Drive Remote Controlled Car using Computer Vision By: Andrei Aron Wei Wei

Transcription

1 rie Remoe Conroe Car using Compuer Vision By: Anrei Aron Wei Wei Absrac he probem of high spee remoe-conroe ehice conro oer an arbirary rajecory is an ineresing an chaenging one. Whie reguar PI conroers work o some exen, hey a hae faws associae o heir reacie naure. On he oher han, preicie echniques can be use o choose a ifferen conroer a each sep. LQR (Linear Quaraic Reguaor is such a echnique. I uses a simpe conroer in conjuncion wih a ehice ynamics moe in orer o simuae he sae of he car for N seps in he fuure. I hen goes back, opimizing he conroers a each sep, uni finay, i prouces a conroer for he curren sep. ince his is a preicie echnique, i usuay achiees beer performance han reguar PI conroers. Experimena eup We use an RC ehice in orer o impemen he conroer. he ony sensor we use is a ony EVI- pan/i coor camera. he reference rajecory is efine wih he hep of a whie ape rack on he ab foor. uring he firs offine phase we exrac a se of waypoins by using compuer ision echniques. uring he secon phase, he car is ocaize wih he hep of coor fiers, an he appropriae commans are sen back o he camera so i can accuraey foow he car a a imes. he car is hen sen conro inpu a ~Hz.. rajecory capure an represenaion For he purposes of he conroer an LQR opimizer, he rajecory nees o be efine by a se of cosey space consecuie waypoins. Howeer, he camera image conains ony a secion of a non-zero hickness whie ape oop. In orer o soe his incompaibiiy, we perform seera operaions. Firs, we use a uminosiy fier on each rack image, an obain a binary mask. We hen projec a se of such masks ha coer he whoe rack ono he foor pane by using reerse samping. Now, we hae a goba mask oer he foor pane ha represens he rack srip. We use he Run of Pixes agorihm o eec cusers an we fier heir conex coers sizes (he rack is usuay he arges cuser. Finay, we coner he rack ino a se of coorinaes. We o his by siing a square oer he whie srip an recoring is cener coorinaes as consecuie waypoins. he ineresing par is acuay moing he recange in such a way ha i wi foow he rajecory. We achiee his by aking he borers of he or 3 inersecions of he borers of he recange wih he rajecory an combining heir ceners o obain a new irecion.. racking We use wo coor paches on he fron an back of he car o eermine is posiion an orienaion a runime. We use simpe fiers on heir coors (re an bue in orer o iffereniae beween he wo.

2 .3 Camera posiion iscriminaion an pan/i error correcion In orer o projec he posiion of he car a any ime, in aiion o he posiion of he car wihin he camera image, we aso nee he curren pan an i anges. Howeer, he camera has a sma probem: whie i is moing, i repors sae pan/i anges. herefore, whie he camera is moing in orer o rack he ehice, he projece posiion seems o jump beween wo coorinaes. his is a grae probem for he conroer, because i inrouces a arge amoun of noise ino he eociy esimaion. We soe his probem by oing wo hings. Firsy, we iscreize he camera orienaion ino 6 quarans. he camera ony moes when he car is abou o exi he curren quaran. econy, we use a saic coor marker on he foor whose posiion we know in orer o correc he pan/i error as i occurs. hese echniques proie he necessary sensing infrasrucure in orer o impemen he conroer. 3 PI pee Conroer We chose o separae he seering an spee conro probems. We eeope a PI spee conroer, an une i manuay using OpenCV siers. We ese i on a ooping rajecory achiee by seing he harware inerface seering ange o a non-zero consan. We use he foowing formua: acceoupu k * ARGE_P k p * error - k * erroreriaie k i * errorinegra; Fig. A po of he reference rajecory (bue s he performance of he P-seeringconroer a high spee (green.

3 Fig. he space inexe moe of he car on he rajecory. 4 Opimizing using pace Inexe LQR 4. Linear Quaraic Reguaion he aue funcion for he ime inex case is he foowing equaion: V min( Q u R u Q ( u Howeer, using ime inexe aue funcion has a o of isaanages when a some fuure ime, we may appear a wo isinc ocaions wih exacy he same ime inex. he conro for ifferen ocaions wi be ery ifferen. o, if we opimize he aue funcion wih respec o conro, he opima conro we ge a simuaion may no be appropriae o appy a rea ime. We change i o space inexe. Like shown in he figure, we on upae he sae uness i is hiing one of he ines ha are perpenicuar o our inex poin in he rajecory. We use he Gabe s Conroer[] o simuae he inpu k of he conro signa. i. e δ arcan( eociy of he car, an k is he ange gain of he conroer., where is he cross rack error, is he Pseuo Coe for opimizing conro parameers: Run forwar simuaion using formua A B u, o simuae ime samps an obain he foowing:,,,, A, A,, A, B, B,, B, u, u,, u, * Iniiaize Q o beq, ge K For : * * K R B Q B B Q A ( * u K Compue opima u using ubsiue he new opima conro o compue he V we hen ge a Q : * Q Q K R K ( A B K Q ( A B K En Loop 3

4 4 4. Vehice Moe Our ehice moe is space inexe, an we hae our sae ecor as foowing: o upae he ae accoring o preious saes: / ( V ( a ( (3 φ (4 (5 L an (6 δ (7 In he aboe equaions, is he cross rack error when he car in on he perpenicuar ine of he rajecory, is he eociy of he car, is he ime ha he car akes o rae from curren inex poin o he nex inex poin. is he ime ha akes o reach his poin from he beginning. is he ange beween our car an he rajecory, φ is he change in he angen beween h an (h inex poins on he reference rajecory. is curren heaing of he car. is he anguar eociy of he car. is he ange beween whee an he car, which is aso our conro inpu δ. he aboe equaions can be wrien in he form of u B A, in which marix A is a 8x8 marix as foowing: an( cos L A φ Noe ha our A marix conains our rajecory informaion. he B marix is 8x marix, an conro ecor u gien in he foowing equaions:

5 5 B k a u δ arcan( We wi use he aboe formua o simuae forwar a number of seps, he use he agorihm escribe in secion 4. o opimize he conro u. Our goa is o minimize he square of he cross rack error, an we wi ry o minimize he conro parameer as we. o, our as Q marix wi be: Q β R Wih he Q an R marix, we can use LQR an opimize he conros. Fig. 3 imuaion using Gabes Conroer 5 Acknowegemens We reay appreciae Mark Woowar for heping us seing up he ision sysem for he RC car. 6 Reference []Hoffmann, Gabe; Auomobie Pah racking Conro, Hybri ysems Laboraory, anfor Uniersiy.