A Real-time Local Path Planning Method Based on SVM for UGV

Transcription

1 A Real-tme Local Path Plannng Method Based on SVM for UGV Chengchen Zhuge School of Computer Scence and Engneerng, Nanjng Unversty of Scence and Technology, Nanjng, Chna Zhenmn Tang* School of Computer Scence and Engneerng, Nanjng Unversty of Scence and Technology, Nanjng, Chna *Correspondng author(e-mal: Abstract Path plannng s one of essentals of unmanned ground vehcle (UGV). For the case of poor lghtng and weather, tradtonal vson based methods can not extract effectve route boundares to generate reasonable path stably n unstructured road. By takng advantage of dstance-sensng technology (e.g. 64-beam LDAR), th s paper proposes an effcent real-tme path plannng approach. In ths approach, gven grd map from 64-beam LDAR, obstacles on both sdes of the road are regarded as two classes fed to Support Vector Machne (SVM) to generate an ntal safe path. Durng drvng, a tme weght based least square fttng s adopted to refne path from multple safe paths whch wll be descrbed by quartc polynomal, provdng stable drvng route. Combned wth UGV's state, controls ponts from the refned path are adopted to generate the fnal path through Bezer curve fttng. Experments on real UGV under dfferent road scenaro are conducted, showng that the proposed method can obtan stable and reasonable path wth promsng performance. Key words: Real-tme, Path plannng, UGV, LDAR, SVM, Least square. 1. INTRODUCTION In recent years, Unmanned Ground Vehcle (UGV) has become a hot research topc n the feld of artfcal ntellgence (Fassbender, Mueller and Wuensche, 2014; We et al., 2014). UGV system s usually composed of percepton module, fuson module, path plannng module and control module. UGV reles on equpped sensors (e.g. camera, LDAR, nertal navgaton system) to perceve and model envron ment. Such tasks are acheved through road detecton, obstacle detecton, target recognton and so on. As one of the essental parts, path plannng module s to generate a safe path effectvely and effcently gven current envron mental nformaton, tasks and state of the UGV. If road boundares can be detected effect vely, path plannng module can generate a trajectory along the road and gude UGV to drve safely. Accordng to curvature of the road ahead, the upfront steer and speed control can ensure the UGV pass the curve road safely and smoothly. At present, most of the road detecton methods are vson based (Amn and Karasf, 2016; Maarr and Boukhalene, 2016; Wang, Sun and Zhao, 2015; Zu et al., 2015), whch can obtan excellent results n structured road (see Fg. 1(a)) and sem structured road (see Fg. 1(b)). However, vson based methods cannot works stably n unstructured envronment because of the lack of lane, fuzzy boundary, and uneven surface materals (see Fg. 1(c)). Sometmes, the poor lghtng and weather also nfluence the performance of the vson based methods (see Fg. 1(d)). On the contrary, grd map generated by 64-beam LDAR can show road structure nformaton effectvely (see Fg. 2). Many typcal approach such as Vorono graph (Canny, 1985; Takahash and Schllng, 1989) or potental feld (Khatb, 1986; Koren and Borensten, 1991) can be adopted on the grd map to generate a cost map whch mples the path nformaton, then a search method s adopted to fnd the safe path. Yu and Qu (2013) generates Vorono graph from grd map as road skeleton, then uses Fast Marchng Method (FMM) to search the path. However, the generated path s nether safe nor smooth. The Fast Marchng square Method (FM 2 ) (Gómez, Mavrds and Garrdo, 2014) s then proposed to compute safe and smooth trajectores effectvely. FM 2 frstly apples the FMM to generate a velocty map, then uses the FMM on the velocty map to search a safe and smooth path to the goal pont. However, the FM 2 needs a lot of computng resources. Lnear Dscrmnant Analyss (LDA) s adopted to classfy the obstacles on both sdes of the road by Lu, Tang and Ren (2011). Road boundares are then ftted whch can be used for path plannng n real-tme. However, the LDA mentoned cannot deal wth the road wth large curvature (see Fg. 2). To effectvely address above shortcomngs, n ths paper, a local path plannng method based on non-lnear SVM and least square fttng s proposed. Ths method can generate a safe, smooth, and executable path for UGV n real-tme. It can effectvely deal wth the problem of path plannng n unstructured road envronment wth grd map. Non-lnear SVM ensures accurate road boundares detecton and least square fttng provdes smooth and consstent path generaton. The valdty and correctness of the proposed method s verfed on a real vehcle. 487

2 (a) (b) (c) (d) Fgure 1. Dfferent road scenaros. (a) Structured road (b) Sem structured road (c) Unstructured road (d) Ran and n the tunnel Fgure 2. Local grd map The overall organzaton of ths paper s as follows: In Secton 2, path extracton based on non-lnear SVM s ntroduced. Secton 3 manly focuses on the whole local path plannng method. In Secton 4, experments and analyss n real-world case s presented. Conclusons are drawn n Secton TRAJECTORY GENERATED BASED ON NON-LINEAR SVM SVM (Bron et al., 2015; Gómez, Mavrds, and Garrdo, 2014) s one of the most commonly used classfer learnng methods. The obtaned optmal classfcaton hyperplane can maxmze the class margn. In Fg. 3, obstacles on both sdes of the road can be regarded as two knds of targets, whch can be served as samples fed to SVM. SVM can provde a hyperplane wth a maxmal dstance to obstacles. The projected trajectory of the classfed hyperplane on the 2D grd map s not only smooth but also far away from the obstacles, so t can be tracked by the UGV. 488

3 Fgure 3. SVM classfcaton hyperplane schematc dagram Let ( p, ) be obstacle sample, where p ( x, y ) j j represents coordnate of the j j j the vehcle-centered coordnate system and the 1, 1 functon s gven by j th j obstacle under represents class label. The dscrmnaton n T T j j j 1 f ( p ) w p b p p b where n represents the number of s upport vectors, represents Lagrange multpler. (1) Note that lnear classfer cannot deal wth road wth large curvature. SVM s adopted to determne nonlnear separatng hyperplane wth kernel trcks. In ths paper, Radal Bass Functon (RBF) kernel s utlzed for tranng and testng due to ts excellent performance than other kernels n our e xperments. RBF kernel K(, ) s defned as 2 p pj K( p, pj ) exp( ) 2 (2) where s kernel parameter. Then the tranng process s to solve the dual problem as follows: Fnally, the hyperplane equaton s obtaned: n n 1 max K ( p, p ) 2 j j j 1, j 1 s. t., 0, 1,, n n n 1 0 j j 1 f ( p ) K( p, p ) b 0 (3) (4) w and b, solutons of the prmal problem, can also be obtaned. The ponts on the separatng functon Eq. 4 can be treated as a safe path snce t can maxmally separate obstacles on both sdes of the road. Then ponts are sampled wth equal-step from the hyperplane trajectory. As shown n Fg. 3, the SVM classfcaton hyperplane trajectory can effectvely separate obstacles on both sdes of the road. Due to the property that the obstacles correspondng to the support vectors are the nearest ponts to the trajectory (safe path) and they are dstrbuted on the narrowest parts of the road, these obstacles can be used to estmate the traversablty of the road. The dstance from support vector to the hyperplane can be calculated as follows: D( p ) The road s not safe f there s a support vector w p b w (5) p such that: 489

4 where D( p ) w / 2 d (6) w car represents car wdth, d safe s a safety parameter whch can be determned expermentally. 3. REAL-TIME LOCAL PATH PLANNING METHOD car When UGV s movng, the local grd map wll be updated at a fxed frequency whch s decded by the workng frequency of the 64-beam LDAR. A new trajectory (.e. hyperplane) s obtaned n each update. Due to uncertanty of envronment (e.g. new obstacles, measurement errors caused by vehcle turbulence), the trajectores obtaned are not consstent all the tme. Fg. 4 shows the trajectores n multple updates. If no otherwse specfed, the unt of the values n the fgures s cm. Note that these trajectores are projected wthn the same coordnate system. It s clear to see that these trajectores are not concdent. In ths paper, least square fttng (Goldhammer et al., 2015; Matchen and Nadler, 2014; Wlson et al., 2015) s used to estmate the path model from multple trajectores. The whole process to generate the fnal safe local path s llustrated n Fg. 5. There are manly three phases: 1) ntal safe path generaton; 2) path refnement by least square fttng; 3) fnal path generaton. safe Fgure 4. Mult-frame projected data schematc dagram Fgure 5. Flow dagram of the local path plannng algorthm 490

5 3.1. Intal Safe Path Generaton In ths paper, the sze of local grd map s 30m 30m, and the grd resoluton s 12.5cm 12.5cm. The orgnal grd map s shown n Fg. 6(a). The orgnal grd data s not sutable to be fed to SVM drectly. It needs to be pre-processed and labeled. The specfc process s descrbed as follows. The orgnal grd map s treated as a bnary mage and processed wth dlaton and eroson (see Fg. 6(b)). The wndow sze s (pxels) whch s approxmately equal to the car wdth n real-world. Then chan code trackng s appled to get the obstacles contour nformaton (Sngh et al., 2015). Each closed contour s labeled as an obstacle target (see Fg. 6(c)). (a) (b) (c) (d) Fgure 6. Data pre-processng and classfcaton. (a) Orgnal grd map (b) Dlaton and eroson (c) Extract and separate the obstacles (d)the best result Let p ( x, y ) be the coordnate of the j j j barycentrc coordnate of the th obstacle, and ( j ) th j contour pont of the th obstacle, pc ( x c, yc ) be the p, s the tranng sample used n ths paper. The N obs obstacles wll be transformed nto the polar coordnate and be separated nto two groups. If there s no SVM classfer from prevous map, obstacles need to be labeled for tranng by SVM. The obstacles on the left of the separatng lne wll be labeled wth 1 and the obstacles on the rght of the separatng lne wll be labeled wth 1. For example, there are four obstacles labeled as regon A, B, C and D n Fg. 6(c), and there are fve separatng results corresponded to vs. A B C D, A vs. B C D, A B vs. C D, A B C vs. D, A B C D vs. When the group s, ponts on the boundary of the local map are chosen as the tranng samples. Then N obs 1 groups of the tranng samp le ( p, ) wll be traned to obtan N obs 1 sets of ( w, b ) and the corresponded hyperplanes. j Fnally, the best hyperplane H best wth the maxmum dstance to the two categores of obstacles s saved. As shown n Fg. 6d, the pro jected trajectory of the hyperplane H best n grd map s a safe and smooth path for the UGV. 491

6 j j j When UGV s movng, the extended trend of the road can be consdered to be changng slowly. Therefore, when a new frame of grd map arrves, the obstacles n the new frame can be classfed by the SVM hyperplane H ' of the prevous frame. In ths case, the classfed obstacles can be treated as new tranng samples to obtan a new SVM hyperplane H as the new frame. In contrast, wthout SVM hyperplane H ' from prevous frame, multple tranng groups are generated to tran multple SVM hyperplanes. The detal process s descrbed as follows: Frstly, all the p ( x, y ) of N obs obstacles n current frame are transformed nto the vehclecentered coordnate system of prevous frame, denoted by pj ' ( x j ', yj '). Then, these pj ' ( x j ', yj ') are classfed by the SVM hyperplane H ' of prevous frame and be labeled by 1, 1. It s assumed that the extended trend of the road changes slowly, the label of the same obstacle n the adjacent frames should be the same, although the coordnates are dfferent n the adjacent frames. Fnally, the new tranng samples ( p, ) are traned to obtan the new SVM hyperplane H. j 3.2. Path Refnement The road model s approxmated wth a quartc polynomal as follows: where f ( y ) s the road model to be estmated and f ( y) a a y a y a y a y (7) a s the model parameter. The postve y-axs s the headng of the UGV n the vehcle-centered coordnate system. In ths paper, a tme weght based least square fttng s adopted on the mult-frame projected data (see Fg. 4) to estmate the road model. The least square problem can be defned as follows: N 4 2 j j j (8) j 1 0 mn ( a, a, a, a, a ) mn ( f ( y ) a y ) a where N s the number of the ftt ng ponts and 0,1 j a s the tme weght. Optmal soluton for the parameter can be obtaned wth gradent when the objectve functon becomes zero (see Eq.9). 0, 0,, 4 a (9) The pseudo code for the tme weght based least square fttng s shown n Algorth m. 1. At tme t, the hyperplane trajectory H s sampled nto dscrete ponts whch are stored n P. Then P s assgned wth an t ntal tme weght t 1 (see Lne 2-3 n Algorth m. 1) whch wll reduced by 1 T each tme. T decdes how long the tme queue wll be mantaned. It means that the new hyperplane trajectory has greater effect than the old ones n the least square ftt ng procedure. The tme weght of the hstorcal projected ponts, whch are already stored n global_ponts, s updated before the hstorcal projected ponts merge wth the P (see Lne 4 n Algorthm. 1). After the hstorcal projected ponts n the global coordnate system are transformed nto the local vehclecentered coordnate system and be saved n local_ponts, P s also added to local_ponts (see Lne 5 n Algorth m. 1). The local ponts whch have postve y value and postve tme weght are retaned n the global_ponts and severed as the nput for the next cycle (see Lne 7-10 n Algorthm. 1). Algorthm 1. Path refnement based on the least square Input : global_ponts : The mult-frame projected ponts n the global map; Ht : SVM hyperplane at tme t 1. Intalzaton : local_ponts ; 2. P t Sample(H t); 3. Pt.ω ωt; 4. UpdateWeght(global_ponts); 5. local_ponts TransformToLocal(global_ponts) P t; 6. global_ponts ; 7. for each pont p n local_ponts do 8. f (p.y > 0 and p.ω > 0) then t t t t 492

7 9. global_ponts TransformToGlobal(p ); 10. end 11. end 12. EstmateModel(global_ponts); Output : Road model M. Fg. 7 shows the dfferent paths ftted respectvely by least square fttng (LSF) and tme weght based least square fttng (TWLSF). The lght astersks are the projected result of the mult-frame SVM hyperplane trajectores at tme t whle the dark ones are the results. As shown n Fg. 7, the small obstacle hasn t been detected by 64-beam LDAR n the early tme, so the path ftted by all the projected ponts s close to the obstacle. The path ftted by tme weght based least square s relatvely safer due to hstorcal projected ponts have a lttle effect n the fttng procedure. Note that, the SVM hyperplane trajectores are not concdent, the refned trajectory s decded by the large number of ponts whch belong to SVM hyperplane trajectores. The refned trajectory s also away from the obstacles, and the complex hyperplane equaton s transformed nto a smple fourth order polynomal whch s convenent for the followng process. Fgure 7. Result of tme weght based least square fttng 3.3. Fnal Path Generaton In the real world, UGV's state should be consdered durng path plannng. In ths secton, ths nformaton s combned wth the least square path to generate the fnal path by Bezer functon. The least square path s dvded evenly nto fve segments and the length of each segment s l. Then the control pont C 1 s selected. As shown n Fg. 8, the angle between vector OC1, pont O s the front axle center,, t and the drecton of the vehcle's nstant velocty s 1 represents the steerng angle at tme t, s the maxmum executable steerng angle n each executon cycle. The coordnate of 1, Pont C 1 can be calculated by Eq. 10 n whch the value of 1 should mnmze the value of the Eq. 11. Fgure 8. The selecton of control ponts 493

8 x y C1 l sn( + ) t 1 l cos( + ) C1 t 1 w w dx 1 2 [, ] d max argmn ( ) where d x represents the horzontal dstance between pont C and the least square fttng path, dmax max( d x ). The frst term of the Eq. 11 controls the curve of the path and the second term makes the path close to the least square fttng path whch means keepng away from the obstacles. th The subsequent control ponts are selected by Eq. 11. When selectng the control pont C C between 1 C C and 2 1 s whch satsfes. The control pont (10) (11) C, the angle C s determned when mnmzes the va lue of the Eq. 11. Then the fnal executable path s ftted by Bezer functon wth those control ponts. 5! B t t t t 5 5 ( ) (1 ) C, [0,1] 0!(5 )! (12) 4. EXPERIMENTS AND ANALYSIS 4.1. Expermental comparson In order to verfy the feasblty of the proposed method, experments n the unstructured road envronment s conducted on the UGV Xngjan (see Fg. 9). Fgure 9. Experment platform The method proposed n ths paper s compared wth FM 2, LDA method and Crcle-based method (Chen, Rckert and Knoll, 2016). In the Crcle-based method, the crcles, whch radus are the dstance to the closest obstacle, extend from the start poston n a tree-lke manner. When the goal poston s reached, a heurstc search whch consders the knodynamc vehcle model s adopted on the crcle-path to generate an obstacle clearance path. An example of Crcle-based method s shown n Fg. 10. The analyss s based on the expermental data of several typcal scenes ncludng straght road, branch road and curve road. The test results of these four methods are based on our own mplementaton. All tests run on a machne wth 2.3GHz CPU and 8GB RAM. In the experment, two endponts of the trajectory generated by proposed method s set be the startng and endng pont of the FM 2 and Crcle-based method. As shown n Fg. 11, the trajectores generated by proposed method s smoother than FM 2. In the velocty map generated by FM 2, the farther the area s away from the obstacle, the hgher the ve locty of the area s, so FM 2 wll search the path along the hgh velocty area (see Fg. 11(f)). However, ths wll add extra length nto the total path n some cases, such as, on the branch road whle the proposed method and LDA method wll not. The Crcle-based method also suffers from the same problem as shown n Fg. 11(h). 494

9 Fgure 10. Crcle-based path plannng method In the straght road case, the path of the proposed method s a lttle curve because of non-lnear SVM (see Fg. 11(a) and Fg. 11(e). However, the path can be consdered smlar to a straght path. The results of the LDA method are more reasonable relatvely (see Fg. 11(c) and Fg. 11(g)) due to ts lnearty. As shown n Fg. 11(k), the LDA method cannot deal wth the road wth large curvature. (a) Proposed (b) FM 2 (c) LDA (d) Crcle-based (e) Proposed (f) FM 2 (g) LDA (h) Crcle-based () Proposed (j) FM 2 (k) LDA (l) Crcle-based Fgure 11. The results of our proposed method, FM 2, LDA method and Crcle-based method for dfferent scenaros. (a)-(d) scenaro 1: straght road; (e)-(h) scenaro 2: branch road; ()-(l) scenaro 3: curve road The maxmum, mnmum and average dstance between the path and obstacle are shown n Fg. 12. From the pont vew of the path safety, the proposed method s better than LDA method and Crcle-based method n straght road and curve road scenaros, and FM 2 only has one tem better than the proposed method n straght road and curve road scenaros. In the branch scenaro, FM 2 and Crcle-based method has larger maxmum dstance than the proposed method due to the characterstc descrbed above, and the proposed method also has relatvely safety dstance away from the obstacles. 495

10 The runtme of four methods are shown n Fg. 13. FM 2 has the worst performance, LDA method s almost wthn 50ms and Crcle-based method s almost wthn 80ms. The runnng tme of the proposed method s almost wthn 25ms whch can satsfy the requrement of the real-tme path plannng for UGV. Fgure 12. Dstance away from obstacles Fgure 13. Run tme 4.2. Path smoothness analyss The comparsons of the path smoothness n dfferent scenaros are shown n Fg Because of the result of LDA method s just a straght lne, the co mparsons only take account the other three methods. Note that, the result of FM 2, whch s grd-based, has been ftted by Bezer functon. Then the paths of FM 2, Crclebased method and the proposed method are all resampled unformly. Let q 1, q and q 1 be the contnuous q q q q resamplng ponts. The angle between 1 and 1 s used to represent the change rate of q. As shown n Fg , the change rate of the whole path of the proposed method s relatvely s mall n contrast wth the other two methods. It s smooth enough for UGV to trace. The change rate of the whole path of FM 2 changes greatly. Although the path of FM 2 s safe enough, t can not be traced by the UGV s moothly. The path of Crcle-based method s affected by the postons of the crcles whch extend randomly. However the knodynamc vehcle model s consdered, the path s also not smooth enough. Fgure 14. The comparson of the change rate on straght road 496

11 Fgure 15. The comparson of the change rate on branch road Fgure 16. The comparson of the change rate on curve road 4.3. Road curvature analyss The road curvature analyss can effectvely control speed and mprove safety and comfort when the UGV s drvng. So n ths paper, the road radus of three dfferent road sectons are compared and analyzed based on the fourth order polynomal. The mnmal radus of the refned path n each frame by tme weght based least square fttng can be calculated by Eq. 13. Three knds of road sectons are analyzed. Road secton 1 s a twsty road, road secton 2 s the case of leavng the sharp turn, and road secton 3 s a straght road. The results are shown n Fg r (1 f ( y)' ) f ( y)'' (13) (a) Mult-frame grd map (b) Mnmal radus of each frame Fgure 17. Road secton 1 497

12 (a) Mult-frame grd map (b) Mnmal radus of each frame Fgure 18. Road secton 2 (a) Mult-frame grd map (b) Mnmal radus of each frame Fgure 19. Road secton 3 As shown n Fg. 17, the mnmal radus profle of road secton 1 has two valleys (see Fg. 17(b)) whch represents the two curves (see Fg. 17(a)). As shown n Fg. 18, the mnmal radus profle of road secton 2 becomes bg gradually (see Fg. 18(b)) whch represents the case of leavng the sharp turn (see Fg. 18(a)). As shown n Fg. 19, the mnmal radus profle of road secton 3 s obvously larger (see Fg. 19(b)) than that of the other two road sectons. Ths result s n accord wth the fact that road secton 3 s a straght road (see Fg. 19(a)). However, the mnmal radus profle of road secton 3 has a large degree of fluctuaton, the refned path by least square fttng has no drastc changes from macro pont of vew due to the value of mnmal radus s very large. So t has almost no nfluence on judgng the road secton 3 as a straght road. Note that, the mnmal radus s not the true value of the road. Accordng to the trend of the mnmal radus, the curve degree of the road can be dentfed and be treated as pror nformaton for the steerng control and velocty control of the UGV. 4. CONCLUS ION EXPERIMENTS AND ANALYSIS A real-tme local path plannng method based on 64-beam LDAR and SVM s proposed. Ths method can effectvely extract the path from the grd map and make up for the performance of vson based road detecton algorth ms s lmted by poor lghtng and weather n unstructured road envronment. The fnal path s smooth, safe and easy to be tracked by controller. The valdty and the correctness of the proposed method s verfed on a real vehcle. The curve degree of the road has been smply dentfed accordng to the road model based on fourth order polynomal. Future work wll focus on the further processng of curvature data and how to combne the curvature data wth the steerng control and velocty control of the UGV. Acknowledgements Ths work s supported by Natonal Scence Foundaton of Chna (No and No ); Chna Post Doctor Foundaton (2014M561654); Specalzed Research Fund for the Doctoral Program of Hgher 498

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