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2 16 Tracking Control for Reliable Outoor Navigation Using Curb Detection Seung-Hun Kim Korea Electronics Technology Institute, Korea 1. Introuction In the past several years there has been increasing interest in applications of a mobile robot. Personal service robots perform the missions of guiing tourists in museum, cleaning room an nursing the elerly [1]. Mobile robots have been use for the purpose of patrol, reconnaissance, surveillance an exploring planets, etc [2]. The inoor environment has a variety of features such as walls, oors an furniture that can be use for mapping an navigation of a mobile robot. In contrast to the inoor cases, it is har to fin any specific features in outoor environment without some artificial lanmarks [3]. Fortunately, the existence of curbs on roaways is very useful to buil a map an localization in outoor environment. The etecte curb information coul be use for not only map builing an localization but also navigating safely [4]. An also the mobile robot ecies to go or stop using the with of the roa calculate from the etecte curb. The present paper eals with the evelopment of a robot which can patrol areas such as inustrial complexes an research centers. We have alreay reporte about outoor navigation of a mobile robot [5]. The extene Kalman filter is applie for the fusion between oometry an Differential Global Positioning System(DGPS) measurement ata. It is insufficient for reliable navigation since the error of DGPS measurement ata increase near high builings an trees [6]. Hence, it is necessary to correct the pose of a mobile robot when the position ata from the oometry an DGPS are inaccurate. This chapter proposes the curb etection algorithm an calculate the pose error from the curb ege ata an then use it to correct the pose of the mobile robot. 2. Outoor mobile robot system The outoor mobile robot system on an ATRV-mini from RWI Inc. is constructe as shown in Fig. 1. It is a four-wheele robot esigne for outoor use an equippe with oometry. This robot is chosen because it can climb up an own over spee bumps an slopes. It is ae a laser range finer to etect obstacles an buil a map of the environment. For global localization, a DGPS receiver is ae. A camera that can zoom-in an zoom-out, was installe to sen the image ata to the control station. Fig. 2 shows the software architecture of the mobile robot system. The system consists of three parts which are the mobile server, the navigation server an the remote server. The mobile sever controls the motor in the ATRV accoring to the velocity an angular velocity

3 328 Recent Avances in Mobile Robotics Fig. 1. Mobile robot system configuration. (a) DGPS antenna (b) PC (c) Image camera () LMS200 laser range finer (e) Attitue/heaing sensor (f) Wireless LAN briges (g) Joypa (h) Control station from the navigation server an transfers the oometry to the navigation server. The navigation server makes the mobile robot localize using latitue an longitue ata from the DGPS an attitue from 3-axis angle sensor. It etects curbs using istance from the tilte laser range finer an sens the istance, image an navigation ata to the remote server through the wireless LAN. The remote server operates in two moes, autonomous moe or teleoperate moe, isplay the image an the navigation information. Fig. 2. Software iagram of the mobile robot system.

4 Tracking Control for Reliable Outoor Navigation Using Curb Detection Curb etection The outoor mobile robot requires ability to navigate in a ynamic an potentially angerous environment ue to curbs an obstacles. Using the laser range finer, it can measure the istance from the obstacles an calculate the istance between obstacles. These ata obtaine from the laser range finer can be use in environment mapping an obstacle avoiance. An important feature of roa environment is the existence of curbs as shown in Fig. 3. The curbs coul be use in mobile robot navigation. Fig. 3. Roa an curb on the roa. The propose algorithm is to etect curbs through the laser range finer, which was positione on the mobile robot an looking own the roa with a small tilt angle as shown in Fig. 4. The tilte laser range finer projects three-imensional shape of curbs on twoimension space. An then it extracts curb ege points. Fig. 4. Tilte laser range finer on the mobile robot. The mobile robot buils the map of the curbs of roas an the map is use for tracking an localization. ( nx, L, y L) is obtaine by the laser range finer, where n represents n-th ata an xl, y L are the istance ata in the laser range finer s coorinate as shown in Fig. 5. The curb eges on the both sies of the mobile robot is use for mapping an tracking.

5 330 Recent Avances in Mobile Robotics Fig. 5. Curb etection on the roa. Even though the angle between the robot an the curb changes, the feature points of the curb o not change as shown in Fig. 6. The points aroun 1600mm of the axis Y represent the roa surface an the curve points between 0mm an 2000mm of the axis X are the curb of the roa. Fig. 6. Angles (0, 30, -30 ) between the mobile robot an the curb an raw ata.

6 Tracking Control for Reliable Outoor Navigation Using Curb Detection 331 Fig. 7. Projection of collinear points onto a line. 3.1 Extracting the longest straight line The laser range finer senses the surface of roas ue to the small angle between the laser range finer an the mobile robot. Therefore, the longest straight line of the raw ata from laser range finer is the surface of roas an the curbs locates the eges of the roa. The longest straight line is extracte using Hough Transform [7], [8], [9]. In Hough transform, each line is represente by two parameters, commonly calle ρ an θ, which represent the length an angle from the origin of a normal to the line. Using this parameterization, an equation of the line can be written as: ρ = x cosθ + y sinθ (1) n ( xn, y n) is the n-th measurement ata, where n is 1 to 361 an θ [0,2 π ). The ominant ρ an θ are obtaine by Hough Transform, calle ρ an θ as shown in Fig. 8. n Fig. 8. Dominant ρ an θ foun by Hough Transform. The straight line in Fig. 9. shows the longest straight line represente by ρ an θ.

7 332 Recent Avances in Mobile Robotics Fig. 9. Raw ata an the longest straight line. 3.2 Fitting the points aroun the longest straight line It is neee to fit the raw ata points corresponing to the straight line for ientifying the roa surface an the curbs. The roa surface an curbs exist on the bounary of the straight line from Fig. 10. To obtain the bounary points of the line, ρ is first calculate by Eq. (1) for each raw scan ata with θ. An then, choose the points satisfying the following Eq. (2). The points of Fig. 6 show the fitting points with Δ ρ of 100mm. ρ Δρ ρ ρ +Δ ρ (2) Fig. 10. Points aroun the longest straight line. 3.3 Grouping the points an fining the roa surface The points aroun the longest straight line inclue the roa surface an obstacles. To extract the roa surface, we classify into six groups (ellipses in Fig. 11). Points of each group are continuous. The biggest group among the six groups inicates the sense roa surface.

8 Tracking Control for Reliable Outoor Navigation Using Curb Detection 333 Fig. 11. Groupe points an foun roa surface. 3.4 Extracting the curb ege points The scanne ata of a flat roa surface has two specific characteristics. One is that the scanne ata of roa surface is on the straight line an the interval between ajacent two points is small. The other is that the slope of the straight line is parallel to the irection X of L a laser range finer. When the istance between ajacent two points is continuously within an the slope between them is less than σ, the two points are consiere as being on the straight line (Eq. (3)). The en points (stars in Fig. 12) of the straight line are the roa eges an also the start points of the curbs. Therefore the curb ege points coul be obtaine by fining the en points of the straight line. 2 2 i i+ 1 i i+ 1 ( x x ) + ( y y ) an yi yi tan xi x i+ 1 σ (3) Fig. 12. Extracte curb ege points.

9 334 Recent Avances in Mobile Robotics 3.5 Parameter estimation of curb The position of the mobile robot an the extracte curb point can be simultaneously represente in global coorinates. If we can calculate the relative pose of the mobile robot to the curb position, we can correct the mobile robot s pose against its colliing with the curb. Fig. 13 represents the both position in global coorinates. Y R(k) β k k ( nx k, Lk ( ), ylk ( )) ( x, y ) Ck ( ) Ck ( ) X R(k) φ k Y R(k-1) α k β k-1 ( n, x, y ( x, y ) k-1 Lk ( -1) Lk ( -1) Ck ( -1) Ck ( -1) k-1 Y G X R(k-1) X G φk-1 αk-1 xk : x position of the robot in global coorinate yk : y position of the robot in global coorinate θ : orientation of the robot in global coorinate x y x y k Lk ( ) Lk ( ) Ck ( ) Ck ( ) : x position of the curb in robot coorinate :y position of the curb in robot coorinate : x position of the curb in global coorinate : y position of the curb in global coorinate Fig. 13. Positions of the mobile robot an curbs in global coorinate. We have obtaine ( nk, xl( k), yl( k) ) from curb etection metho as explaine in Section III. Curb position ( xck ( ), y Ck ( )) in global coorinate can be obtaine from the curb position ( x y ) as shown in Eq. (4). Lk ( ), Lk ( ) xck ( ) sinθk cosθk xk xlk ( ) yck ( ) = cosθk sinθk yk ylk ( ) (4)

10 Tracking Control for Reliable Outoor Navigation Using Curb Detection Curb line equation If we assume that the curb is straight, we can express the curb eges to a line equation such as Eq. (5). ax + by + c = 0 (5) From the subsequent two curb points ( xck ( ), y Ck ( )) an ( xck ( 1), yck ( 1) ), we can fin the line equation parameters ( abc,, ) as shown in Eq. (6). y y y y = ( x x ) Ck ( ) Ck ( 1) Ck ( ) Ck ( ) xck ( ) xck ( 1) ( y y ) x+ ( x x ) y Ck ( ) Ck ( 1) Ck ( 1) Ck ( ) + ( x y x y ) = 0 a= y y Ck ( ) Ck ( 1) Ck ( 1) Ck ( ) Ck ( ) Ck ( 1) b = x x Ck ( 1) Ck ( ) c = x y x y Ck ( ) Ck ( 1) Ck ( 1) Ck ( ) (6) 3.7 Distance an angle between robot an curb We can also obtain the istance k between the robot an the curb from the line equation an angle φ k between robot an curb by geometric relation as shown in Fig. 11. Eq. (7) shows the istance k. k = ax + by + c k a k b (7) The angle φ k can be obtaine such as Eq. (8). φ = α β k k k α = atan2( y, x ) k L( k) L( k) βk = acos( ) x k 2 2 Lk ( ) + y Lk ( ) φk = atan2( yl( k), xl( k) ) acos( ) x k 2 2 Lk ( ) + y Lk ( ) (8) The propose curb etection algorithm is experimente to ientify the performance of it. The mobile robot was riven along a roa with the istance (1m) between the mobile robot an curbs. The tilte angle ( φ L in Fig. 4) between the mobile robot an the laser range finer is 25. The values an σ as 50mm an π /4 are selecte in Eq. (4.3). The navigation server sens the ata of curb ege points (position ata of stars in Fig. 14) to the remote server. The remote server receives the image an curbs eges ata from the navigation server an isplays the map of curbs an navigation information as shown in Fig. 16. The rectangular an the ots in the map represent the mobile robot an curb ege points, respectively.

11 336 Recent Avances in Mobile Robotics Fig. 14. Extracte curb ege points on the roa. (a) Fig. 15. Curb etection experiment. (a) The mobile robot tracking the curbs (b) Robot path an etecte curbs. (b)

12 Tracking Control for Reliable Outoor Navigation Using Curb Detection 337 Fig. 16. Screen of the remote server. The left an right-sie stars an the black triangles in Fig. 15(b), 17 show the etecte curbs an the robot path, respectively. The left-sie stars in Figures are irregular because the rightsie curb has regular shape (height: 13cm), but the left-sie of the roa is not the curb. It is just the structure with low height (2cm). Even though the mobile robot moves zigzag, the etecte right-sie curb path is smooth. The average error of the curb points is 2cm. Fig. 17. Robot path an extracte curb positions.

13 338 Recent Avances in Mobile Robotics Fig. 18 shows the istance between robot an curb, the curb ege angle α an angle φ between robot an curb, respectively. We can know that the propose curb etection algorithm prouces proper results an the istance an angle information calculate from the curb position coul be use for reliable an safe navigation. (a) (b) Fig 18. Results for curb etection. (a) Distance between robot an curb (b) Curb ege angle α

14 Tracking Control for Reliable Outoor Navigation Using Curb Detection 339 Fig. 18. Results for curb etection. (c) Angle φ between robot an curb. (c) 4. Tracking control using curb position An ATRV-mini is a nonholonomic mobile robot, equivalent to a four-wheele ifferential rive. Kanayama propose a kinematic control law in Cartesian coorinates for solving the trajectory tracking problems [10]. We a a term relate to the istance between the robot an the right-sie curb of roas to Kanayama controller. Y G Y r y r e θ r X r θ r e x Y c e y X c y c c O θ c xc xr X G Fig. 19. Mobile robot an reference robot.

15 340 Recent Avances in Mobile Robotics Consiering the Fig. 19, in which the mobile robot c is represente by the coorinates p = [ x ] T c yc θ of the center of mass, moving over plane with linear velocity υ an angular velocity ω. The matrix equation that escribes the kinematic moel of a mobile robot is given by x c cosθ sinθ υ y c sinθ cosθ = ω θ 0 1 (9) The posture tracking error vector e p is calculate in the reference robot frame Xr, Y r. e = R( θ )( p p) where R( θ ) is the rotation matrix. Differentiating the Eq. (10), yiels p r e x cosθ sinθ 0 xr xc ep e y sinθ cosθ 0 yr y, (10) = = c e θ θr θ c e ωey υ + υrcos( e ) x θ e y = ωex + υrsin( eθ ) e ω θ r ω The asymptotic convergence of posture error can be obtaine (11) V c υc kxex+ υrcos( eθ ) = ω = c ωr+ kyυr ey+ kθυrsin( eθ), (12) where k, k an k θ are positive constants, efine as controller gains. x y For reliable an safe navigation, we esign a new controller V by aing the extracte curb istance an angle information to the above Kanayama controller. e = V ref υ kxex+ υrcos( eθ ), (13) = ω = ωr+ υr( ky ey+ kθ sin( eθ) + ke+ kφsin φ) where ref is the reference istance from the curb for safety an k, k φ are positive constants as controller gains. If the robot is too close to the curb, the ae terms of the propose controller try to prohibit the robot colliing with curbs, an vice versa. We have performe two kins of experiments to evaluate the performance of the propose path tracking controller in outoor environment. One is that the mobile robot has to follow a straight path. The other is that the mobile robot has to follow a curve path.

16 Tracking Control for Reliable Outoor Navigation Using Curb Detection Straight path tracking We have performe a straight path tracking experiment, which target point is (78m, -22m) an linear velocity is 0.5m/sec. The gains of controller were etermine by some simulations an experiments. Fig. 20 shows the reference path an the error of path, position an angle of the robot. Fig. 20(a) shows the reference path an tracking path an the position error of 20cm at the final point, respectively. Even though DGPS position error of 1m has occurre at the point of 12m from X-axis, the mobile robot returne to its reference path by the stable tracking controller. Reference an Tracking path 30 reference path tracking path (a) 0.7 Commane linear velocity linear velocity [m/sec] Time [sec] (b) Fig. 20. (Continue)

17 342 Recent Avances in Mobile Robotics 20 Commane angular velocity 15 angular velocity [eg/sec] Time [sec] 0.2 (c) X-axis position error [m] Time [sec] 0.4 () Y-axis position error [m] Fig. 20. (Continue) Time [sec] (e)

18 Tracking Control for Reliable Outoor Navigation Using Curb Detection angle error [eg] Time [sec] (f) Fig. 20. Results for straight path tracking. (a) Reference path an tracking path (b) Controller linear velocity (c) Controller angular velocity () X-axis position error for robot coorinate (e) Y-axis position error for robot coorinate (f) Angle error for robot coorinate. 4.2 Curve path tracking We have performe a curve path tracking experiment, which linear velocity is 0.3m/sec an angular velocity is 0.06ra/s. Fig. 21 shows the reference path an the error of path, position an angle of the robot. Fig. 21(a) shows the reference path an tracking path. The X-axis position error an the angular error are 40cm an 7 at the final point, respectively. The reason that the errors are bigger than the straight path tracking experiment is relate to the characteristic of ski steering system of our mobile robot platform. It is necessary to optimize the gains of controller to reuce the errors Reference an Traking path reference path tracking path 6 Y [m] Fig. 21. (Continue) X [m] (a)

19 344 Recent Avances in Mobile Robotics 0.35 Commane linear velocity linear velocity [m/sec] Time [sec] 14 (b) Commane angular velocity angular velocity [eg/sec] Time [sec] (c) X-axis position error [m] Fig. 21. (Continue) Time [sec] ()

20 Tracking Control for Reliable Outoor Navigation Using Curb Detection Y-axis position error [m] Time [sec] (e) 8 angle error [eg] Time [sec] (f) Fig. 21. Results for curve path tracking. (a) Reference path an tracking path (b) Controller linear velocity (c) Controller angular velocity () X-axis position error for robot coorinate (e) Y-axis position error for robot coorinate (f) Angle error for robot coorinate 5. Conclusion In this chapter, an algorithm is escribe to etect roa curb position through a laser range finer. The curbs map was built an the with of the roa was calculate by the etecte curbs. The propose algorithm is to calculate the istance an the angle between the mobile robot an the curb. A new controller is esigne by aing the extracte curb istance an angle information to the tracking controller. It helps the mobile robot to navigate safely an reliably. To ientify the availability of the propose algorithm, navigation experiments was performe in outoor environment an proper results was obtaine.

21 346 Recent Avances in Mobile Robotics 6. References [1] S. Thrun at el. (2000). Probabilistic Algorithms an the Interactive Museum Tour-Guie Robot Minerva, International Journal of Robotics Research, Vol.19, No.11, pp [2] Richar Thrapp at el. (2001). Robust localization algorithms for an autonomous campus tour guie, Proc. of IEEE Int l Conf. on Robotics an Automation, pp [3] C.C. Wang an C. Thorpe, Simultaneous Localization an Mapping with Detection an Tracking of Moving Objects, Proc. of IEEE Int l Conf. on Robotics an Automation, 2002, pp [4] W. S. Wijesoma, K. R. S. Koagoa, an Arjuna P. Balasuriya, Roa-Bounary Detection an Tracking Using Laar Sensing, IEEE Trans. On Robotics an Automation, Vol.20, No.3, 2004 [5] Seung-Hun Kim at el. (2006). A hybri autonomous/teleoperate strategy for reliable mobile robot outoor navigation, SICE-ICASE Int. Joint Conf., pp [6] K. Ohno at el. (2003). Outoor Navigation of a Mobile Robot between Builings base on DGPS an Oometry Data Fusion, Proc. of IEEE Int l Conf. on Robotics an Automation, pp [7] J. Forsberg at el. (March 1995). Mobile robot navigation using the rangeweighte Hough transform, IEEE Robotics & Automation Magazine, vol. 2, pp [8] R. O. Dua. & P. E. Hart. (1972). Use of the Hough transformation to etect lines an curves in pictures, Communications of the ACM, vol. 15, pp [9] P. V. C. Hough. (December 1962). Methos an means for recognizing complex patterns, in U.S. Patent [10] Y. Kanayama at el. (1990). A stable tracking control metho for an autonomous mobile robot, IEEE Int. Conf. on Robotics an Automation, vol. 1, pp

22 Recent Avances in Mobile Robotics Eite by Dr. Anon Topalov ISBN Har cover, 452 pages Publisher InTech Publishe online 14, December, 2011 Publishe in print eition December, 2011 Mobile robots are the focus of a great eal of current research in robotics. Mobile robotics is a young, multiisciplinary fiel involving knowlege from many areas, incluing electrical, electronic an mechanical engineering, computer, cognitive an social sciences. Being engage in the esign of automate systems, it lies at the intersection of artificial intelligence, computational vision, an robotics. Thanks to the numerous researchers sharing their goals, visions an results within the community, mobile robotics is becoming a very rich an stimulating area. The book Recent Avances in Mobile Robotics aresses the topic by integrating contributions from many researchers aroun the globe. It emphasizes the computational methos of programming mobile robots, rather than the methos of constructing the harware. Its content reflects ifferent complementary aspects of theory an practice, which have recently taken place. We believe that it will serve as a valuable hanbook to those who work in research an evelopment of mobile robots. How to reference In orer to correctly reference this scholarly work, feel free to copy an paste the following: Seung-Hun Kim (2011). Tracking Control for Reliable Outoor Navigation Using Curb Detection, Recent Avances in Mobile Robotics, Dr. Anon Topalov (E.), ISBN: , InTech, Available from: InTech Europe University Campus STeP Ri Slavka Krautzeka 83/A Rijeka, Croatia Phone: +385 (51) Fax: +385 (51) InTech China Unit 405, Office Block, Hotel Equatorial Shanghai No.65, Yan An Roa (West), Shanghai, , China Phone: Fax:

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