece Actual-No Feedback diff brakig Actual-Feedback diff brakig Cotroller Active Figure 5.23 Path ad headig agle profile for the cases with ad without the brake stability cotrol respectively. The advatage with this method is that the steerig wheel oscillatio at the ed of the maoeuvre will be decreased. This ca be couted as a big improvemet for driver iteractio poit of view. Therefore as the fial cofiguratio for differetial brakig applicatio, the differetial brakig is used at begiig of the maoeuvre as the feed-forward iput ad at the ed of maoeuvre as the feedback for compesatig the offset. The rest of the maoeuvre is left for the steerig actuator. It should be also stated here that a very light brakig before the maoeuvre starts should be applied to the vehicle. There are differet advatages with this actio. o o o o o Gettig the proper iformatio about the frictio o the road Keepig the brakes as fast as possible i order to havig less delay while usig differetial brakig Makig the tire more laterally stiff ad therefore gettig a better steerig performace at the begiig of the maoeuvre Pre-tesioig the seat belt Warig the driver This part is ot cosidered i the simulatio. CHALMERS, Applied Mechaics, Master s Thesis 211 4

54 Required logitudial distace, a [m] 5.7 Path cotrol sesitivity study Figure 5.24 shows the required logitudial distace to perform a RECA maoeuvre with respect to the iitial logitudial velocity. Comparig these results with Figure 5.1, it is observed that the itersectio poit betwee the brakig curve with a x = 6 m/s^2 ad the steerig curve with a y = 3.6 m/s^2 is moved to 87 km/h which meas that the steerig strategy becomes better tha brakig i eve higher velocities Steerig Fy/m = 3.6 m/s 2 Steerig Fy/m = 2 m/s 2 Brakig Fx/m = 7 m/s 2 Brakig Fx/m = 6 m/s Iitial logitudial velocity V x [kph] Figure 5.24 Required logitudial distace versus iitial logitudial velocity. 5.8 Compariso of optimal ad path stability cotrol Cosiderig the pure steerig actuator cofiguratio, results of optimal ad path cotrol are compared for two differet cases. It ca be observed i the Figure 5.25, that the optimal results are better tha the path cotrol as it is expected. However this differece is larger tha expected. The reaso for this is the additioal costraits o the path cotrol decisio algorithm such as steerig agle rate that makes the path cotroller results worse tha the optimal cotrol. Moreover after 14 meter of logitudial displacemet, the path stability cotrol simulatio logitudial distace does ot decrease by the velocity. The reaso for this behaviour is the costraits o steerig agle ad steerig agle rate i path stability cotrol decisio algorithm which does ot allow less logitudial distace. Note that the delay o the force geeratio is set to zero for both optimal ad path stability cotrol simulatio. CHALMERS, Applied Mechaics, Master s Thesis

55 Required logitudial Distace,a [m] Required logitudial distace,a [m] Fy/m = 2 m/s 2 optimal cotrol results Fy/m = 3.6 m/s 2 optimal cotrol results Fy/m = 2 m/s 2 path cotrol results Fy/m = 3.6 m/s 2 path cotrol results Iitial logitudial velocity V x [kph] Figure 5.25 Required logitudial distace versus iitial logitudial velocity for steerig actuator cofiguratio. Cosiderig the pure brakig actuator cofiguratio, results of optimal ad path cotrol are compared for two differet cases. Figure 5.25 shows that the optimal cotrol results are better tha the path stability cotrol simulatio results. The differece is a bit larger tha expected ad this differece is due to the brakig force distributio o the axles. It worth to metio that for makig a logical compariso the delays o force geeratio is set to zero i both optimal cotrol ad path stability cotrol simulatio Brakig Fx/m = 6 m/s 2 optimal cotrol results Brakig Fx/m = 7 m/s 2 optimal cotrol results Brakig Fx/m = 6 m/s 2 path cotrol results Brakig Fx/m = 7 m/s 2 path cotrol results Iitial logitudial velocity, V x [kph] Figure 5.26 Required logitudial distace versus iitial logitudial velocity for brakig actuator cofiguratio. CHALMERS, Applied Mechaics, Master s Thesis

56 6 Ru-off-road prevetio (RORP) 6.1 Path cotrol simulatio RORP maoeuvre o straight road Ru-off prevetio sceario is simulated i two differet cofiguratios. First cofiguratio deals with Ru-off prevetio o a straight road. Secod case studies the same sceario where a curved road is cosidered with a large radius. The differece i these two cases is that i the first case there is a false actio by the driver due to the drowsiess for istace while i secod case, lack of actio from driver is detected. Therefore the job of cotroller i first case is to correct the driver ad take the vehicle back to road, while i secod case the cotroller tries to compesate the absece of driver s actio. I this sceario the vehicle is movig logitudially with the speed of 65 km/h. Driver applies a small steerig agle. Whe the vehicle reaches oe of the headig agle or lateral displacemet limit, the cotroller goes active ad takes the vehicle back to the road. The Driver iput is modelled by a feed forward steerig iput to the vehicle. The feasible logitudial distace is the result of path plaig which satisfies the costraits o decisio algorithm. The limitatio o headig agle ad lateral displacemet is as follow. ψ max = 5 deg y max = 2 cm Figure 6.1 shows a schematic sketch of the simulatio maoeuvre setup. Log distace Figure 6.1 RORP simulatio maeuver setup CHALMERS, Applied Mechaics, Master s Thesis

57 Table 6.1 shows the parameters for settig up the simulatio as well as the costraits which are active i decisio algorithm. Parameters Values Iput Values: Frictio, µ.7 HV iitial velocity, V 65 km/h Logitudial distace, a 16 m (from path plaig) Preview time, t p.4 s Target values: Maximum lateral acceleratio, a y 3.6 m/s^2 Maximum had wheel Agle, δ 6 deg Maximum had wheel agle rate, ω 5 deg/s Maximum torque o the wheel, T 115 Nm Table 6.1 RORP maeuver parameter settig. CHALMERS, Applied Mechaics, Master s Thesis

58 i [m/s 3 ] d/dt [deg/s] a y [m/s 2 ] /dt [deg] Lateral distace Y [m] 6.2 Path cotrol results for RORP o straight road The results of the path stability cotrol are divided ito two parts. First the path plaig results will be show ad later the path stability cotrol simulatio results will be illustrated. Note that oly the steerig cotrol is used i this simulatio. The simulatio is doe o high μ surface Path plaig Followig plots show the path plaig outputs which are cofirmed by the decisio algorithm. As it ca be observed, first part of the path is give by a feed forward steerig agle which is ot iside the cotroller active zoe. Whe the vehicle reaches the limitatio of either lateral displacemet or headig agle, the cotroller becomes active. For cotroller active zoe the logitudial distace is icreased i steps to meet the costraits at the decisio algorithm Referece path optimizatio procedure Logitudial distace X [m] 4 Lateral acceleratio 1 Steerig wheel agle Logitudial distace X [m] Lateral jerk Logitudial Distace X [m] Steerig wheel agle rate Logitudial distace X [m] Logitudial Distace X [m] Figure 6.2 Path plaig results for RORP sceario. CHALMERS, Applied Mechaics, Master s Thesis

59 d/dt[deg/s] a y [m/s 2 ] Yaw agle [deg] Lateral Distace Y [m] Simulatio results 2 Truck Path Logitudial Distace X [m] 3 Yaw agle Logitudial Distace X [m] Truck right frot corer Truck right rear corer Obstacle Preview Referece Actual Cotroller Active Figure 6.3 Path stability cotrol results for RORP sceario- positio ad headig agle As it is observed i plots, i absece of the cotroller the vehicle will follow the dashed red lie 4 Lateral acceleratio 2 Steerig Wheel agle [deg] Logitudial Distace X [m] Lateral Jerk Logitudial Distace X [m] Wheel Steerig agle rate i [m/s 3 ] Logitudial Distace X [m] Logitudial Distace X [m] Figure 6.4 Path stability cotrol results for RORP sceario-steerig wheel agle ad their time drivitives CHALMERS, Applied Mechaics, Master s Thesis

60 dt/dx [Nm/s] Tire Capacity [ % ] T [Nm] Couter steerig which is doe by the feedback cotroller is observed. Couter steerig is very small here due to small gais o the feedback cotrol. High peaks of steerig agle rate ad also the lateral jerk ad torque will be filtered if applied to a actuator. Therefore the eed of filterig them i the simulatio was ot observed. Tire forces o wheel i,j; i=axle umber j=side First axle, Left First axle, Right Secod axle, Left Secod axle, Right Third axle, Left -1 Third axle, Right Logitudial Distace X [m].5 Torque o the wheel 1 x 14 Torque rate o the wheel Logitudial Distace X [m] Logitudial Distace X [m] Figure 6.5 Path stability cotrol results for RORP sceario tire capacity ad the torque profile Similar to previous sceario, the tire capacity is ot used a lot i this case. The same reaso ca be motivated here as well. By icreasig the gais o the feedback cotrol, more of tire capacity will be used by pealizig the stability. Table 6.2 shows the results of the simulatio for some parameters of iterest. Maximum value for each parameter, the positio of the maximum value as well as the target value ad the value of the parameter at the obstacle is metioed bellow. The high values of steerig agle rate ad wheel torque rate will ot be this high i implemetatio sice they will be filtered by actuator dyamics. Table 6.2 RORP path cotrol simulatio result CHALMERS, Applied Mechaics, Master s Thesis

61 6.3 Path cotrol simulatio RORP maoeuvre o curved road I this simulatio maoeuvre cofiguratio the driver is drivig with the velocity of 65 km/h o a curved road with a high radius. O the curve the driver stops steerig which is eeded to stay o the road. The cotroller becomes active ad takes the vehicle back to the road whe either headig agle or lateral displacemet limitatio is reached by the vehicle. The limitatio o headig agle ad lateral displacemet is as follow. ψ max = 5 deg y max = 1 cm Figure 6.6 shows a schematic sketch of the simulatio maoeuvre setup. Log distace Figure 6.6 RORP simulatio setup CHALMERS, Applied Mechaics, Master s Thesis

62 Table 6.3 shows the parameters for settig up the simulatio as well as the costraits which are active i decisio algorithm. Parameters Values Iput Values: Frictio, µ.7 HV iitial velocity, V 8 km/h Logitudial distace, a 32 m (from path plaig) Preview distace t p 18 m Target values: Maximum lateral acceleratio, a y 3.6 m/s^2 Maximum had wheel Agle, δ 6 deg Maximum had wheel agle velocity ω 5 deg/s Maximum torque o the wheel T 115 Nm Table 6.3 RORP maeuver parameter settig. CHALMERS, Applied Mechaics, Master s Thesis

63 i [m/s 3 ] d/dt [deg/s] Lateral distace Y [m] 6.1 Path cotrol results for RORP o curved road The results of the path stability cotrol are divided ito two parts. First the path plaig results will be show ad later the path stability cotrol simulatio results will be illustrated. Note that oly the steerig cotrol is used i this simulatio. The simulatio is doe o high μ surface Path plaig Followig plots show the path plaig outputs which are cofirmed by the decisio algorithm. Whe the vehicle reaches the limitatio of either lateral displacemet or headig agle, the cotroller becomes active. For cotroller active zoe the logitudial distace is icreased i steps to meet the costraits at the decisio algorithm. Note that oly the steerig cotrol is used i this simulatio. The simulatio is doe o high μ surface. 4 Referece path optimizatio procedure Logitudial distace X [m] 4 Lateral acceleratio 8 Steerig wheel agle a y [m/s 2 ] Logitudial distace X [m] Lateral jerk 2 [deg] Logitudial Distace X [m] Steerig wheel agle rate Logitudial distace X [m] Logitudial Distace X [m] Figure 6.7 Path plaig results for RORP sceario CHALMERS, Applied Mechaics, Master s Thesis 211 5

64 Lateral Distace Y [m] Yaw agle [deg] Lateral Distace Y [m] Simulatio results 2 Truck Path Logitudial Distace X [m] 3 Yaw agle Logitudial Distace X [m] Obstacle Preview Referece Actual Truck Path Road lie Preview Referece Actual Logitudial Distace X [m] Figure 6.8 Path cotrol results for RORP sceario- positio ad headig agle CHALMERS, Applied Mechaics, Master s Thesis

65 d/dt[deg/s] a y [m/s 2 ] It is visible i the plots that similar to previous results, the cotroller makes the vehicle to cut the corers therefore less lateral acceleratio comparig to path plaig results will be obtaied. The reaso for discotiuity i jerk ad steerig wheel agle profile is the problem i cotrollig the fifth order polyomial sice oly the iitial ad fial coditio ca be cotrolled while the curvature itself will ot be i cotrol. Therefore the fial coditio of the polyomial is chaged slightly which is ot exactly the iitial coditio for the circle as the ext segmet. 4 Lateral acceleratio 2 Steerig Wheel agle Logitudial Distace X [m] Lateral Jerk 1 [deg] Logitudial Distace X [m] Wheel Steerig agle rate 1 i [m/s 3 ] Logitudial Distace X [m] Logitudial Distace X [m] Figure 6.9 Path cotrol results for RORP sceario-steerig wheel agle ad their time drivitives. This cotributes to a discotiuity at the ed of polyomial curve. I order to solve this problem, a path made of smaller segmets with lower order curves is recommeded. Couter steerig is observed i the plots similar to previous results. The poit metioed about the peak of steerig agle rate as well as the lateral jerk ad torque profile also holds i this case CHALMERS, Applied Mechaics, Master s Thesis

66 dt/dx [Nm/s] Tire Capacity [ % ] T [Nm] Tire forces o wheel i,j; i=axle umber j=side First axle, Left First axle, Right Secod axle, Left Secod axle, Right Third axle, Left Third axle, Right Torque o the wheel Logitudial Distace X [m] 1 x 14 Torque rate o the wheel Logitudial Distace X [m] Logitudial Distace X [m] Figure 6.1 Path cotrol results for RORP sceario tire capacity ad the torque profile. Table 6.4 RORP path cotrol simulatio results. Table 6.4 shows the results of the simulatio for some parameters of iterest. Maximum value for each parameter, the positio of the maximum value as well as the target value ad the value of the parameter at the obstacle is metioed bellow. The high values of steerig agle rate ad wheel torque rate will ot be this high i implemetatio sice they will be filtered by actuator dyamics. CHALMERS, Applied Mechaics, Master s Thesis