Low-Cost MEMS Sensors and Vision System for Motion and Position Estimation of a Scooter

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1 Sensors 203, 3, ; do:0.3390/s Arcle OPEN ACCESS sensors ISSN Low-Cos MEMS Sensors and Vson Sysem for Moon and Poson Esmaon of a Scooer Albero Guarner *, Francesco Pro and Anono Veore CIRGEO, Inerdeparmen Research Cener for Geomacs, Unversy of Padova, vale dell Unversà 6, Legnaro, Padova, Ialy; E-Mals: francesco.pro@unpd. (F.P.); anono.veore@unpd. (A.V.) * Auhor o whom correspondence should be addressed; E-Mal: albero.guarner@unpd.; Tel.: ; Fax: Receved: 7 December 202; n revsed form: 8 January 203 / Acceped: 2 January 203 / Publshed: 24 January 203 Absrac: The possbly o denfy wh sgnfcan accuracy he poson of a vehcle n a mappng reference frame for drvng drecons and bes-roue analyss s a opc whch s aracng a lo of neres from he research and developmen secor. To reach he objecve of accurae vehcle posonng and negrae response evens, s necessary o esmae poson, orenaon and velocy of he sysem wh hgh measuremen raes. In hs work we es a sysem whch uses low-cos sensors, based on Mcro Elecro-Mechancal Sysems (MEMS) echnology, coupled wh nformaon derved from a vdeo camera placed on a wo-wheel moor vehcle (scooer). In comparson o a four-wheel vehcle; he dynamcs of a wo-wheel vehcle feaure a hgher level of complexy gven ha more degrees of freedom mus be aken no accoun. For example a moorcycle can ws sdeways; hus generang a roll angle. A slgh pch angle has o be consdered as well; snce wheel suspensons have a hgher degree of moon compared o four-wheel moor vehcles. In hs paper we presen a mehod for he accurae reconsrucon of he rajecory of a Vespa scooer; whch can be used as alernave o he classcal approach based on GPS/INS sensor negraon. Poson and orenaon of he scooer are obaned by negrang MEMS-based orenaon sensor daa wh dgal mages hrough a cascade of a Kalman fler and a Bayesan parcle fler. Keywords: Bayesan parcle fler; Kalman fler; MEMS; Whppel model; moorcycle

2 Sensors 203, 3 5. Inroducon The developmen of elecronc sysems for deermnng he poson and orenaon of movng objecs n real-me has been a crcal research opc for he las decade. Applcaons vary n many felds and range from rgd frames aeral and land-based vehcles as well as dynamc and complex frames lke a human body [,2]. The objecve of measurng such parameers can also vary a lo; n remoe sensng s a crucal aspec for correc georeferencng of daa acqured from opcal sensors. Navgaon and road safey purposes have also become common applcaons. Two man resuls of he echnologcal progress n hs feld are represened by he Elecronc Sably Program (ESP), an evoluon of he An-Blockng Sysem (ABS), and saelle posonng of vehcles. In he auomove secor, due o lmed budges and szes, navgaon sensors rely on he negraon beween a low cos GPS recever and an Ineral Measuremen Un (IMU) based on Mcro Elecro-Mechancal Sysem (MEMS) echnology. Such negraon s commonly realzed hrough an exended Kalman fler [3 7], whch provdes opmal resuls for offses, drfs and scale facors of employed sensors. However he applcaon of hs fler o moorcycle dynamcs does no perform smlarly. Unlke cars, moorcycles are able o roae around her own longudnal axs (roll), bendng o he lef and he rgh, herefore he yaw angular velocy s no measured by jus one sensor, raher s he resul of he measuremens of all hree angular sensors, whch conrbue dfferenly n me accordng o he curren lng of he moorcycle. Consequenly, an error on he esmae of he roll angle a me wll affec he esmae of he pch and yaw angles a nex me + as well. In hs paper we consder he problem of deecng he poson and orenaon of a Vespa, a popular Ialan scooer brand, usng a low cos Posonng and Orenaon Sysem (POS) and mages acqured by an on-board dgal vdeo camera. The esmae of he parameers (poson n space and orenaon angles) of he dynamc model of he scooer s acheved by negrang n a Bayesan parcle fler he measuremens acqured wh a MEMS-based navgaon sensor and a double frequency GPS recever. In order o furher mprove he accuracy of orenaon daa, roll and pch angles provded by he MEMS sensor are pre-flered n a Kalman fler wh hose compued wh he applcaon of he cumulaed Hough ransform o he dgal mages capured by a vdeo-camera. In he nex secons, afer an overvew of he sysem componens, he mehod adoped for rajecory reconsrucon s descrbed n deal. Specfcally, n Secon 3 we presen he Whpple model [8,9], whch consues he mahemacal bass of he dynamc model of he moorcycle, and n Secon 4 we focus on he esmae of he roll angle from he mages recorded by he vdeo-camera usng he cumulaed Hough ransform [0 2]. Then n Secon 5 we dscuss he use of he Bayesan parcle fler o negrae MEMS sensor daa wh GPS measuremens. Resuls acheved wh he proposed mehod are repored n Secon 6, whle fnal conclusons are dscussed n Secon Sysem Componens The mehod for he moon esmaon of a moorcycle proposed n hs work has been esed on a Vespa, a common Ialan scooer, whch was equpped wh a se of navgaon sensors as shown n Fgure. The sysem consss of an XSens MT-G MEMS-based Ineral Measuremen Un (IMU) and a.3 Megapxel SONY Progressve Scan color CCD camera. The man echncal specfcaons of he

3 Sensors 203, 3 52 Xsens MT-G are summarzed n Table. Daa acquson and sensor synchronzaon were handled by a Noebook PC (Acer Travelmae) provded wh,024 MB of RAM and a CPU processng speed of.66 GHz. A Novael DL-4 double frequency GPS recever was also fxed on he scooer and used o collec daa for reference rajecory deermnaon. Fgure. Sde vew of he Vespa scooer showng he daa acquson sensors. The dgal vdeo camera was placed on he rgh boom sde of he moorcycle. Table. Man echncal specfcaons of Xsens MT-G. Sac accuracy (roll/pch) Sac accuracy (headng) Dynamc accuracy Angular resoluon Dynamc range: - Pch - Roll/Headng Accuracy poson (SPS) Maxmum updae rae: - Onboard processng - Exernal processng <0.5 deg < deg deg RMS 0.05 deg ±90 deg ±80 deg 2.5 m CEP 20 Hz 52 Hz Dmensons mm (W L H) Wegh 68 g Amben emperaure (operang range) C 3. The Whpple Model The Whpple model [8,9] consss n an nverse pendulum fxed n a frame movng along a lne wh he wheels whch are consdered o be dscs wh no wdh (Fgure 2). The vehcle s enre mass m s assumed o be concenraed a s mass cener, whch s locaed a hegh h above he ground and dsance b from he rear wheel, along he x axs. The parameer ψ represens he yaw angle, ϕ he roll angle, δ he seerng angle and w s he dsance beween he wo wheels. In hs model he moorcycle

4 Sensors 203, 3 53 moon s assumed o be consraned so ha no laeral moon of he res s allowed (non-holonomc consran). The mahemacal model does no ake no accoun he possble oscllaon of he scooer s wheel suspensons neher he movemen of a drver. The moon equaons are herefore descrbed by: x = vcosψ cosθ y = vsnψ cosθ () z = vsnθ where x, y and z represen he real-me vehcle posons n he spaal frame, v s he forward velocy, and θ s he pch angle (no shown n Fgure 2). From he geomery of he sysem he rae of change (.e., frs dervave) of he yaw angle s defned as follows: an δ v ψ = v = = σ v wcosϕ R (2) where σ s he nsananeous curvaure of he pah followed by he moorcycle n he xy plane and R s he nsananeous curvaure ray (σ = R ). Fgure 2. The nvered pendulum moorcycle model. Accordng o he nvered pendulum dynamcs; he roll angle sasfes he followng equaon: h = g + h v + b 2 ϕ sn ϕ ( σ sn ϕ ) σ ψ cosϕ (3) where g s he acceleraon due o gravy. The erm hσ snϕ can be rewren as a funcon of he seerng angle δ and he roll angle ϕ: h hσ snϕ = an δ anϕ w and gven ha angles δ and ϕ do no smulaneously assume hgh values, he erm hδ snϕ can be negleced. Therefore, akng no accoun also Equaon (2), Equaon (3) becomes: (4) h = g v + b v + v 2 ϕ sn ϕ σ ( σ σ ) cosϕ (5) Assumng ha we can measure he roll angle ϕ(), he pch angle θ() and he velocy v(), Equaon (5) could be used o esmae he curvaure σ. Indeed, by negrang Equaon (5) we can

5 Sensors 203, 3 54 compue he nsananeous curvaure σ(), provded ha an nal condon σ(0) s gven. Smlarly, knowng he profle σ, f we negrae he non-holonomc knemac model () from an nal poson [x(0), y(0), z(0)] he pah followed by he moorcycle can be fully reconsruced. In nex secons we wll dscuss how we esmae he parameers φ, θ and v, whose knowledge s crucal for he applcaon of he proposed mehod. 4. Roll and Pch Angle Esmaon Roll and pch angles can be esmaed by usng he frames recorded from he vdeocamera, whch s rgdly fxed o he moorcycle, and deecng he poson n he mage of he horzon lne esmang slope and dsance of hs lne from he mage orgn. Usng he perspecve projecon camera model, he horzon lne projeced ono he mage plane can be descrbed n erms of roll and pch angles as follows (see [0,] for deals): cosθ cosϕv snϕu = snθ cosϕ where (U,V) denoe he mage plane coordnaes of a pon P wh coordnaes [x,y,z] n he camera frame Σ c. Therefore, he pch and roll angles θ and ϕ can be deermned knowng he poson of he horzon lne n he mage. Despe he horzon canno be easly deermned due o occlusons frequenly occurrng n he scene, roll and pch raes can be robusly esmaed by comparng wo consecuve mages. Indeed, gven he horzon lne n he frame a me, I( ), n he nex frame a me +, I( +), he horzon s descrbed by he followng relaonshp: cos( θ +Δ θ)cos( ϕ +Δϕ) V sn( ϕ +Δ ϕ) U = sn( θ +Δ θ)cos( ϕ +Δϕ) Lnearzng Equaon (7) abou θ() and ϕ(), neglecng erms of order hgher han one n Δ and assumng small pch angles (θ 0), we oban: snϕ Δ ϕv + cosϕ Δ ϕu = Δθ cosϕ Equaon (8) shows ha n wo successve frames, he horzon roaes by Δϕ and ranslaes by Δθ cosϕ. These wo quanes (Δϕ, Δθ) can be measured by compung he Hough ransform on a regon of neres cenered around a neghborhood of he curren esmaon of he horzon lne. The Hough ransform [2] s a feaure exracon echnque used n mage analyss, compuer vson, and dgal mage processng, whose purpose s o fnd mperfec nsances of objecs whn a ceran class of shapes by a vong procedure. Ths vong procedure s carred ou n a parameer space, from whch objec canddaes are obaned as local maxma n a so-called accumulaor space ha s explcly consruced by he algorhm for compung he Hough ransform. In hs case hs ransform s used o deermne he horzon lne n he mages acqured by he scooer s on-board vdeocamera. To hs am polar coordnaes (ρ,α) are used as space parameers and are relaed o he mage coordnaes (U,V) as follows: (6) (7) (8) ρ = U cosα + V snα (9) An example of such mage space paramerzaon s shown n Fgure 3.

6 Sensors 203, 3 55 Fgure 3. The parameer space (ρ,α) of he Hough ransform adoped for lne deecon. Gven hs parameerzaon, pons n parameer space (ρ, α) correspond o lnes n he mage space, whle pons n he mage space correspond o snusods n parameer space, and vceversa (Fgure 4). The Hough ransform allows herefore o deermne a lne (e.g., he horzon) n he mage as nersecon, n parameer space, of snusods correspondng o a se of co-lnear mage pons. Such pons can be obaned by applyng an edge deecon algorhm. Fgure 4. Image pons mapped no he parameer space. The seps needed o compue he raes (Δϕ, Δθ) can be summarzed as follows:. Apply an edge deecon o a predefned regon of neres of he mage; 2. Perform a dscrezaon he parameer space (ρ, α) by subdvdng n a se of cells (bns); 3. Consderng ha each edge canddae s an nfne lne segmen of polar coordnaes (ρ, α), he number of edges fallng n each bn s couned; 4. Through hs accumulaon an hsogram of an mage n coordnaes (ρ, α) s generaed, whose nensy values are proporonal o he number of edges fallng n each bn. Ths hsogram represens he Hough ransform H(ρ, α) of he mage. From each hsogram he correspondng cumulaed Hough ransform s derved. Ths ransform s a modfcaon of he Hough ransform and s defned as follows: H E = ( α ) H ( ρ, α ) ρ E (0)

7 Sensors 203, 3 Equaon (0) holds for he roll angle (α = ϕ), whle for he pch angle (α = θ) becomes: H E ( ρ ρ = ) H E α ( ρ, α ) 56 () An example of he cumulaed Hough ransform s shown n Fgures 5 7. Fgure 5. (Lef): Image acqured from he on-board camera. (Rgh): edge deecon of he horzon lne. Fgure 6. (Lef): Hough ransform obaned from he (Rgh): correspondng cumulaed Hough ransform. se of edges n Fgure 5. Fgure 7. (Lef): Image acqured durng a drve es. (Rgh): Correspondng Hough ransform. I can be proved ha f he same edges are vsble a me and +Δ, ( and smlarly for he pch angle) holds ha: H ( ) E ( + Δ ) ϕ = H ( E ( ) ϕ +Δ ϕ()) ϕ [ 0,π ) hen for he roll angle (2) In presence of nose and consderng ha no all edges vsble a me reman vsble a me +Δ, a good esmaon of Δϕ(Δ) can be obaned mnmzng he Eucldean dsance beween each of he cumulaed ransforms a me and +Δ:

8 Sensors 203, 3 57 ( ) ( ) Δϕ( Δ ) = argmn H ρ, α Δα dρ H ρ, α dρ Δα +Δ Smlarly, he esmae of he ncremen of he roll angle θ s compued as follows: Δθ ( Δ ) = argmn H+Δ ( ρ ρ, α) dα H( ρ, α) dα cosϕ Δ Δρ (3) (4) Afer hese seps, he esmaes of he roll and pch angles are compued by me negraon of he raes Δϕ and Δθ. 5. The Bayesan Parcle Fler The key pon of all navgaon and rackng applcaons s he moon model o whch bayesan recursve flers (as he parcle fler [3]) can be appled. Models whch are lnear n he sae dynamcs and non-lnear n he measuremens can be descrbed as follows: x+ = Ax + Buu + B f f (5) y = h( x ) + e where x s he sae vecor a me, u he npu, f he error model, y he measuremens and e he measuremen error. In hs model, ndpenden dsrbuons are assumed for f, e and he nal sae x 0, wh known probably denses p e, p f and p x0, respecvely, bu no necessarly Gaussan. We denoe he se of avalable observaons a me as: {,..., } Y = y y 0 The Bayesan soluon o equaons (5) deals wh he compung of he a pror dsrbuon p(x + Y ), gven pas dsrbuon p(x Y ). In case he nose can be modeled by ndpenden, whe and gaussan wh zero mean probably densy funcons, and h(x ) s a lnear funcon, hen he opmal soluon s provded by he Kalman fler. Should be hs condon no sasfed, an approxmaon of he a pror dsrbuon p(x + Y ) can be sll provded usng a Bayesan parcle fler [3]. Ths fler s an erave process by whch a collecon of parcles, each one represenng a possble arge sae, approxmaes he a pror probably dsrbuon, whch descrbes he possble saes of he arge. Each parcle s assgned a wegh w, whose value wll ncrease as closer o rue value he relaed sample wll be. When a new observaon arrves, he parcles are me updaed o reflec he me of he observaon. Then, a lkelhood funcon s used o updaed he weghs of he parcles based on he new nformaon conaned n he observaon. Fnally, resamplng s performed o replace low wegh parcles wh randomly perurbed copes of hgh wegh parcles. A block dagram of he parcle fler s presened n Fgure 8. (6)

9 Sensors 203, 3 58 Fgure 8. Block dagram of he Bayesan parcle fler. Snce he compuaonal cos of a parcle fler s que hgh, only an adequae mnmum number of varables has been ncluded n he dynamc model of he scooer. I was herefore chosen o neglec any movemen along he z axs (e.g., bouncng of suspensons), and o accoun for poson varables x and y, speed v, he hree angles needed for modellng he orenaon (φ, θ, ψ) and he flered verson of he curvaure σ. In order o furher mprove he accuracy of orenaon daa, roll and pch angles provded by he MEMS sensor have been combned and pre-flered n a Kalman fler wh hose compued usng he cumulaed Hough ransform appled o he dgal mages capured by a vdeo-camera. Assumng ha he sysem s now represened as a collecon of N parcles, he dynamcs of he generc parcle s (.e., a possble sysem sae) s descrbed by he followng model: 2 x+ = x + v cos( ψ ) cos( θ ) Δ T + N(0, Δx ) 2 y+ = y + v sn( ψ )cos( θ ) Δ T + N(0, Δy ) 2 v+ = v + ( a gcos( θ ) Δ T + N(0, Δv ) 2 σ f v ϕ + = ( γ )( ϕ + r ϕ Δ ) + γ arcan T r g θ + = θ + θδt 2 ψ + = ψ + ψ Δ + (0, Δψ ) T N ψ σ f = ( γ ) σ + γ + s f s v wp ( p) w + = N j ( ) wp j = p (7) where: ΔT s he samplng nerval; N(0, x 2 ) represens he measuremen nose of he X coordnae, modeled as a Gaussan funcon wh a zero mean and sandard devaon x. Smlar assumpon holds for measuremen noses N(0, y 2 ), N(0, v 2 ) and N(0, ψ 2 ); s he weghed combnaon of he curvaure esmaed a prevous me ( ) and he curren σ f + ψ v npu, beng γ s he weghng erm (γ s = /0); σ f

10 Sensors 203, 3 59 w s wegh of he -h parcle; P ( s he mporance funcon,.e., he lkelhood funcon hrough whch he weghs are s) updaed accordng o he followng relaonshp: γ r s a coeffcen whch dynamcally changes n order o gve more wegh o mnmal curvaures and roll angular veloces as denoed by: w w P( y x ) = + ( )( ) γ σ σ ϕ ϕ σ < σ ϕ < m l f l f f ϕ l and l γ r = 0 oherwse (8) (9) where σ l and ϕ l are he hresholds for he maxmum curvaure and roll angular velocy respecvely. We se γ m = /500, σ l = /00 m and ϕ l = 30 /s. In he model Equaon (7) we used dfferen formulas for he dervaves of he orenaon angles ϕ, θ and. Ths s due o he fac ha he angular veloces (ω x, ω y, ω z ) measured by he MEMS ψ sensor are relaed o he body frame (.e., he coordnae sysem fxed wh he scooer) whle orenaon angles (φ, θ, ψ) are deermned n a world reference frame (e.g., he GPS coordnae sysem, WGS-84). A frame ransformaon from he body o he world frame s herefore needed, whch leads o dfferen equaons for he orenaon angles. The componens of he sae vecor a me are hen compued as weghed average of he varables esmaed by he fler, usng he weghs w of all parcles s : N T ( x y v ϕ θ ψ σ ) w ( x y v ϕ θ ψ σ f ) In order o lm he compuaonal effor of he fler, he updae of he parcle weghs w s no performed a every sep of he algorhm, bu raher when he GPS daa are avalable from he recever. 6. Resuls and Dscusson = = Three drve ess were carred ou on he same rack n order o evaluae he measuremen repeaably, whose resuls for he roll angle are shown n Fgure 9. A slgh dfference can be observed for es No. 3 where he speed was slower han for he oher wo ess. An example of he rack reconsruced from he daa receved durng one of he hree ess s shown n Fgure 0. Here he rajecory (doed lne) esmaed wh he Bayesan parcle fler s compared wh he reference rajecory derved from dfferenally correced GPS measuremens (sold lne). Beyond vbraons, offses and scale facors, furher neresng sources of error o be esed are wrong nal condons and noses of he roll and pch angles. Durng he es he roll angle was brough o more han 20 o evaluae he performance of he fler; no GPS updae was used by he Bayesan parcle fler o esmae he rajecory covered by he scooer. The algorhm was able o converge, albe slowly, owards he real angle. Some sascs hghlghng he resdual dsances beween he reference rajecory shown n Fgure 0 and ha esmaed wh he parcle fler are summarzed n Table 2. T (20)

11 Sensors 203, Fgure 9. Roll angle profles resulng from he performed ess. Fgure 0. The esmaed rajecory (doed lne) overmposed ono he GPS reference rack (sold lne). Table 2. Sascs of he resdual dsplacemens bw. he GPS reference rajecory and ha esmaed by he parcle fler shown n Fgure 0. Mnmum m Maxmum 0.6 Mean.033 Absolue mean 3.2 m Sandard devaon (operang range) m Developmens of he proposed mehod wll deal wh he encodng of he Bayesan fler nsde an negraed sysem whch can be used o equp he scooer. Ths can lead n he fuure o provde even moorcycles wh racon conrol sysems. Furher developmens wll be he ncluson n he dynamc model of he suspensons moon along he Z axs, and also he sudy of he nfluence of he seerng angle (δ) on he esmaon of he roll angle. These wo parameers are ndeed relaed by he followng relaonshp, whch can be easly derved from Equaon (2): anδ ϕ = arc cos Wσ (2)

12 Sensors 203, Conclusons In hs paper we have presened an alernave mehod for he reconsrucon of he rajecory of a moorcycle ( Vespa scooer) wh respec o he classcal approach based on GPS/INS sensor negraon. In our mplemenaon poson and orenaon of he scooer are obaned by negrang MEMS-based orenaon sensor daa wh dgal mages hrough a cascade of a Kalman fler and a Bayesan parcle fler. As shown, he proposed mehod provdes que accepable resuls hough s applcaon s affeced by envronmen condons. Indeed he roll angle esmaon based on he Hough ransform requres a mnmal amoun of lnear elemens n he scene, whose absence can degrade he resuls achevable for he roll angle. For example a complex skylne and low conras beween he road segmen and neghborng objec can be problemac, even f no common. References. Zeng, H.; Zhao, Y. Sensng Movemen: Mcrosensors for Body Moon Measuremen. Sensors 20,, Grard, G.; Côé, S.; Zlaanova, S.; Baree, Y.; S-Perre, J.; Van Ooserom, P. Indoor Pedesran Navgaon Usng Foo-Mouned IMU and Porable Ulrasound Range. Sensors 20,, Q, H.; Moore, J.B. Drec Kalman Flerng Approach for GPS/INS Inegraon. IEEE Trans. Aerosp. Elecron. Sys. 2002, 38, El-Shemy, N.; Schwarz, K. Inegrang Dfferenal GPS Recevers wh an INS and CCD Cameras for Moble GIS Daa Collecon. In Proceedngs of ISPRS Commsson II Symposum, Oawa, ON, Canada, Barbarella, M.; Gandolf, S.; Meffe, A.; Burch, A. A Tes Feld for Moble Mappng Sysem: Desgn, Se up and Frs Tes Resuls. In Proceedngs of 7h Inernaonal Symposyum on Moble Mappng Technology, Cracow, Poland, 3 6 June Pras, M.; Cna, A.; Lngua, A. Low Cos Moble Mappng Sysems: An Ialan Experence. In Proceedngs of IEEE/ION Poson Locaon and Navgaon Symposum, Monerey, CA, USA, 5 6 May De Agosno, M.; Lngua, A.; Marenchno, D.; Nex, F.; Pras, M. GIMPHI: A New Inegraon Approach for Early Impac Assessmen. Appl. Geomacs 20, 3, Whpple, F.J.W. The Sably of he Moon of a Bcycle. Quarerly J. Pure Appl. Mah. 899, 30, Lmebeer, D.J.N.; Sharp, R.S. Bcycles, Moorcycles and Models. IEEE Conrol Sys. Mag. 2006, 26, Frezza, R.; Veore, A. Moon Esmaon by Vson for Moble Mappng wh a Moorcycle. In Proceedngs of 3rd Inernaonal Symposum on Moble Mappng Technology, Caro, Egyp, 3 5 January Nor, F.; Frezza, R. Accurae Reconsrucon of he Pah Followed by a Moorcycle from on Board Camera Images. In IEEE Inellgen Vehcles Symposum, Columbus, OH, USA, 9 June, 2003.

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