DRIVER BEHAVIOR MODELING USING HYBRID DYNAMIC SYSTEMS FOR DRIVER-AWARE ACTIVE VEHICLE SAFETY

DRIVER BEHAVIOR MODELING USING HYBRID DYNAMIC SYSTEMS FOR DRIVER-AWARE ACTIVE VEHICLE SAFETY Pin Boyz, Amdeep Sthynyn, John H.L. Hnsen Eik Jonsson School o Engineeing nd Compute Science Univesity o Texs t Dlls Richdson, TX, USA ABSTRACT Moden sety systems e tnsoming vehicles om humn-contolled pssive devices into humn-centic intelligent/ ctive systems. Thee is wide nge o systems om ully utonomous vehicles to humnugmented contol devices which hve emeged in this ield. In cuent tends, co-opetive ctive systems hve the dive in the decision nd contol pocesses e voed o thei humn-centic ppoch. Howeve, these systems pose chllenge in the design pocess since obtining elible humn behvio models e diicult due to the complex ntue o diving tsk in dynmic tic envionment. Fom contol theoy pespective, diving cn be seen s combintion o continuous contol segments combined with discete decision pocess. In this study, we will model dive behvio utilizing Hybid Dynmic Systems (HDS) combining stochstic modeling tools (such s Hidden Mkov Models) with contol theoetic models. A subset o CAN-Bus nd video chnnels om demogphiclly blnced UTDive Copus contining video ( chnnels: dive nd od scene), udio, nd CAN-Bus signls o elistic diving sessions o 77 dives e used to veiy HDS models o ltel nd longitudinl contol behviou. The model is used to suggest dive-we ctive sety system cpble o ssisting the dive in sevel ltel contol tsks; lnekeeping, cuve-negotition nd lne chnging. INTRODUCTION Undestnding, nlyzing nd modeling humn dive behviou in elistic wy is extemely impotnt in enhncing the sety o the vehicles. In study suppoted by NHTSA, it ws ound tht dive eo ws the mjo contibuto in moe thn 9% o the cshes exmined []. Coopetive dive ssisting systems (DAS) o humn-centic ctive vehicle sety (AVS) pesents n oppotunity to pevent/void some o these ccidents. These pomising technologies cn be elized with n ssocited cost in esech nd implementtion tils. The diiculty ises becuse o the co-opetion equiement with humn nd the humn diving behvio is pooly undestood subject. The dynmics o diving come om thee souces: dive, vehicle nd the envionment. Although, sevel systems exist to impove the vehicle dynmics nd hndling, the dive behviou nd the ole o the envionment emined the ovelooked components o the sety poblem until now. The vehicle component ws the ist one to be exmined nd impoved thnks to pecise non-line, continuous vehicle models nd numeicl simultions. The uncetin, non-sttiony, highly dynmic, stochstic o discete event-diven chcteistics o diving comes minly om humn dive nd tic context imposing on the dive to ect in cetin wy. These chcteistics o diving e moe diicult to model, undestnd nd contol nd they concel the undelying cuse o most o the ccidents. Theeoe, utue ctive sety systems need to tke dive behviou nd tic context into ccount o eicient ccident voidnce/ pevention. In othe wods, AVS o DAS should be divewe nd context-we. The context weness cn be chieved by monitoing nd nlyzing the mico-tic envionment ound the host-vehicle. The sub-systems o such system my include compute vision system o lne mk, vehicle nd pedestin detection nd tcking togethe with od sign ecognition. In ecent yes, such systems e designed nd epoted with get pospects o being beneicil [, 3]. Fo n exmple in context-we systems, one cn ee to [4]. In this ppe, the ocus is dive-weness to be ble to design humn- Boyz

centic AVS nd dptive DAS with pticul inteest in ltel contol. The ppe is ognized in the ollowing wy. Fist, citicl suvey o dive behviou modeling ppoches is given identiying the need o hybid elistic model speciiclly designed o the use o DAS o AVS development. In this section, lso the dive models e ctegoized to give moe insight into the poblem o which model is moe ppopite o wht type o pplictions. Next the min me o the poposed dive model is pesented togethe with the theoeticl methods nd implictions om humn ctos engineeing studies. It is extemely impotnt tht the model delives both theoeticl mewok which is mthemticlly tctble nd n explntion o physicl nd cognitive pocesses involved in contol sttegy o humn dive. The poposed model is divided into ltel nd longitudinl pts; howeve, these two models e coupled nd the ull model is given next. Ate constuction o the theoeticl mewok suppoted with expeimentl obsevtions om pevious studies the model is vlidted using diving dt which is collected in el tic envionment. Finlly, the dvntges nd limittions o the poposed model e pesented in the conclusion section. Citicl Suvey o Dive Modeling Appoches Dive models e needed o dieent puposes om ssessing vehicle dynmics to monitoing dive sttus o just simply to bette undestnd the undelying dynmics in dive behviou. In ddition to sevel types o need o dive models, ech elted esech ield emphsizes dieent spect o the dive (i.e. cognition, peception, pocessing ection, contol). Dive modeling ppoches cn be oughly divided into ollowing goups: humn ctos, contol theoetic, stochstic/ non-line nd hybid models. A schemtic o dive modeling ppoches is given in Fig.. It is noticeble tht especilly ltel contol hs been modeled by contol theoetic ppoch due to its continuous chcteistics. An exmple o this type o dive model cn be ound in [5] employing contol theoetic ppoches o ltel contol behviou. This model includes dive s delys, eedbck in om o ltel position eo, nd neuo-muscul esponse tken om n elie wok on light-pilot modeling studies [6]. Figue. A schemtic gouping o dive modeling ppoches Othe noticeble nd widely known contol theoetic models o ltel contol cn be listed s McRue s model [7] contining nticiptoy, compenstoy nd pecognitive contol o bette epesenttion, nd McAdm s optiml peview contol model [8]. The common popety o these models is tht ll o them gee with coss-ove model [9] which cn explin single loop mnul tsks peomed by humns. The dvntge o contol theoetic models is tht they give physicl/cusl eltionship between the input nd output vibles. In this spect, the contol theoetic models my give insight into dive behviou. Although some o them ignoe the nonlineity, they povide sound mthemticl mewok in nlyzing dive behviou in contol level. Howeve useul they my be, it should be noted though tht most o the contol theoetic models e designed to be used in impoving vehicle dynmics nd hndling qulity, but not o explining dive behviou o design o co-opetive systems. These dive models hve low idelity in epoducing dive contol commnds tht hve simil chcteistics to el dive in time-domin. The min eson o this inidelity is tht these models e designed o tcking the cente o the lne o od-medin lmost peectly, whees el dive would devite om the medin moe s demonstted by []. The humn dive llows the ltel position eo to build up until it eches theshold tht dive peceives it s devition nd mkes coection. This is known s Boyz

complcency, nd it is lso elted to the ct tht most o the sensoy input tht dive uses is not instnt mesuement o the ltel position but visul cues nd vestibul eedbck. In ode to peceive nd pocess this eedbck tkes time nd it is not instntly used by the dive but delyed. A simil behviou is obseved lso in longitudinl contol while collowing nd ws tken into ccount in Lubshewsky s tionl dive model []. Since the existing contol theoetic models cnnot ccount o complcency, [] used dive simulto dt to identiy ltel contol model o the dive using system identiiction tools nd ARX models. In [] dive steeing model ws identiied with pticul inteest in stuctued nd unstuctued model uncetinty. Thei wok is impotnt s they imply tht the stuctued uncetinty cn be used to monito dive nd use dptive contol mewok to ddess the isk om dive peomnce deteiotion whees the unstuctued cetinty coming om unmodelled nonlineity cn be ddessed by obust contol. The non-sttiony, uncetin nd non-line ntue o dive behviou ws undestood by othe eseches too. In [3] cscded Neul Netwoks (NN) e used with some lexibility employing Extended Klmn Filtes (EKF) o updte nd vible ctivtion in newly dded neuon lyes. HMM is used to mesue the stochstic simility [4] between the model output nd el dive dt. This mesue is epoted to be bette thn men sque eo since the ntue o diving is stochstic nd we should be looking o min tends in the dt not the exct mtch in numeicl sense. In ct, Mkov Chins wee used to sequence bnk o Klmn Filtes o pedicting dive ctions using peptoy input ctions [5]. Hidden Mkov Models (HMM) wee used to len humn ction nd tnse humn skills o tele-obotics pplictions [6]. HMMs hs lte poved to be vey convenient tool in modeling diving contol inputs o obseved vehicle dynmics nd it is widely used to model dive behviou in sevel mewoks. In [7] HMM mewok is used to ecognize dieent dive mneuves nd [8] used simil mewok o top to bottom ppoch in sech o divemes, the meningul smllest unit o diving signls. In ou pevious studies, HMMs wee used to ecognize mneuves nd detect the dive distction o dive ults using hiechicl ppoch [9, ]. Although HMMs e vey poweul nd cn epoduce the dive behviou with high stochstic idelity, we lck the cpbility o explining the physicl/cusl mening o the esulting models. In ddition to mthemticl ppoches lge goup o dive models e deived in humn cto engineeing. These models conside cognitive, peceptul, nd neuo-muscul limittions o humn. These models povide vey impotnt insight into dive behviou especilly explining some o the uncetinty, dely nd non-line chcteistics. In ddition to this, the contol theoetic nd stochstic models tend to use mesued (i.e. obsevble) dt nd they oten sty in the contol level modeling. The tcticl nd sttegic levels in Michon s hiechicl model [] cnnot be modeled with contol theoetic o stochstic ppoches. [] poposed ACT-R cognitive model o the dive modeling the inomtion pocessing nd inheent delys o the humn cognitive system. As it cn be seen, the models deived om humn cto engineeing e vey useul; howeve, they do not epesent ull dive model. Theeoe, combined model stuctues including contol spects, stochstic pocesses nd cognitive cpbilities e poposed. These models cn be descibed s hybid models. This ppoch is eltively new nd vey pomising o obtining compehensive models. Fo exmple, [3] descibed humn peception pocess by discete event technique the execution pt is modeled by genel pedictive contolles nd the velocity contol is epesented by inite stte mchine to evel its discontinuous contol dynmics. In [4], eseches used contolle switching model o modeling collision voidnce mneuve employing piecewise polynomils. Futhemoe [5] used simil ppoch o modeling vehicle ollowing tsk dividing the c ollowing contol into ou dieent modes. Anothe model using switching contol is used by [6] employing simple contol lws nd deining the switching ule by knowledge bse. In this ppe, hybid dive model combining stochstic, contol theoetic nd humn cto ppoches is poposed. The min im is to obtin compehensive dive model including ll vilble knowledge nd stte-o-t methods in dive modeling o development o humn-centic ctive sety. Poposed Dive Model The poposed dive model includes stochstic longitudinl velocity contol model coupled with elistic contol theoetic ltel model bsed on [5]. Although the ltel model is bsed on limited Boyz 3

contol theoetic model the complcency phenomen is epesented by delying the position eedbck to epesent the humn limittion. The vehicle model used in Hess model is updted by the velocity supplied by longitudinl model theeoe coupling the contol sttegies. This ppoch is moe elistic thn ssuming the vehicle longitudinl velocity constnt in the ltel model. The min im o the model is to obtin dive-dptble (tunble) nd elistic ltel contol model coupled with longitudinl dynmics to use in DAS nd AVS development. In next sections longitudinl, ltel contol sttegies e given nd inlly the ull dive model is explined. constnt, incesing nd decesing. The tnsitions between ny o the two the sttes out o thee e possible nd dynmic vible indicted s d cn be etieved s the model stys t one stte in cetin time. These witing times cn ccount o cetin contol sttegy in speed contol dopted nd the stte tnsition pobbilities give insight into how sevel contol sttegies e switched to obtin plusible speed contol. The emission output o ech stte is epesented by continuous unction to model the speed poile with pmetes o line. Longitudinl Contol Sttegy Longitudinl contol sttegy o dive is inheently discontinuous since the contol is chieved by chnging between gs nd bke t discete times. In ddition to this, the undelying contol ule cnnot be esily eveled without including the mico-tic context (i.e. c ollowing, congestion o ee diving). Fo this eson stochstic modeling ppoch such s HMM cn help us len the velocity contol o dive om obsevtions. HMM is ntully suitble tool to model dive behvio o the ollowing esons: HMMs cn model the stochstic ntue o the diving behvio, poviding suicient sttisticl smoothing while oeing eective tempol modeling, The vitions in the diving signls coss the dives cn be modeled (dive identiiction) o suppessed (dive-independent oute models) ccoding to the equiements o the desied tsk. HMMs cn be chcteised by: () A set o distinct sttes S={S i } with q t denoting stte t time t, with numbe N () The initil stte distibution П={ П i } (3) The stte tnsition pobbility distibution A={ ij } (4) Ech stte cn poduce one o M distinct obsevtion symbols om the set V={V i } (5)The obsevtion pobbility distibution unction in stte j, B j Theeoe, HMMs cn be witten in the om o vecto λ={n,m,a,b, Π}. Fo uthe inomtion, edes should ee to [7]. In modelling velocity contol behviou o humn dive by HMM we used topology seen in Figue. This model epesents thee sttes in velocity contol: Figue. HMM topology o velocity contol Ltel Contol Sttegy The ltel contol sttegy o dive is modeled using modiied contol theoetic model bsed on Hess s wok [5]. Two impovements to this model e: () intoduction o ded zone which iltes out the ltel position eos below cetin theshold bnd ccounting o complcency o dives () eplcement o the constnt velocity LTI model o ltel vehicle dynmics model with LTV model updting the speed nd eclculting the model with the inputs om longitudinl velocity model. The modiied ltel dive model nd complcency tem is shown in Figue 3. Some o the constnts seen in the block digm o ltel dive model e tken om [5], howeve, the tuning pmetes o ω c (coss ove equency) nd time constnts T, T nd T 3 e exploed in nge to bette it the model to el dive steeing signls. In ddition to this, the complcency tem ded-zone bnd chnges om one dive to nothe. Some dives e moe sensitive nd coect the eos moe oten while othes let the Boyz 4

ltel position eo to ccumulte. This bnd cn be elted to expeience nd one s conidence in thei diving skills. Figue 3. Dive model o ltel contol The vehicle model used is known s bicycle model [8] o clculting the ltel dynmics o the vehicle nd lineized t constnt longitudinl velocity. In ode to obtin moe elistic behviou om this model, it is updted by chnging longitudinl velocity t discete time steps. Theeoe the esulting vehicle model is hybid system contining set o line-continuous time, timeinvint models o vehicle switched by discete updte diven by longitudinl speed chnges. As consequence the esultnt model is non-line nd close to elistic vehicle esponse. The model inputs e steeing wheel ngle, longitudinl vehicle velocity nd outputs e ltel cceletion nd side slip ngle. The ltel cceletion output o this model is used to clculte the ltel speed nd inlly ltel position o the vehicle employing numeicl integtion by tpezoids. The vibles o model e given in Tble. Tble. Vibles o vehicle model Symbol c o c J m U y c τ α o α β ρ e ψ ψ d ω Mening coneing stiness coeicients o ont nd bck tie Yw moment o ineti bout z-xis pssing t CG Mss o the vehicle Yw te o vehicle t CG Vehicle speed t CG Ltel oset o devition t CG Wheel steeing ngle o the ont tye Slip ngle o ont o e tye Vehicle side slip ngle t CG Reeence od cuvtue Yw/ heding ngle Desied yw ngle Angul equency o the vehicle The equtions o motion using the vibles given in Tble e pesented in equtions (-).. β = β. b b Whee, in omt x = Ax Bu,.. x = β, A =, b, B = u = τ b And in the output omt, y = Cx Du s c β = Whee, y = τ c β τ d c c s, β C = () d nd D =. The elements o the mtices e given explicitly hee: = ( C C ) mu, / = [( h C h C ) / mu = ( h C h C ) J, = ( h C h ) JU / b = C / mu, b = h C / J c = [( C C ) / m] [ l ( h C c = [( h C ] / h C ) / mu ] l [( h C s s h C ) / J ] h C )/ JU ] d = [( C / m) l ( h C / )] () s J Boyz 5

Combined Full Dive Model As mentioned beoe, the ltel nd longitudinl models e coupled vi the updte o vehicle model using the velocity outputs o HMM model o dive velocity contol. HMM model uses - sec histoy o velocity om CAN-Bus to pedict the utue sequence. Theeoe the vehicle model in ltel dive model is updted beoe the dive input to this model eches o new clcultion o ltel position. The longitudinl nd ltel contol sttegies e closely elted in two-wy eltionship: () In highe speeds, the dive is expected to coect the steeing wheel with smlle mgnitudes. () In shp tuns, the dive might pee to educe the longitudinl speed nd duing the lne chnge towds ste lne the speed should be incesed to void inteeence with the upcoming tic. The combined model hs non-line nd stochstic popeties togethe nd ccounts o the complcency o humn dive. The next session epots on model veiiction using el CAN-Bus dt. Selected Model Veiiction Results In model veiiction, CAN-Bus dt is used to ssess the model in its idelity to epoduce steeing wheel ngle nd vehicle speed commnds. The model ws ble to epoduce the expected signls with some dwbcks nd dvntges: () The steeing wheel ngle contined high equency tem () The identiiction ok K nd T pmetes in ltel contol equie sevel itetions. Howeve, once it is set, these pmetes cn epesent dive chcteistics o sttus. The model is cpble o epoducing steeing wheel ngle commnds in lne keeping, cuve negotition nd lne chnge poiles. The ppliction o complcency zone in the model ws ound vey useul since it gives the sety mgin o the dive in the ltel contol tsk nd it is dive-speciic chcteistic. In ddition to this intenl dely due to pocessing nd the gin o eedbck om popioeceptive system e exploed. It ws obseved tht incesing the intenl dely om.5 (nominl) to -5 sec intevl epesenting dive distction cused the eo building in ltel position nd the vehicle dited. It ws lso obseved tht incesing the gin om popioeceptive eedbck educes the eos in ltel position tcking. This is lso obseved duing the expeiments; the novice dives elying on only visul eedbck hve lge eos while the expet dives depend on the eedbck om neuo-muscul system (i.e. thus thei gin is highe in tht component) nd hve less ltel positioning eos. The eect o vestibul/popioeceptive eedbck gin is epesented om vlidtion expeiments peomed in Simulink (Figue 4 nd 5). steeing ngle [d] ltel position [m].5.5 x -4 4 6 8 4 6 8 4 6 8 4 6 8 simultion time Figue 4. Dit in lne keeping tsk (mx m) with intenl dely o sec nd popioeceptive gin o. ltel position [m ] steeing ngle [d] x -4 - - 5 5 5..5..5 5 5 5 simulted time Figue 5. Dit in lne keeping tsk with n intenl dely o sec nd popioeceptive gin o. Boyz 6

CONCLUSIONS In this ppe, hybid model using stochstic model o velocity contol nd continuous contol theoetic model o ltel contol e combined. The ltel model is modiied in ode to epesent dive complcency. In ddition to tht intenl pocessing time is epesented by dely tem which cn ccount o distction since it blocks the pocessing souces o the dive. Finlly the impotnce o vestibul eedbck is shown by obseving the dit in using the eedbck om this system less (Fig..4) o moe (Fig.5). This type o chnge cn epesent the dieence between novice nd expet dive, since the expet dive would tust moe on muscle system/lened skills thn visul input. In summy, the poposed dive model cn ccount o humn deiciencies o bottlenecks in inomtion pocessing, complcency. Also, the model cn explin the eects o the distction in tcking tsk (i.e. lne keeping) nd the expeience level (i.e. chnging gins in dieent eedbck chnnels). Fo these esons, the model is vey convenient to be used in developing humn-centic lne ssistnce/ contol systems. In ou utue wok, the poposed model will be impoved nd sevel dive behviou, peomnce nd chcteistics will be linked nd dded using Hybid Dynmic Systems nd stochstic modeling tools. REFERENCES [] Hendicks, D.L. Fell, J.C., nd Feedmn, M., The eltive equency o unse diving cts in seious tic cshes, Repot no: DOT-HS-89-6, Jn. [] McCll, J.C., Tivedi, M.M., Video-Bsed Lne Estimtion nd Tcking o Dive Assistnce: Suvey, System nd Evlution, IEEE Tnsctions on Intelligent Tnspottion Systems, vol. 7, no., pp. -37, Mch 6. [3] Kim, Z., Robust Lne Detection nd Tcking in Chllnging Scenios,, IEEE Tnsctions on Intelligent Tnspottion Systems, vol. 9, no., pp. 6-6, Mch 8. [4] Rkotoniiny, A., Mie, F., Context-Awe Diving Behviou Model, In Poceeedings o the 9th Intentionl Technicl Coneence on the Enhnced Sety o Vehicles (ESV 9),5. [5] Hess, R.A., Modjthedzdeh, A Contol Theoetic Model o Dive Steeing Behvio, IEEE Contol Systems Mgzine,pp.3-8, 99. [6] Hess, R.A., A model bsed theoy o nlyzing humn contol behvio, in Advnces in Mn- Mchine System Resech, W.B.House (ed.), vol., London, JAI Pess, pp. 9-75, 985. [7]McRue, D., Wei, D., Theoy o mnul vehicul contol, Egonom., vol., pp.599-633, 969. [8] McAdm, C., Appliction o n optiml peview contol o simultion o closed-loop utomobile diving, IEEE Tns. Syst. Mn. Cybn., vol. SMC-, pp.393-399, Sept 98. [9] ] McRue, D.T., Kendel, E., Mthemticl models o humn pilot behvio, AGARDogph, No.88. Jn 974. [] Pilutti, T., Ulsoy, A.G., Identiiction o Dive Stte o Lne Keeping Tsks, IEEE Tns. on Syst., Mn, Cyben., Pt A: Syst. And Humns, vol.9, no.5, Sept 999. [] Lubshevsky, I., Wgne, P., Mhnke, R., Bounded tionl dive models, Euopen Physicl Jounl B, vol.3, p.43. [] Chen, L-K, Ulsoy, A.G., Identiiction o dive steeing model, nd model uncetinty om dive simulto dt, Jounl o Dynmic Systems, Meusement nd Contol,vol.3, pp. 63-69,. [3]Nechyb, M.C., Xu, Y., Humn Contol Sttegy: Abstction, Veiiction nd Repliction, IEEE Contol Systems Mg., pp. 48-6, Oct. 997. [4] Nechyb, M.C., Xu, Y., On Discontinuous Humn Contol Sttegies,In Poceedings IEEE Int. Coneence on Robotics nd Automtion, vol.3.,pp. 37-43, 998. [5] Petlnd, A., Liu, A., Modeling nd Pediction o Humn Behvio, Neul Computtion, vol.,pp.9-4, 999. [6] Yng, J., Xu, Y., Chen, C., Humn Action Lening vi Hidden Mkov Model, IEEE Tns. on Syst. Mn Cyben, Pt A: Syst. And Humns,vol.7, no., pp. 34-44, 997. [7] Mitovic, D., Relible Method o Events Recognition, IEEE Tns. on Intelligent Tnsp. Syst., vol. 6, no., pp. 98-5, June, 5. [8] K. Tokkol, S. Venktesn, H. Liu, Senso Sequence Modeling o Diving, FLAIRS Coneence, pp. 7-77, Clewte Bech, Floid, USA,, 5. [online souce: DBLP, http://dblp.unitie.de] Boyz 7

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