THE STUDY OF THE PREDICTION MODEL IN THE SIMUROSOT

Transcription

1 THE STUDY OF THE PEDICTION MODE IN THE SIMUOSOT SHI Ha-bin, ZHANG i, I Xia-an, YAN Jian-feng,UO Xin Schl f Cmputer, Nrthwestern Pltechnical Universit N.17 West Yui ad, Xi an Cit, Shaani Prvince, (71007), P..China ABSTACT Given t the real-time perfrmance f mtin cntrl accepted in the strateg f SimurSt, the mtin predictin f the rbt and the ball is a necessar and effective wa t imprve the perfrmance f the team in a match. Based n the analzed kinematics mdels f the ball and the rbt in the platfrm f SimurSt 11vs11, a valid and practical methd t predict the mtin f the rbt and the ball is put frward, and its validit is prved b the eperiments. 1. INTODUCTION Fr difficulties in mtin cntrl, real-time perfrmance f instructins accepted and hardware prblems, it is uneas fr the real rbt t perfrm difficult actins. Thus, advanced mtin cntrl, grup arrangement and strateg are tested firstl in the simulatin platfrm as in SimurSt rather than in MirSt match []. T make the rbts carr ut a strateg, a gd mtin cntrl is a necessar precnditin. A human ftball team member with gd understanding f strateg but pr master f skills cannt be cnsidered as a gd plaer, because he can nt even get the ftball passed t him frm ther plaers [7]. S des the sccer rbt in the SimurSt. Given that a rbt with respnsibilit f defense can nt alwas reach the designated psitin, hw can it further carr ut the strateg?. AN EXAMPE In SimurSt, because f diversit f strateg and high mtin speed f bth rbt and ball, the cnditin changes with ever secnd. S an accurate predictin f mtin f bth rbt and ball is necessar t render the rbt plaers t finish the preset actins [6]. Suppse a ball is mving fast tward the gal and a ftball rbt is cming frm the ther directin t hit it, as in figure 1. If the instructin sent t the rbt nl requires it t g t the psitin n which the ball is at the mment (figure 1.a), when the rbt gets nearer t the preset psitin, it will find the ball has alread left. Therefre, a secnd instructin has t be given t the rbt t get t the psitin f the ball again. Cmpared with the passive strateg abve, a different strateg can be adpted t make the rbt mre effectivel chase the ball. If the strateg can predict a psitin that the ball will reach in perids and the time the rbt need t reach that pint, the rbt can adjust its speed t reach the psitin at the same time with the ball t hit it (figure 1.b). (Psitin) (Psitin) (Psitin1) (a) (Psitin1) (b) Ball Ball bt bt (Aims at 1) (Aims at ) Figure 1 Tw different was t hit the ball Frm the tw strategies discussed abve, it can be seen clearl that thugh the frmer is easier, the latter is mre effective and is the right chice. But t adpt the latter ne, an accurate mtin predictin is needed, which will be discussed in the fllwing part. 3. KINEMATICS MODES IN THE PATFOM

2 The match platfrm adpted in SimurSt11vs11 is develped b Harbin Institute f Technlg in China. In rder t predict the mtin f rbt and ball, the kinematics mdels in the platfrm have t be studied first. 3.1 Kinematics mdel f the ball An range glf ball with a radius f 5 piels shuld be adpted as the match ball accrding t the rules. And mtin f the ball must be the same when mving t an directin. The ball is suppsed t be a pure elastmer. Hence, the mtin f the ball has t fllw the mtin rules f elastmer. Obstacles here refer t the bundaries f the game field and the side surface f the rbt ecept the frnt and backside f the rbt [8]. Usuall, the ball keeps still r mves in a straight line with a cnstant deceleratin. And frictin is a factr when cnsidering the mtin. Accrding t phsics, the value f a cnstant deceleratin shuld be calculated as fllw: a = f / m= µ N / m= µ mg/ m = µ g (1) where µ represents the factr f the sliding frictin, N is the pressure between the surfaces. 3. Kinematics mdel f the rbt A standard rbt is a square rbt with 10*10 piels in size and it shuld have nl ne frnt side. The platfrm sends the centrid crdinate and directin angle ever perid. As is illustrated in figure, is the distance between the left and right wheel, is radius when the rbt wheeling, is the speed and ω is the angular velcit and, are speed f right and left wheels respectivel. The Kinematics mdel is illustrated as fllws [3][5]: = ω( /) () = ω( + /) (3) = 1/ ( + ) (4) ω = ( ) / (5) = ( + ) /[ ( ) ] (6) As is shwn in the figure, adjusting the speed f the right wheel and the left ne can cntrl mtin f rbt. When the speed f the left wheel is the same as the right ne, is infinite and the rbt mves straightl; when eceeds, the rbt mves circumferentiall with the centre f the circle n the right side; ice versa. During a match, speed f the wheel can be set with different value ever perid. Displacement a rbt mves during ne perid is nl related t the speed f the wheels and mtin f the rbt in ne perid can be seen as a piece f circular arc. Based n the settings abve, an accurate predictin can be carried ut. 3.3 Cllisin mdel between a rbt and a ball T make the ball reach a designated psitin r t render a ball mve in a directin, the fre-and-aft speed f the ball after hit must be knwn. Because the ball is cnsidered as a pure elastmer and the hit prcess takes nl a little time, frictin can be mitted cmpared with the frce upn the ball in the cllisin [1][4]. S the whle prcess f the ball hit b a rbt is a prcess f bth cnservatin f mmentum and cnversatin f energ [9]. ( ) m m m m M m M m1 m1 ω Figure Kinematics mdel f rbt As shwn in figure 3, the relatin is epressed as: MM + mm1 = MM + mm (7) MM + mm1 = MM + mm1 where M is qualit f the rbt; m is qualit f the ball; m and Figure 3 Cllisin mdel between rbt and ball m are fre-and-aft speed f the ball after hit;

3 m1 and m1 are prjectins f m and m in the directin f the hit; m and m are prjectins f m and m in the directin plumb f that f the cllisin; M is speed f the rbt befre the hit; M is speed f the rbt after the hit; When m 1 is wrked ut, it can be calculated with m t figure ut m. 4. BUIDIND OF THE PEDICTION MODE 4.1 The predictin mdel f the ball As mentined in the frmer parts, the ball will start t mve in a straight line with a cnstant deceleratin after hit b a rbt. Given t this ideal mdel, we can get the current velcit and deceleratin f the ball directl frm the difference f the three sets f data: the current psitin f the rbt, the psitin f the rbt in the last perid, and the psitin f the rbt in the perid befre the last. Thus, we can easil wrk ut the psitin f the ball in several perids. This is crrect thereticall, but the predictin results are far frm the factual psitin f the ball after the perids. After studing, we can find that it results frm the platfrm itself. The data sent b the platfrm have alwas been cnverted t integers instead f the duble tpe, causing that if initial velcit is gt frm nl ne r tw perids, it will be prbabl far frm crrect. T get relativel accurate initial velcit, histric psitins f the ball as man as pssible shuld be used and the average velcit calculated ut as the initial velcit. Hwever, this new methd brings ut new prblem that whether all f the histr data recrded can be used. Hw t pick ut the prper nes is need t slve first. The ball is hit b the surrunding rbts time and time again in the real match, causing that the velcit f the ball changes with ever a few perids, as what we can get in the mdel f cllisin between a rbt and a ball. The ke prblem is t find the ball s last cllisin psitin because nl thse data recrded after this psitin can be used t calculate the initial velcit. Based n tests, we find that if a ball mve in a straight line withut hit b an rbt, its displacements in an tw perids has such relatins as fllws: d d C (C is a cnstant) (8) d d C Frm this relatin, it is quite eas t find ut the cllisin pint f the ball. And this methd is als suitable fr the pints that the ball hits n a blckade and then rebunds as well as the pint n which the rbt hits the ball. And then, average velcit can be calculated ut frm thse valid data. Suppse that data f the past perids can be used, and the psitin f the ball after n perids needs t be predicted. Equatins are listed as fllws: 1 d = ( n + /) + a cs( θ ) ( n + /) (9) 1 d = ( n + /) + a sin( θ ) ( n + /) where θ represents the directin angle f the mtin f the ball, d and d respectivel represents the displacement f the ball n hrizntal directin and vertical directin, a represents the deceleratin f the ball and and respectivel represents the initial velcit f the ball n hrizntal directin and vertical directin. Apart frm this, the fact that the velcit f the ball will never be less than zer and its psitin culd nt be bend the bundar f the field shuld be cnsidered. Therefre, if the result cming ut f the predictin cntradicts with this basic truth, certain treatment shuld be dne t the data. 4. The predictin mdel f the rbt It is the first thing t make accurate predictin f the displacement f the rbt in certain perids in rder t predict ut the time a rbt needs t reach the gal psitin. et s start frm ne perid. As mentined abve, the mtin f rbt in ever perid can be seen as an instant circular mtin. As in figure.4, α is the current directin angle f the rbt, θ is the angle subtended in the center f the circle crrespnding t the arc and d, d are the displacement f the rbt in ne perid n hrizntal directin and vertical directin respectivel, is the length f the arc alng which the rbt mves in this perid. The crrespnding kinematics is illustrated as d = θ cs( α θ) d = θ sin( α θ) (10) θ = ω 1 The fulfillment f the calculatin als depends n the relatinship between the radius f wheeling and the velcit f the rbt s left wheel and the right ne, which has been alread put frward in (5) and (6) abve. Frm this pint, we can see that the current preset velcit f the left and the right wheel is a necessar precnditin if the displacement predictin f rbt is needed. On the ther hand, we can find that in mst ccasins in the strateg, the preset velcit depends n the psitin and the directin angle f the rbt, which makes that the psitin f the rbt and the velcit f the wheel has mutual dependenc. Thus, t predict the psitin f the rbt after several perids, we must knw the velcit f the tw wheels in each f these net perids.

4 θ α Times Needed Times Predicted Times 30 θ 0 10 Figure 4 Accurate predictin mdel f rbt Seemingl impssible, but it is still can be slved if a recurrence algrithm is adpted. The psitin after ne perid can easil be gt frm the current data and the current velcit, and if this predictin result is taken back t the functin used in the predictin, the velcit set in the net perid can be wrked ut. Then, with these velcities, the psitin after tw perids can be wrked ut, s n and n. A whle prcess can be simulated in just ne perid in this wa and the final psitin after several perids can be wrked ut. In the same wa, t predict hw man times a rbt needs t reach gal pint is pssible The results f eperiment and analsis Having prved in the eperiments dne n the SimurSt11vs11 platfrm, this methd has an ecellent accurac. Take the eperiment n the predictin f rbt as eample. In this eperiment, the times a rbt needs t reach certain pints in real mtin and crrespnding results frm the predictin are cmpared in figure 5. We have cllected 900 cuples f data and each cuple includes the time that the rbt needs t mve t a certain pint and the time that is predicted t take fr the rbt t mve there. The are divided int 60 grups, the first ne f which, fr eample, is listed in table 1 with detailed errr infrmatin f each cuple. Meanwhile, table shws the statistical infrmatin f the maimum errr and the average errr f all the 60 grups, which are calculated ut accrding t the 900 cuples f data that we have recrded. The statistical data includes the maimum, minimum, epectatin and variance f the maimum errr and the average errr respectivel. Seen frm the figures abve, a quite high accurac can be reached n the prblem f predicting times a rbt needs t reach certain pints. The errr is alwas kept within 5.7% and the average errr within 1.70%. The epectatins and variances illustrate a relativel narrw Figure 5 esults f the eperiment n predicting the mtin f a rbt errr range. Thereticall, an even higher accurac can be gt if such a predictin mdel which strictl accrds with the kinematics mdel f the platfrm be built crrectl. Hwever, because f the cnverting n data frm duble tpe t integer b the platfrm itself and these errrs accumulated in the recurrence, such errrs are unavidable. Hwever, luckil t see the errr has been kept within an acceptable etent. Table 1 First grup f data Inde Times Times Errr needed predicted % % % % % % % % % % % % % % % Table Statistical infrmatin f 60 grups errr (Unit: %) Ma. Min. EX DX ma errr avg errr

5 5. CONCUSION After analzing and intrducing the kinematics mdel in the platfrm f SimurSt11vs11, a methd t predict the mtin f the rbt and the ball accuratel has been put frward. Prved b eperiments, the methd is valid and practical and the errr is acceptable. Seen frm the eample presented in the ver beginning, we can safel arrive at the cnclusin that it will pla a psitive rle in the actin design f the rbt and an ptimistic estimatin culd be made that it will prbabl help a lt in the develpment f real rbt in the recent future. Internatinal Cnference n Intelligent Prcessing Sstem, [s.l.]: [s.n.]: pp , [8] Wu i-jian, Zhang Chun-hui, and Xu Xin-he, "An A- ttack Strateg in bt Sccer Sstem,", Prceeding f the 3rd ASCC, [s.l.]: [s.n.], 000. [9] ZhangWei and Zhang Da-zhi, "A ecurrence Algrithm fr Attack Path and Kick Psture f Sccer bt," Jurnal f Harbin Institute f Technlg, 004. ACKNOWEDGEMENT This research was supprted b the innvatin engineering prject OBOT SOCCE COMPETITION frm Nrthwestern Pltechnical Universit f China. EFEENCES [1] Egerstedt M., "Mtin Planning and Cntrl f Mbile bts," Mathematics al Institute f Technlg Stckhlm, 000. [] Kim H, Shim H, Jung M, et al., "Actin selectin mechanism fr sccer rbt," Prceedings f IEEE Internatinal Smpsium n Cmputatinal Intelligence in btics and Autmatin, [s.l.]: [s.n.], [3] Hng Bing-rng, Ga Quan-sheng, Chu Hai-ta, "bt Sccer Simulatin Cmpetitin Platfrm Based On Multi-Agent," Jurnal f Harbin Institute f Technlg (New Series), 8(3): pp.03-06, 001. [4] ee S, Bautista J., "Mtin cntrl fr micr-rbts plaing sccer games," Prceedings f IEEE Internatinal Cnference n btics & Autmatin, euven: Belgium, [5] i Jian-wei, Hng Bing-rng, Ha Zng-b, Ga Quan-sheng, Gu Qi, "Imprvement f simulated rbt sccer cmpetitin platfrm," Jurnal f Harbin Institute f Technlg, 9(35): pp , 003. [6] i Zu-shu, Chen Qing-chun, i Xue-mei, et al., "Human simulating intelligent cntrl and its applicatin t swinging up f cartpengdulum," Prceedings f 6 th IEEE Internatinal Wrkshp n bt and Human Cmmunicatin 97 Man[C], [s.l.]: [s.n]: 18-3, [7] Tu Ya-qing, "Design methd fr a nvel human simulatin intelligent cntrller," The 1997 IEEE