- Email: [email protected]
The Improvement of Sonar-Based Mobile Robot Localization Method by Multiple Beacons
Copyrighl © 1996IFAC 13th Triennial World Cong re~. Sill) Francisco , USA
Jb-06S
TIlE IMPROVEMENT OF SONAR·BASED MOBILE ROBOT WCALIZATION METIIOD BY MULTIPLE BEACONS
H.R. Btom·, KoI. Koh* and H.S.
Coo··
* Research &: Development Laboratory LG Industrial Systems, Co" Lld. 533 Hog(U -dong, Dongan-go_ Anyang, 430-
*.
Professor, lkpartment of Mechanical Engineering Korea Advanced Institute of Science and Technology 373-/ Kusong-dong, Yusong-gu, Taejon, 305-701, Korea. e-maii:/[email protected]@lca.kaist.ac.kr
Abstract: This paper proposes a new method. of estimating the plsition and heading angle of a mobile robot navigating in indoor environments. In this paper, typical positioning errors of a localization method of using two beacons are computed. TIle proposed localization method utilizes three passive beacons in order to reliably detennine the mobile robot08 current position and heading angle. Localization experiments using two beacons as well as three beacons are conducted in indoor environments. 1be perfonnance and validity of the proposed method. were evaluated through a series of the experiments and the experimental results of the navigation were presented.
KeywOl'ds: Mobile robots; Ultrasonic Transducer; Position Estimation; &ror analysis.
1. INTRODUCTION Most robotic vehicles follow a guidepath which is a buried wire or reflective strips placed on the floor. As the factories progress towards the automation, the transportation duties of
the mobile robots will become increasingly more complex and will require the mobile robot with the navigation systems which are accurate and do not depend on tracks or buried wires. Many automated guidance systems have been proposed and developed in the past year (Tsumura. 1991; 1992). More advanced vehicles. so called free ranging mobile robot, navigate with dead reckoning system which rely on the integration of wheel rotation increments (Yuta. et al.. 1985). Due to the effects of wheel slippage and wheel imperfection however, the tracking error is accumulated. Therefore. absolute position and heading angle determination is necessary for accurately locating free ranging mobile robot.
Obtaining the accurate position and orientation information of a mobile robot is not a new topic. The main design objccti yes of a localization system is speed, cost and accuracy. Various sensors such as vision. optical range fmders. ultrasonic beacons and ultrasonic sensors have been used in localization procedure. Vision guided localization methods result in superior accuracy except the reduction of speed and increased C05l. In relation to these many algorithms have bun proposed to reduce the extensive computation time (1Cim and Cho, 1992). The beacon navigation system uses optical wave or sound wave. The system using optical wave consists of a laser beam.
three corner cuhes and a photo detector (Tsumura, 1991; Nishide, et al .• 1986). The reflective strips in the environment and a rotating laser mounted on the mobile robot were used to estimate the current position and orientation (Cox, 1991). The system using sound wave consists of one ultrasonic receiver
199
and several ultrasonic transmitters (Kleeman, 1992). TIle transmitters here acting as ultrasonic beacons ftre the coded ultrasonic pulses, and this method requires additional transmitter controller. Ultrasonic beacon method dramatically improves speed with an expected decrease in accuracy due to ultrasonic sensors with large beamwidth. However. it requires that the environment should be redefined by addition of ultrasonic beacons. Research. in pure ultrasonic ranging has been directed towards map matching techniques such as statistical map matching, wall matching and individual sensor matching techniques. Several studies (Drurnbeller, 1981; Leonard and DurnntWhite, 1992; Holenstein, et al., 1992) have tried to localize a mobile robot using a matching technique, which compares the ultrasonic sensor data with an environment model. Drumheller (1981) modeled a room a.< a list of line segments indicating the position of walls and determined several candidates of the position and heading angle of a mobile robot by correlating the straight line segments extracted from sonar contour in range data with the room model. Leonard and Durrant-White (1991 and 1992) mode led a room using the map of the locations of geometric beacons, which can be observed by successively measuring the objects such as walls, comers and edges naturally existing in the environment. The position and heading angle were then determined by matching between observed geometric beacons and a priori map of beacon location. These model-based methods are, however, not suitable for dynamicalJy changing environment or complex environment with many geometric beacons. Even though various localization systems have been proposed, none of them have proven superiority over other methods. mainly because the used sensors have been subject to limited accuracy and degraded by disturbance and environmental conditions.
In the previous study (Beom and Cho, 1995), we proposed an effective mobile robot localization method using a single rotating sonar sensor and two passive cylindrical beacons. The method does not require a complex environment model since the artificially designed cylinders are used as passive beacons. lbis method offers advantage of simplicity and cost. [n mis paper, typical positioning errors of the method of using two beacons are computed and a new method of using three beacons for localization of the mobile robot in indoor environments is proposed. The localization system described in this paper is a significant improvement over an earlier version (Beom and Cbo. 1995) in terms of accuracy. TIlls system takes the same approach as the one in the previous study ex.cept using an additional beacon. "The experimental results suppon that excellent positioning accuracy is possible over a workspace irrespective of mobile robot locations. Unlike dead reckoning systems. navigation errors of the proposed method are dependent solely upon the mobile robot's position in the workspace and not the traveled distance. Based on the results of the error analysis of localization method with two beacons. we propose a locaJization method always
reliably estimating the mobile robot posluon and heading angle by the addition of a beacon. Also, we present a method of selecting either one of two sets of position and heading angle calculated by using an additional beacon. The performance and validity of the proposed method are evaluated through the analysis of the experimental results.
2. MOBILE ROBOT LOCALIZATION In order to localize the mobile robot using only a sonar scan
data obtained from a single mobile robot location, more than two cylinders with different diameters are required as shown in Fig. 1. Each cylinder can be distinguished by using the angular extents in the previous paper. In this figure, R_ := 4Dm and RIIIil1 = O.45m denote the maximum and the minimum measurement ranges of a single rotating ultrasonic sensor, respectively. The cIl j denotes the angle difference between the large beacon LB j and me small beacon SB. The angle ~ I is used to select either one of two beacon pairs,
LBI-SB and LB2-SB. The R, = O.3m denotes the radius of the mobile robot.
Fig. 1. 1be measurement ranges and relationship between three beacons and a mobile robol.
Let us consider that the mobile robot is locatod at an unknown point (x" y,) with respect to the world coordinate frame (W) fixed at a point 0 as shown in Fig. 2. In this figure. the center positions of the large and small beacons are given by (x"h) and (x"Ys)' respectively, and the radii of the large
and small beacons are given by r, = O.07m and TS =O.OI9m , respectively. Accordingly, we can find the position and heading angle of mobile robot because 0" '1', and q>, can be acquired from sonar scan data 10 be explained later. Here, the 0Land li s denote the range values which are
a"
measured by a single rotating sonar sensor . The mobile robot positions correspond to the intersection points of two circles
200
whtch are the loci of possible positions corresponding to the measured angles q) L and
mobile robot moves by one step towards the sub-goal position.
If estimation values are reasonable, the mobile robot updates its posture and moves (owards the goal position.
"-
; ~
/
...
' -~
... !
'x
._SmIO.oon b••
{~t
:
~
• x
0
a3 ( 16.31rn, 6.1J5,m, O.l»rlild) al' (16.41m, UQm, O.OOrad)
Fig. 2 . Analytic geometry solution. :it
experiments using two beacons are performed in an indoor lobby with different arrangements of objects and the lobby is fiat, approximately 19.4m by 9.475m wide. Fig. 3 shows a sketch of the top view of the room with the object drawn in the hatched line. TIle mobile robot was initially located at the origin of the world coordinate frame {WJ and the goal position was given as (l69m.7.Om). In the experiments. two
beacon pairs were utilized to determine the absolute position and heading angle of the mobile robot. The small beacon and large one consisting of a beacon pair in the vicinity of the goal position were located at the two positions, (17 .85m,6.S8m) and (I S.9Sm,7.91 m), respectively. A small beacon and large one of another beacon pair were located at the two positions, (7.90m,4.85m) and (9.90m,4.8Sml, respectively. The localization operation was performed within two circles (1.2 and L3) with a radius of O.4m and the conters at (8.90m,6.16ml and (16.45m ,6.58m), re spectively . The conters of the three
circles play a role of a experiments.
sub~goal
point in navigation
From the start position, the mobile robot with sonar~based navigation system (Beam, 1994) moves towards the sub-goal position while avoiding the obstacles. When the mobile robot is placed within the specified localization zones, the mobile robot stops. Using the localization algorithm presented in the references (Beom and Cbo, 1995; Beom, 1994), the mobile robot estimates its CWTcnt location and heading angle. If localization fails, the scanning operation resumes after the
0
.)
Af1GIe. (raG)
lncaliUJlion experiments using two beacons. Localization
P ..,h Itngl h=ZI.6Om, .1iIp$~ li~' 36.7heo, .v.rage velocilywO. 15B0rn'MK:
Fig. 3. The environment for localization experiments with two beacons system and the experimental results. Fig. 3 shows the experimental results when the localization operations are perfonned within two circles. L2 and D . The figure shows the location of obstacles, the robot trajectories and its heading angles calculated by the dead reckoning system and includes four robot postures wruch are expressed by position and heading angle. 1be and _: listed in each
_I
figure denote the robot postW"es calculated within L, circle by the dead reckoner and the beacon system. respectively. As can be seen from the experimental navigation results, the robot trajectories show discontinuities within two circles, L2 and L3. These disconlinuities in the trajectory and heading angle were caused by corrective action of the localization system with two beacons. These discontinuities result from the inaccuracy in the dead reckoning sensor, the variation of the distance between two wheels due to unevenness of the ground and the slipp"ge between the wheel and the ground. The large heading angle error almost resulted from the wheels' slippage when the mobile robot changes its direction. Even if the wheel slippage occurs, the true position and heading angle of the mobile robot could be updated by two beacon pairs and consequently the mobile robot could arrive at the given goal position while avoiding the obstacles.
201
3. THE IMPROVEMENT OF TWO BEACON SYSTEM
If two beacons are used to detennine the absolute posture of the mobile robot. the estimation accuracy depends on tbe location of loca1ization zones. This can be verified through theoretical error analysis of the beacon system consisting of two cylindrical beacons. Then, based upon the results obtained from error analysis we will propose a new method of using three beacons and present a scheme of appropriately selecting a proper pair hetween two pairs of position and heading angle of mobile robot which can be obtained by three beacons.
where ~L and
Ss
range over all possible values of range
measurement error and sup denotes the supremum. Just as the position error, a heading angle error is defined as the worst case angle error, E;(dL . ds'~L) ' as follows:
3.1. Theoretical analysis of the position and heading angle errors As long as x.' y. and 9 arc totally differentiable with
respect to the measured distances and angles S L ' 15 s'
where the ~.
ranges over all possible values of angle
measurement error_
y
-+-+---f-_e-+-+--x
Fig. 4. The mobile robot workspace for error analysis of the proposed localization method.
In this paper, we define the position error as the worst case displacement, E~ (dL.ds}' between the ideal and measured positions_ 100 worst case position error is defined by
(a) Errors I,., he-o.alng angle
(10) [;",-,-O,.s I,.. POSition
Fig. S. 1he worst case errors at the various locations of mobile robot. Using the Eqs. (I) and (2), the wo",! case errors are evaluated over the workspace where two beacons can be always detected by rotating sonar. The lightly shaded region shown in Fig. 4
202
represen(s the region where two beacons can be always simultaneously de~ted by a single rotating sonar. The darkly shaded two circles represent the large and small beacons . TIle analysis of the position and beading angle error is done inside tbe lightly shaded region . It is assumed that the tolerant distance and angle error are iO.OIm and ±w o, respectively, and that the small and large beacons are located at coordinate points (0.9,.,0.0..) and (.O.9m,O.Om), respectively. Here, the distance do between the centers of two beacons is 1.&n. Small and large beacons drawn by the darldy shaded two circles are the cylinders with radii rs = 0.Ql9m and r" = 0.07m, respectively. First, after calculating all the errors with variations of ~ L ,~s and ~tI at a position inside the lightly shaded region, the position and heading angle errors at the position take the maximum value among all the calculated errors, respectively. If the above procedure is applied to all the positions inside tbe lightly shaded region, all the worst case errors drawn in Fig. 5(a) and (b) can be obtained. As can be seen from these figures. the estimation errors of a method using two cylindrical beacons get larger when the mobile robot is near to X-axis. Namely, the estimation errors depends on the absolute value of the angle difference <1>, sbown in Fig. I. Here , <1>, denotes ~ = i-I's -
'1'"1.
If <1>" (0 s: <1>, s: It)
0
approaches 180 • the estimation errors become large due to inaccuracy of ultrasonic sensor. It is required to use an additional beacon so that there exists at least one location of mobi le robot where the three center points of two beacons and the mobile robot are not placed on the straight line.
3.2. Localization experiments using three beacons ' .25
T'"--:;,.---------......--, SB{O.3m . '.2m) \
L82(2.1m. 1.2m)
\ \ \
E .\. _ 0.00 +--............................................... pa'h p, ).;'
updating the POSIUon and heading angle. we conducted a series of experiments using two large beacons. LB I and LB2, and a small beacon SB. The three beacons were arranged as shown in FIg. 6. The position and beading angle of the mobile robot can be calculated from a beacon pair composed of a large beacon and a small beacon. From two beacon pairs B 1 and B2 shown in Fig. 6, two pairs of position and heading angle can be found. The beacon pair BI consists of LBI and SB while the beacon pair B2 consists of LB2 and SB. The position and beading angle of the mobile robot are calculated by two beacon pairs, BI and B2, respectively, at the location marked as dark rectangle on a straight line path PI as shown in Fig. 6.
The experimental results; The experimental procedure of three beacon system is the same as that of the method of using two beacon system. The mobile robot stops at the locations marked as dark rectangles on the path PI shown in Fig. 6 . Then, the robot scans the front area to acquire the sonar scan data. In this case, when the mobile robot is placed a t the origin (0,0) of the frame (W\ as shown in Fig. 6. From these sonar scan data, all the RCD' , associated with beacons are obtained by applying, in turn, the smoOlhness and symmetricily conditions. 1ben. we apply a priori known information of the beacon pair B I to the obtained ReO's. As a consequence of the above procedure, only two remained ReD's are used to determine the position and heading angle of the mobile robot. Once the position and heading angle of the robot are determined by applying a priori known information of the beacon pair B2 to the above obtained RCD's, another position and heading angle of the robot using the beacon pair B2 should be obtained. Finally, we can calculate the two pairs of position and heading angle of the robot from two beacon pairs B I and B2. Also, the angles 4»/ ~jtql are obtained simultaneously as shown in Fig. 7(c). These angles are used to decide which pair of two positions and heading angles is suitable for updating the position and beading angle of the roboe Fig. 7 shows the experimental results at all tbe locations marked as rectangle on the planned path PI. Figs. 7(a) and (b) show the errors in position and heading angle, respectively, while Fig. 7(c) shows the value of '1>, =I~I . The position and heading angle errors, E" and
E, ' are defined, as foU ows. Beaoon pair B1 : SB, LB1 Beacon pair 82: S8, LB2
\
E"
=~(XR -xT )' + (Y. -
YT) '
E,=16-6 I
(3)
T
LB1(1.8m, -a.9m)
" .25
+-------,...-------l
0.00
1.25 X, (m)
2.50
Fig. 6. Three beacon arrangement and a straightlin. path for experiments,
Experimental conditions; In order to find a method of reliably
In the above equations, the
(.t~ , y~)
and e
denote the
position and the heading angle of the mobile robot estimated by a localization method, while (XT'YT ) and eT denote the actual position and the beading angle, respectively. The actual position and tbe beading angle were calculated from the positions of the two wheels using tiles (3Ocmx3Ocm) decorated on me Ooor. As can be seen from Fig. 7. the estimation errors
203
become large as the
IA
180 0 • The position and
heading angle obtained by the beacon pair B2 are found to be more accurate than those obtained by the beacon pair B 1. In order to select a set of the two pairs of position and heading angle, we used the ct- j =I&,,(i = 1,2) :S 180" or 0"" i,(i = 1,2) :S 26" can not be used as those of the robot. The fanner results in inaccuracy of sensor as shown in error analysis, while the latter results in interference between two beacons. It is important to appropriately build the three beacons so that all the <1>, and <1>, are less than 150" and greater than 26". By properly selecting the beacon pairs in the workspace based on the value of angle difference fIlj = 16
0.3.----------------, ---0--
--
OR method
---+-
o.o,li===-=.",......,(..............- -.......&;:=a~ 0.0 0.5 1.0 1.5 2.0 X,(m)
la) 6~---------------.----------,
0.5
1.0
1.5
2.0
X,(m)
!=t
""lJt
e
---.
..,
-
(b)
0.0
,
0.5
1.0
: :~-3 1.5
2.0
X. (m) (c)
Fig. 7. The experimental results of the estimation of position and heading angle when the mobile robot follows the path PI. 4. CONCLUSIONS After theoretically analyzing the position and beading angle errors, we have developed a mobile robot localization system which makes use of three cylindrical beacons and a single rotating ultrasonic sensor. 1be proposed method can estimate
the position and heading angle of a mobile robot using the sonar scan data obtained from the location of a single mobile robot. Localization experiments were performed by using two beacons as well as three beacons in actual indoor environments. The performance and validity of the proposed method were evaluated through a series of the experiments in actual indoor environment. It is believed that the proposed method can be used as an alternative of mobile robot localization in environment where other methods can not be used. REFERENCES Beom, H. R. and H. S. Cho (1995). Mobile robot locaiization using a single rotating sonar and two cylindrical beacon. Robolica 13, pp. 243-252. Beom, H. R. (1994). A study on the AI-based navigation and obstacle detection for mobile robots. Ph.D. Dissertation, KAIST. Cox, I. J. (1991). Blanche - an experiment in guidance and navigation of an autonomous robot vehecle. IEEE Trans. Robolics and Aulomation, pp. 193-204. Drumheller, M. (1987). Mobile robot localization using sonar. IEEE Trans. Pall. Anal. and Machine Inlell. 9, No.2, pp. 325-332. HoIenstein, A. A., M.A. Muller and E. Badreddin (1992). Mobile robot localization in structured environment cluttered with obstacles. Proc. IEEE Int. Cont Robotics andAulomation , pp.2576-2581. !Gm, J. H. and H.S. Cho (1992). Real-time determination of a mobile robot's position by linear scanning of a landmark. Robolica 10, pp. 309-319. Kleeman. L. (1992). Optimal estimation of position and heading for mobile robots using ultrasonic beacons and dead reckoning. Proc. IEEE 1nl. Con/. Robotics and Aulomalion. pp.2582-2587. Leonard, J. J. and H. F. Durrant-Whyte (1991). Mobile robot localization by tracking geometric beacons. IEEE Trans. Robolics and AUlomalion 7, No.3, pp. 376-382. Leonard, J. J. and H. F. Durrant-Whyte (1992). Dynamic map building for an autonomous mobile robot. The Inlemntional Journal of Robolics Research 11, No.4, pp . 286-298. Nishide, K .. M. Hanawa and T. Kondo (1986). Automatic position findings of vehicle by means of Laser. Proc. IEEE 1nl. Con/. Robotics and AUlomalion, pp.1343-1348. Tsumura, T. (1994). AGY in japan - recent trends of advanced research, development, and industrial applications. Proc. 1nl. Con[.lnlelligenl Robols and Syslems, pp. 1477-1484. Tsumura, T. (1991). Recent advances of intelligent vehicle perspective. SICE vo!. 30, No. 1, pp. 1-8. Yuta, S., Y. Kanayarn.. T. Yajima and S. Shimamura (1985). An implementation of MICHI-A locomotion command system for intelligent mobile robot. Proc. 1nl. Con[. Advanced Robolics, pp. 127-134.
204
Jb-06S
TIlE IMPROVEMENT OF SONAR·BASED MOBILE ROBOT WCALIZATION METIIOD BY MULTIPLE BEACONS
H.R. Btom·, KoI. Koh* and H.S.
Coo··
* Research &: Development Laboratory LG Industrial Systems, Co" Lld. 533 Hog(U -dong, Dongan-go_ Anyang, 430-
*.
Professor, lkpartment of Mechanical Engineering Korea Advanced Institute of Science and Technology 373-/ Kusong-dong, Yusong-gu, Taejon, 305-701, Korea. e-maii:/[email protected]@lca.kaist.ac.kr
Abstract: This paper proposes a new method. of estimating the plsition and heading angle of a mobile robot navigating in indoor environments. In this paper, typical positioning errors of a localization method of using two beacons are computed. TIle proposed localization method utilizes three passive beacons in order to reliably detennine the mobile robot08 current position and heading angle. Localization experiments using two beacons as well as three beacons are conducted in indoor environments. 1be perfonnance and validity of the proposed method. were evaluated through a series of the experiments and the experimental results of the navigation were presented.
KeywOl'ds: Mobile robots; Ultrasonic Transducer; Position Estimation; &ror analysis.
1. INTRODUCTION Most robotic vehicles follow a guidepath which is a buried wire or reflective strips placed on the floor. As the factories progress towards the automation, the transportation duties of
the mobile robots will become increasingly more complex and will require the mobile robot with the navigation systems which are accurate and do not depend on tracks or buried wires. Many automated guidance systems have been proposed and developed in the past year (Tsumura. 1991; 1992). More advanced vehicles. so called free ranging mobile robot, navigate with dead reckoning system which rely on the integration of wheel rotation increments (Yuta. et al.. 1985). Due to the effects of wheel slippage and wheel imperfection however, the tracking error is accumulated. Therefore. absolute position and heading angle determination is necessary for accurately locating free ranging mobile robot.
Obtaining the accurate position and orientation information of a mobile robot is not a new topic. The main design objccti yes of a localization system is speed, cost and accuracy. Various sensors such as vision. optical range fmders. ultrasonic beacons and ultrasonic sensors have been used in localization procedure. Vision guided localization methods result in superior accuracy except the reduction of speed and increased C05l. In relation to these many algorithms have bun proposed to reduce the extensive computation time (1Cim and Cho, 1992). The beacon navigation system uses optical wave or sound wave. The system using optical wave consists of a laser beam.
three corner cuhes and a photo detector (Tsumura, 1991; Nishide, et al .• 1986). The reflective strips in the environment and a rotating laser mounted on the mobile robot were used to estimate the current position and orientation (Cox, 1991). The system using sound wave consists of one ultrasonic receiver
199
and several ultrasonic transmitters (Kleeman, 1992). TIle transmitters here acting as ultrasonic beacons ftre the coded ultrasonic pulses, and this method requires additional transmitter controller. Ultrasonic beacon method dramatically improves speed with an expected decrease in accuracy due to ultrasonic sensors with large beamwidth. However. it requires that the environment should be redefined by addition of ultrasonic beacons. Research. in pure ultrasonic ranging has been directed towards map matching techniques such as statistical map matching, wall matching and individual sensor matching techniques. Several studies (Drurnbeller, 1981; Leonard and DurnntWhite, 1992; Holenstein, et al., 1992) have tried to localize a mobile robot using a matching technique, which compares the ultrasonic sensor data with an environment model. Drumheller (1981) modeled a room a.< a list of line segments indicating the position of walls and determined several candidates of the position and heading angle of a mobile robot by correlating the straight line segments extracted from sonar contour in range data with the room model. Leonard and Durrant-White (1991 and 1992) mode led a room using the map of the locations of geometric beacons, which can be observed by successively measuring the objects such as walls, comers and edges naturally existing in the environment. The position and heading angle were then determined by matching between observed geometric beacons and a priori map of beacon location. These model-based methods are, however, not suitable for dynamicalJy changing environment or complex environment with many geometric beacons. Even though various localization systems have been proposed, none of them have proven superiority over other methods. mainly because the used sensors have been subject to limited accuracy and degraded by disturbance and environmental conditions.
In the previous study (Beom and Cho, 1995), we proposed an effective mobile robot localization method using a single rotating sonar sensor and two passive cylindrical beacons. The method does not require a complex environment model since the artificially designed cylinders are used as passive beacons. lbis method offers advantage of simplicity and cost. [n mis paper, typical positioning errors of the method of using two beacons are computed and a new method of using three beacons for localization of the mobile robot in indoor environments is proposed. The localization system described in this paper is a significant improvement over an earlier version (Beom and Cbo. 1995) in terms of accuracy. TIlls system takes the same approach as the one in the previous study ex.cept using an additional beacon. "The experimental results suppon that excellent positioning accuracy is possible over a workspace irrespective of mobile robot locations. Unlike dead reckoning systems. navigation errors of the proposed method are dependent solely upon the mobile robot's position in the workspace and not the traveled distance. Based on the results of the error analysis of localization method with two beacons. we propose a locaJization method always
reliably estimating the mobile robot posluon and heading angle by the addition of a beacon. Also, we present a method of selecting either one of two sets of position and heading angle calculated by using an additional beacon. The performance and validity of the proposed method are evaluated through the analysis of the experimental results.
2. MOBILE ROBOT LOCALIZATION In order to localize the mobile robot using only a sonar scan
data obtained from a single mobile robot location, more than two cylinders with different diameters are required as shown in Fig. 1. Each cylinder can be distinguished by using the angular extents in the previous paper. In this figure, R_ := 4Dm and RIIIil1 = O.45m denote the maximum and the minimum measurement ranges of a single rotating ultrasonic sensor, respectively. The cIl j denotes the angle difference between the large beacon LB j and me small beacon SB. The angle ~ I is used to select either one of two beacon pairs,
LBI-SB and LB2-SB. The R, = O.3m denotes the radius of the mobile robot.
Fig. 1. 1be measurement ranges and relationship between three beacons and a mobile robol.
Let us consider that the mobile robot is locatod at an unknown point (x" y,) with respect to the world coordinate frame (W) fixed at a point 0 as shown in Fig. 2. In this figure. the center positions of the large and small beacons are given by (x"h) and (x"Ys)' respectively, and the radii of the large
and small beacons are given by r, = O.07m and TS =O.OI9m , respectively. Accordingly, we can find the position and heading angle of mobile robot because 0" '1', and q>, can be acquired from sonar scan data 10 be explained later. Here, the 0Land li s denote the range values which are
a"
measured by a single rotating sonar sensor . The mobile robot positions correspond to the intersection points of two circles
200
whtch are the loci of possible positions corresponding to the measured angles q) L and
mobile robot moves by one step towards the sub-goal position.
If estimation values are reasonable, the mobile robot updates its posture and moves (owards the goal position.
"-
; ~
/
...
' -~
... !
'x
._SmIO.oon b••
{~t
:
~
• x
0
a3 ( 16.31rn, 6.1J5,m, O.l»rlild) al' (16.41m, UQm, O.OOrad)
Fig. 2 . Analytic geometry solution. :it
experiments using two beacons are performed in an indoor lobby with different arrangements of objects and the lobby is fiat, approximately 19.4m by 9.475m wide. Fig. 3 shows a sketch of the top view of the room with the object drawn in the hatched line. TIle mobile robot was initially located at the origin of the world coordinate frame {WJ and the goal position was given as (l69m.7.Om). In the experiments. two
beacon pairs were utilized to determine the absolute position and heading angle of the mobile robot. The small beacon and large one consisting of a beacon pair in the vicinity of the goal position were located at the two positions, (17 .85m,6.S8m) and (I S.9Sm,7.91 m), respectively. A small beacon and large one of another beacon pair were located at the two positions, (7.90m,4.85m) and (9.90m,4.8Sml, respectively. The localization operation was performed within two circles (1.2 and L3) with a radius of O.4m and the conters at (8.90m,6.16ml and (16.45m ,6.58m), re spectively . The conters of the three
circles play a role of a experiments.
sub~goal
point in navigation
From the start position, the mobile robot with sonar~based navigation system (Beam, 1994) moves towards the sub-goal position while avoiding the obstacles. When the mobile robot is placed within the specified localization zones, the mobile robot stops. Using the localization algorithm presented in the references (Beom and Cbo, 1995; Beom, 1994), the mobile robot estimates its CWTcnt location and heading angle. If localization fails, the scanning operation resumes after the
0
.)
Af1GIe. (raG)
lncaliUJlion experiments using two beacons. Localization
P ..,h Itngl h=ZI.6Om, .1iIp$~ li~' 36.7heo, .v.rage velocilywO. 15B0rn'MK:
Fig. 3. The environment for localization experiments with two beacons system and the experimental results. Fig. 3 shows the experimental results when the localization operations are perfonned within two circles. L2 and D . The figure shows the location of obstacles, the robot trajectories and its heading angles calculated by the dead reckoning system and includes four robot postures wruch are expressed by position and heading angle. 1be and _: listed in each
_I
figure denote the robot postW"es calculated within L, circle by the dead reckoner and the beacon system. respectively. As can be seen from the experimental navigation results, the robot trajectories show discontinuities within two circles, L2 and L3. These disconlinuities in the trajectory and heading angle were caused by corrective action of the localization system with two beacons. These discontinuities result from the inaccuracy in the dead reckoning sensor, the variation of the distance between two wheels due to unevenness of the ground and the slipp"ge between the wheel and the ground. The large heading angle error almost resulted from the wheels' slippage when the mobile robot changes its direction. Even if the wheel slippage occurs, the true position and heading angle of the mobile robot could be updated by two beacon pairs and consequently the mobile robot could arrive at the given goal position while avoiding the obstacles.
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3. THE IMPROVEMENT OF TWO BEACON SYSTEM
If two beacons are used to detennine the absolute posture of the mobile robot. the estimation accuracy depends on tbe location of loca1ization zones. This can be verified through theoretical error analysis of the beacon system consisting of two cylindrical beacons. Then, based upon the results obtained from error analysis we will propose a new method of using three beacons and present a scheme of appropriately selecting a proper pair hetween two pairs of position and heading angle of mobile robot which can be obtained by three beacons.
where ~L and
Ss
range over all possible values of range
measurement error and sup denotes the supremum. Just as the position error, a heading angle error is defined as the worst case angle error, E;(dL . ds'~L) ' as follows:
3.1. Theoretical analysis of the position and heading angle errors As long as x.' y. and 9 arc totally differentiable with
respect to the measured distances and angles S L ' 15 s'
where the ~.
ranges over all possible values of angle
measurement error_
y
-+-+---f-_e-+-+--x
Fig. 4. The mobile robot workspace for error analysis of the proposed localization method.
In this paper, we define the position error as the worst case displacement, E~ (dL.ds}' between the ideal and measured positions_ 100 worst case position error is defined by
(a) Errors I,., he-o.alng angle
(10) [;",-,-O,.s I,.. POSition
Fig. S. 1he worst case errors at the various locations of mobile robot. Using the Eqs. (I) and (2), the wo",! case errors are evaluated over the workspace where two beacons can be always detected by rotating sonar. The lightly shaded region shown in Fig. 4
202
represen(s the region where two beacons can be always simultaneously de~ted by a single rotating sonar. The darkly shaded two circles represent the large and small beacons . TIle analysis of the position and beading angle error is done inside tbe lightly shaded region . It is assumed that the tolerant distance and angle error are iO.OIm and ±w o, respectively, and that the small and large beacons are located at coordinate points (0.9,.,0.0..) and (.O.9m,O.Om), respectively. Here, the distance do between the centers of two beacons is 1.&n. Small and large beacons drawn by the darldy shaded two circles are the cylinders with radii rs = 0.Ql9m and r" = 0.07m, respectively. First, after calculating all the errors with variations of ~ L ,~s and ~tI at a position inside the lightly shaded region, the position and heading angle errors at the position take the maximum value among all the calculated errors, respectively. If the above procedure is applied to all the positions inside tbe lightly shaded region, all the worst case errors drawn in Fig. 5(a) and (b) can be obtained. As can be seen from these figures. the estimation errors of a method using two cylindrical beacons get larger when the mobile robot is near to X-axis. Namely, the estimation errors depends on the absolute value of the angle difference <1>, sbown in Fig. I. Here , <1>, denotes ~ = i-I's -
'1'"1.
If <1>" (0 s: <1>, s: It)
0
approaches 180 • the estimation errors become large due to inaccuracy of ultrasonic sensor. It is required to use an additional beacon so that there exists at least one location of mobi le robot where the three center points of two beacons and the mobile robot are not placed on the straight line.
3.2. Localization experiments using three beacons ' .25
T'"--:;,.---------......--, SB{O.3m . '.2m) \
L82(2.1m. 1.2m)
\ \ \
E .\. _ 0.00 +--............................................... pa'h p, ).;'
updating the POSIUon and heading angle. we conducted a series of experiments using two large beacons. LB I and LB2, and a small beacon SB. The three beacons were arranged as shown in FIg. 6. The position and beading angle of the mobile robot can be calculated from a beacon pair composed of a large beacon and a small beacon. From two beacon pairs B 1 and B2 shown in Fig. 6, two pairs of position and heading angle can be found. The beacon pair BI consists of LBI and SB while the beacon pair B2 consists of LB2 and SB. The position and beading angle of the mobile robot are calculated by two beacon pairs, BI and B2, respectively, at the location marked as dark rectangle on a straight line path PI as shown in Fig. 6.
The experimental results; The experimental procedure of three beacon system is the same as that of the method of using two beacon system. The mobile robot stops at the locations marked as dark rectangles on the path PI shown in Fig. 6 . Then, the robot scans the front area to acquire the sonar scan data. In this case, when the mobile robot is placed a t the origin (0,0) of the frame (W\ as shown in Fig. 6. From these sonar scan data, all the RCD' , associated with beacons are obtained by applying, in turn, the smoOlhness and symmetricily conditions. 1ben. we apply a priori known information of the beacon pair B I to the obtained ReO's. As a consequence of the above procedure, only two remained ReD's are used to determine the position and heading angle of the mobile robot. Once the position and heading angle of the robot are determined by applying a priori known information of the beacon pair B2 to the above obtained RCD's, another position and heading angle of the robot using the beacon pair B2 should be obtained. Finally, we can calculate the two pairs of position and heading angle of the robot from two beacon pairs B I and B2. Also, the angles 4»/ ~jtql are obtained simultaneously as shown in Fig. 7(c). These angles are used to decide which pair of two positions and heading angles is suitable for updating the position and beading angle of the roboe Fig. 7 shows the experimental results at all tbe locations marked as rectangle on the planned path PI. Figs. 7(a) and (b) show the errors in position and heading angle, respectively, while Fig. 7(c) shows the value of '1>, =I~I . The position and heading angle errors, E" and
E, ' are defined, as foU ows. Beaoon pair B1 : SB, LB1 Beacon pair 82: S8, LB2
\
E"
=~(XR -xT )' + (Y. -
YT) '
E,=16-6 I
(3)
T
LB1(1.8m, -a.9m)
" .25
+-------,...-------l
0.00
1.25 X, (m)
2.50
Fig. 6. Three beacon arrangement and a straightlin. path for experiments,
Experimental conditions; In order to find a method of reliably
In the above equations, the
(.t~ , y~)
and e
denote the
position and the heading angle of the mobile robot estimated by a localization method, while (XT'YT ) and eT denote the actual position and the beading angle, respectively. The actual position and tbe beading angle were calculated from the positions of the two wheels using tiles (3Ocmx3Ocm) decorated on me Ooor. As can be seen from Fig. 7. the estimation errors
203
become large as the
IA
180 0 • The position and
heading angle obtained by the beacon pair B2 are found to be more accurate than those obtained by the beacon pair B 1. In order to select a set of the two pairs of position and heading angle, we used the ct- j =I&
0.3.----------------, ---0--
--
OR method
---+-
o.o,li===-=.",......,(..............- -.......&;:=a~ 0.0 0.5 1.0 1.5 2.0 X,(m)
la) 6~---------------.----------,
0.5
1.0
1.5
2.0
X,(m)
!=t
""lJt
e
---.
..,
-
(b)
0.0
,
0.5
1.0
: :~-3 1.5
2.0
X. (m) (c)
Fig. 7. The experimental results of the estimation of position and heading angle when the mobile robot follows the path PI. 4. CONCLUSIONS After theoretically analyzing the position and beading angle errors, we have developed a mobile robot localization system which makes use of three cylindrical beacons and a single rotating ultrasonic sensor. 1be proposed method can estimate
the position and heading angle of a mobile robot using the sonar scan data obtained from the location of a single mobile robot. Localization experiments were performed by using two beacons as well as three beacons in actual indoor environments. The performance and validity of the proposed method were evaluated through a series of the experiments in actual indoor environment. It is believed that the proposed method can be used as an alternative of mobile robot localization in environment where other methods can not be used. REFERENCES Beom, H. R. and H. S. Cho (1995). Mobile robot locaiization using a single rotating sonar and two cylindrical beacon. Robolica 13, pp. 243-252. Beom, H. R. (1994). A study on the AI-based navigation and obstacle detection for mobile robots. Ph.D. Dissertation, KAIST. Cox, I. J. (1991). Blanche - an experiment in guidance and navigation of an autonomous robot vehecle. IEEE Trans. Robolics and Aulomation, pp. 193-204. Drumheller, M. (1987). Mobile robot localization using sonar. IEEE Trans. Pall. Anal. and Machine Inlell. 9, No.2, pp. 325-332. HoIenstein, A. A., M.A. Muller and E. Badreddin (1992). Mobile robot localization in structured environment cluttered with obstacles. Proc. IEEE Int. Cont Robotics andAulomation , pp.2576-2581. !Gm, J. H. and H.S. Cho (1992). Real-time determination of a mobile robot's position by linear scanning of a landmark. Robolica 10, pp. 309-319. Kleeman. L. (1992). Optimal estimation of position and heading for mobile robots using ultrasonic beacons and dead reckoning. Proc. IEEE 1nl. Con/. Robotics and Aulomalion. pp.2582-2587. Leonard, J. J. and H. F. Durrant-Whyte (1991). Mobile robot localization by tracking geometric beacons. IEEE Trans. Robolics and AUlomalion 7, No.3, pp. 376-382. Leonard, J. J. and H. F. Durrant-Whyte (1992). Dynamic map building for an autonomous mobile robot. The Inlemntional Journal of Robolics Research 11, No.4, pp . 286-298. Nishide, K .. M. Hanawa and T. Kondo (1986). Automatic position findings of vehicle by means of Laser. Proc. IEEE 1nl. Con/. Robotics and AUlomalion, pp.1343-1348. Tsumura, T. (1994). AGY in japan - recent trends of advanced research, development, and industrial applications. Proc. 1nl. Con[.lnlelligenl Robols and Syslems, pp. 1477-1484. Tsumura, T. (1991). Recent advances of intelligent vehicle perspective. SICE vo!. 30, No. 1, pp. 1-8. Yuta, S., Y. Kanayarn.. T. Yajima and S. Shimamura (1985). An implementation of MICHI-A locomotion command system for intelligent mobile robot. Proc. 1nl. Con[. Advanced Robolics, pp. 127-134.
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