Rob Ot Lo Calization Using Relativ
Robot Localization Using Relative and Absolute Position EstimatesPuneet Goel, Stergios I. Roumeliotis and Gaurav S. Sukhatme puneetjstergiosjgaurav@robotics:usc:eduDepartment of Computer ScienceInstitute for Robotics and Intelligent SystemsUniversity of Southern CaliforniaLos Angeles, CA 90089-0781AbstractA low cost strategy based on well calibrated odometry is presented for localizing mobile robots. Thepaper describes a two-step process for correction of'systematic errors' in encoder measurements followedby fusion of the calibrated odometry with a gyroscopeand GPS resulting in a robust localization scheme.A kalman lter operating on data from the sensorsis used for estimating position and orientation of therobot. Experimental results are presented that show animprovement of at least one order of magnitude in accuracy compared to the un-calibrated, un- ltered case.Our method is systematic, simple and yields very goodresults. We show that this strategy proves useful whenthe robot is using GPS to localize itself as well as whenGPS becomes unavailable for some time. As a resultrobot can move in and out of enclosed spaces, such asbuildings, while keeping track of its position on the y.1 IntroductionIn order to autonomously navigate and performuseful tasks, a mobile robot needs to know its exactposition and orientation. Robot localization is thus akey problem in providing autonomous capabilities to amobile robot. The di erent techniques that have beendeveloped to tackle this problem can be classi ed intotwo main categories:Relative (local) localization: evaluating the position and orientation using information provided byvarious on-board sensors (e.g. encoders, gyroscopes,accelerometers etc).Absolute (global) localization: obtaining the absolute position using beacons, landmarks or satellitebased signals (e.g. GPS). contact author for correspondenceA popular local technique, dead reckoning, employssimple geometric equations (a kinematic model of therobot) on odometric data to compute the position ofthe robot relative to its start position. Dead reckoning cannot be used for long distances because it su ersfrom various drawbacks. The kinematic model alwayhas some inaccuracies, encoders have limited precision and there are external sources a ecting the motion that are not observable by the sensors (e.g. wheelslippage). The localization error grows with time. Applying Kalman lter techniques can provide substantial improvement [1],[9].In case of absolute localization the error growth ismitigated when measurements are available. The position of the robot is externally determined and itsaccuracy is usually time and location independent. Inother words integration of noisy data is not requiredand thus there is no accumulation of error with timeor distance traveled. The problem in absolute localization (e.g. using GPS) is that one cannot keep trackof the robot for small distances (barring exceptionallyaccurate GPS estimates). Commercial o the shelfGPS gives errors on the order of 10 cm at each measurement. If the robot moves at 1 m/s one cannot useGPS at each second since the odometric estimate isless errorprone than the GPS measurement.Various people have presented work related to absolute localization . Leonard and Durrant-Whyte [6]developed a system in which the basic algorithm isformalized as a vehicle tracking problem, employingan Extended Kalman Filter (EKF) to match beaconobservations to a navigation map to maintain an estimate of the position of the mobile robot. Thrunet.al.[10] have developed a learning algorithm that enables a mobile robot to learn what features/landmarksare best suited for localization. They also use mapmatching [11],[4] using information from wheel encoders and information on wall orientation to localize
the robot. In [7] measurements from a sun sensor anda 3-axis accelerometer are used for absolute localization. The authors incorporate two Kalman lters inthe form of a smoother. While one of them has thetypical formulation of an indirect Kalman lter processing sensor measurements as they come in real time,the second one is involved every time an absolute measurement is available and it runs (o -line) backwardsin time to correct the error accumulated in the pathestimates.Several groups have also tried improving odometry for robot localization. J. Borenstein and L. Feng[2] presented a calibration technique called the UMBmark test. The dominant systematic error sourceswere identi ed as the di erence in wheel diameter andthe uncertainty about the e ective wheelbase. In another paper [3] the same authors introduce the term'gyrodometry' where the localization algorithm relieson odometry most of the time while substituting gyrodata only during those brief instances during whichgyro and odometry data di er substantially. The authors in [1] use a low cost INS system (three gyroscopes, a triaxial accelerometer) and two tilt sensors for their localization algorithm. Error models forthe inertial sensors are generated and included in anEKF for estimating the position and orientation of therobot. The major drawback of this work is that orientation information is missing from the calculation ofposition.The major missing element from all the above workis the absence of a technique that can localize a robotboth indoors and outdoors. Also, absolute measurements are useful when the robot is traversing relatively large distances but a careful mix of odometry,inertial sensing and absolute sensing is needed to provide accurate localization when the distances coveredare relatively small and absolute positions are available intermittently. How can one localize a robot inan urban terrain where GPS is lost frequently? In thispaper we propose a solution to this problem by using abackup system based on well calibrated odometry anda gyroscope. The overall scheme is robust and allowsthe robot to reliably navigate in areas where GPS (orany other form of absolute measurement) is availableintermittently.In Section 2 the robot model is presented andthe calibration procedure is described. Section 3 describes the gyroscope model used and the structure ofKalman Filter. Section 4 presents the experimentalresults and one of the many practical instances wherethe proposed strategy is useful. Section 5 concludeswith a summary and a discussion of ongoing and fu-Figure 1: The Pioneer ATture research.2 Robot ModelThe Pioneer AT used for experiments is a fourwheeled robot shown in Figure 1. The wheels on thesame side are mechanically coupled. The encoders return only two distinct speeds; one for the right pairof wheels and other for the left pair of wheels. Thekinematics of the Pioneer AT are given in Equations1-4.xk 1 xk ; vtot dt sin k 1yk 1 yk vtot dt cos k 1 k 1 k dt vR ;l vL vtot vR 2 vL(1)(2)(3)(4)where l is the vehicle axle length, vL and vR are thevelocities of the left and right wheels respectively. xkand yk denote the position of the center of axle. is the yaw rate of the robot in the x-y plane and is the angle between the vehicle axle and x axis. Forthe experiments reported here, the frame of referenceis chosen in such a way that the start location of therobot is the origin facing in the positive y direction.This de nes the co-ordinate system with respect towhich xk and yk are calculated at each time step k.The kinematic quantities of interest are shown in Figure 2.Experiments with the Pioneer AT reveal that localization which relies on velocities returned by theencoders can produce 20%-25% error in the positionestimates. Some of the main reasons for this are thelimited precision of the encoders, the low sampling frequency of their values and the inaccessibility to rawdata that can give angular velocities of the wheels. Inaddition, a signi cant portion of the error comes from
VRYaVLXFigure 2: The Robot Kinematicsthe radius of the wheels chosen to convert rotationalvelocities of the wheels to linear velocities. This contains some systematic error and can be compensatedfor. The calibration procedure followed required theuse of a precise tachometer (Extech MicroprocessorTachometer). While the robot was sitting on a boxand the wheels rotated freely in the air, the velocitymeasurements from the encoders were compared tothe reference (more precise) velocities that were obtained from the wheel RPM measurements given bythe tachometer. The data obtained from this experiment was plotted to give a relationship between thevelocity returned by encoders and by the tachometer.The plot is shown in Figure 3. The proportionalityfactor to convert from the encoder speed to the calibrated speed is denoted by .This form of systematic error is also responsible forpart of the error involved with the calculation of theyaw rate using the velocities from the encoders. Thisis show in the following equation. !R R ;l !L R !L R ;R !R R vR ;R vL (5)lRlRwhere !R and !L are the angular velocities of the rightand left wheel respectively. R is the radius of the twowheels (assumed to be the same for the time being).The velocities returned by the encoders are assumed to be equivalent to !L R and !R R.Another source of systematic error is involved inthe determination of yaw rate in the x ; y plane usingthe velocities from the encoders. The speci cationsfor the Pioneer AT give the axle length l but duringa turn, the wheels do not pivot at their center andthus the e ective axle length is changed. The e ectiveaxle length due to skid steering changes the kinematicconstraint on the vehicle from equation 5 to 6. vR ;R vL vRl; vL(6)lRFigure 3: Finding parameter . Measurements are inmm/sec.We determined ll RR empirically. It was foundthat when the encoders predicted a 200 degree turnthe robot actually turned only 180 degrees. Varioussuch experiments enabled us to determine the valueof . Section 4 shows the improvement in localizationaccuracy as a result of using the calibration factorsand .3 Kalman FilterKalman ltering [5] is a well known technique forstate and parameter estimation. It is a recursive estimation procedure that uses sequential sets of measurements. Prior knowledge of the state (expressedby the covariance matrix) is improved at each step bytaking the prior state estimates and new data for thesubsequent state estimation. In recent years Kalmanlter based localization has become common practice[8],[9] in the robotics literature.To improve on the estimate of yaw rate in the x-yplane an inexpensive gyroscope (QRS14-64-109 fromSystron Donner) with a range of ;64 o s to 64 o swas used. Before using it for estimating orientation itsbias was empirically determined. The mean value ofa set of gyro measurements (when the robot was stationary) was calculated. Observations show that thisvalue (mean) does not change signi cantly with timeand thus it was assumed to be constant for the duration of the motion reported here. The bias (0:4 o s)is thus subtracted each time from the gyro signal.In the experiments reported here the measurementvector used in the localization is composed of the twotranslational speeds of left and right wheels and the
yaw rate of the chassis as measured by the gyro. Thestate estimate is denoted by x, z is the measurementvector, r is the residual vector and z is the measurement estimate.z [vL vR ] T z x [ vL v R ] T r z ; z (7)The Kalman lter consists of two di erent stepspropagation and update. The equations for thepropagation step are:x k 1 k x k kPk 1 k Pk k T QSimple Calib. Kalman FilterExp. No. Odom. Odom.(Gyro &calib. odom.)1.22.7% 14.0%2.5%2.21.5% 17.4%0.4%3.23.1% 17.1%0.9%4.20.5% 15.7%2.6%Table 1:ActualError comparison of three di erent techniques.Final Position ; Estimated Final PositionError (8)(9)Total Distance Traversedshows the estimated path of the robot if no calibrationis performed and only odometry is used. The dasheddotted line shows the estimated path when calibratedSatisfying the constraints given by equation (4) andapplying teh results from calibration discussed earlier,odometry (incorporating both and ) is used for localization and the solid line shows the path from thethe system matrix is given by:complete system, that is, from the Kalman lter that32combines information from calibrated odometry and1 0 0gyroscope. 4 ;10 11 0 5The rst sub- gure in Figure 4 is the case of trill 0angular trajectory. The robot was started pointingtowards the positive y-direction and after completionThe equations for update areof the trajectory it re-orients itself to face the positiveK Pk 1 k (Pk 1 k R);1(10)x-direction. One can easily see how poor raw odometry is.x k 1 k 1 x k 1 k K r(11)In the rest of the three experiments the robot wasPk 1 k 1 (I ; K) Pk 1 k(12)manually moved closeto the start location in the end.The third and fourth experiments are more revealing.where P is the error covariance matrix, Q is the sysIn the third experiment the robot traveled in a straighttem noise covariance matrix, K is the Kalman gainline and followed almost the same straight line whilematrix and R is the measurement noise covariancereturning. The Kalman lter relying on calibratedmatrix.odometry and gyroscope data localizes the robot upThe system noise covariance matrix Q is deterto an accuracy of 1% of the length of the traversemined empirically. Di erent sets of experimental datawhile the estimates from other two methods shown inwere processed to calculate the system driving noise.the gure are quite poor by comparison.The values of measurement noise matrix R are basedThe fourth and last experiment shown here is ilon sensor speci cations as well as empirical observalustrativedue to the number of turns and the lengthtions.of the trajectory. This experiment was performed"#"# indoors on the second oor of the Computer Sci1 92000 83200ence building at USC. The achieved accuracy is 98%.0 1 9200 0 8320Q R ;4;6Table 1 summarizes the results of the four exper00 1000 10iments conducted using three di erent localizationtechniques. These results show that one cannot relyon un-calibrated odometry even for small distances4 Experimental Results(on the order of 10 meters).::::4.1 IndoorsWe rst report here on four indoor experiments.Consider Figure 4. Each sub- gure shows the case ofa di erent trajectory. In every experiment the initialposition of the robot is at (0,0). In each gure allthe measurements are in centimeters. The dashed line4.2 OutdoorsThe Pioneer AT is equipped with GPS (NovAtel3111RE) and is capable of localizing itself globallywhen it is outdoors and the GPS signals are not occluded by tall buildings or other structures. The local-
ization error is constant (1 0:8m) and independentof the time of the day. Its accuracy though, can seriously degrade depending on the location. The numberof satellites in sight determines the achieved level ofaccuracy. When some of these signals are not available the triangulation performed by the GPS providespoor results.The outdoor experiments performed, required therobot to move between pre-speci ed locations. Thepositions of these locations wer marked with the GPSvalue (latitude and longitude). A simple P (proportional) controller was implemented for the purpose ofdriving the robot from one location to the other. Thiscontroller servos on the di erences in the longitudeand latitude between the current and the desired position of the robot. A lower level obstacle avoidancebehavior bypassed it whenever the robot was in dangerof collision with structures or people moving around it.For most of the locations that were tested the performance of the system was satisfactory and the achievedaccuracy was as expected from GPS.When the same robot was commanded to navigatefrom one position to another in the vicinity of tallbuildings, the controller was unable to drive the robotto its goal. Extensive testing revealed that betweenthe initial and desired position there were areas wherethe GPS signals were either unavailable or occluded.To overcome this problem the control strategy had tobe redesigned.The proposed method requires the desired locationsas well as the necessary intermediate ones to be speci ed using two di erent representations. The rstone uses the value of the GPS signal at these locations. The second one (which is used when the abovementioned controller fails) requires the coordinates ofthese locations to be calculated beforehand using amap of the area. These new coordinates with respectto some arbitrary de ned local frame are given in meters (x, y) while the previous ones (longitude, latitude)are in degrees with respect to the geo-centric coordinate system.The new dual controller was tested in a scenariodepicted in Figure 5: the robot was commanded tostart from building A, travel to building B and thenreturn to its initial position. Starting from point o anduntil the position a, the robot depended on the controller which uses the GPS signal to drive the robot tothe goal. At position a, the GPS signal is a ected bythe tall buildings and the system has to switch to theback-up controller which uses the Kalman lter estimate for the current location and the predeterminedmetric information for the destination. The calibratedodometry, fused with the gyro signal in the Kalmanlter, allows for precise localization of the robot andthus the performance of the system remains at thesame level as before switching from the GPS drivencontroller. The robot continues to move between positions a and b by navigating on the metric ( x; y)which is the di erence between its location at everytime step and the desired location (Building B). Atposition b the GPS signal becomes available again andthe robot switches to the controller that uses the GPSsignal. The robot reaches Building B, takes a turn andheads towards Building A. The trajectory followed isalmost parallel to the previous one (there is only onefree path between the two buildings). As before therobot has to switch controllers for the part of the trajectory between positions c and d (in the vicinity of aand b). The GPS signal was poor for the area near a,b, c, and d. Finally, for the rest of its route betweenposition d and Building A the robot again uses theGPS based controller.At this point it is worth mentioning that the accuracy of the GPS signal is almost the same for allthe locations where it is available. However it is notdesirable to fuse it with the gyro signal and the calibrated odometry data in the Kalman lter. For example at each time step (one tenth of a second) therobot moved for about 4 cm while the accuracy of theGPS is (at its best) 80 cm. This is because of thetransformation from the longitude and latitude measurements available in degrees into meters on the planeof motion. This is the main reason for combining thesetwo independent sources of localization information intime instead of in frequency. Switching in time fromone controller (and thus localization algorithm) to theother is very well suited for cases like this where the locations of interest are marked with their coordinatesin the geo-centric coordinate system as well as withtheir coordinates with respect to some arbitrarily dened local (to the area) coordinate frame.Another advantage of the current implementationis that the robot can be used to map its surroundingswithin an area of interest. The precision of the GPSsignal is not adequate when we want to specify thelocations of objects that can be a few meters apart,e.g. when locating landmines. The dual internal representation of locations allows the robot to navigatebetween remote positions without depending solely onthe availability of the GPS signal. At the same timeit provides the capability to mark the locations of objects of interest with higher precision estimates (fromthe Kalman lter based localization) with respect tosome arti cial or natural landmarks. Maps built using
it for some time and when it has moved a su cientlylong distance GPS can be used for absolute localization. We have obtained very good results in localization accuracy and robustness with an inexpensivebackup system. The position estimates have accuracyup to 2% of the distance traveled over traverses aslarge as 100 m with intermittent GPS.In the present system, the e ective length of theaxle is calculated o -line and is assumed to be constant. We plan to build an adaptive Kalman lterwhich can update at each time step. Also we haveneglected gyro drift in this work. In our future workwe plan to incorporate it in the state to provide betterorientation estimates.AcknowledgmentsThe authors thank G. Dedeoglu for help with data collection. Theauthors also thank K. Harbick and J. Montgomery for providinginformation and hardware support on the gyroscope and GPS.This research is sponsored in part by a contract #959816 fromJPL/Caltech and contracts #F04701-97-C-0021 and #DAAE07-98C-L028 from DARPA.Figure 5: An example of GPS failure where the back upsystem is 3-118.289536Table 2: Co-ordinates of various points in two metricspaces.GPS signals as well as Kalman lter based localizationcan coexist in parallel.5 Conclusions and Future WorkIn this paper we have presented a robust localization scheme. We have shown that well calibratedodometry and gyroscopic data provide a backup system that proves to be very useful in the case whenabsolute positioning sensors are unavailable for sometime. Nowadays most outdoor robots use GPS butgiven the constraints of urban terrain GPS is available intermittently. Also such robots are unable tonavigate both indoors and outdoors since there is nomechanism available to switch to an indoor positionestimation system once indoors. Moreover one cannotkeep track of a robot in a local coordinate system using GPS since accuracy is poor for small distances. Ifgood odometry is available then the robot can rely onReferences[1] B. Barshan and H. F. Durrant-Whyte. Inertial navigation systems for mobile robots. IEEE Transactions on Robotics andAutomation, 11(3):328{342, June 1995.[2] J. Borenstein and L. Feng. Correction of systematic concurrency errors in mobile robots. In Proceedings of the 1995 IEEEInternational Conference on Robotics and Automation, pages569{574, 1995.[3] J. Borenstein and L. Feng. Gyrodometry: A new method forcombinig data from gyros and odometry in mobile robots. InProceedings of the 1996 IEEE International Conference onRobotics and Automation, pages 423{428, 1996.[4] A. Elfes. Sonar-based real world mapping and navigation.IEEE Journal of Robotics and Automation, RA-3(3):249{265,June 1987.[5] R.E. Kalman. A new approach to linear ltering and predictionproblems. ASME Journal of Basic Engineering, 86:35{45,1960.[6] J. J. Leonard and H. F. Durrant-Whyte. Mobile robot localization by tracking geometric beacons. IEEE Transactions onRobotics and Automation, 7(3):376{382, June 1991.[7] S.I. Roumeliotis, G.S. Sukhatme, and G.A. Bekey. Smootherbased 3d attitude estimation for mobile robot localization.Technical report, University of Southern California, August1998.[8] S.I. Roumeliotis, G.S. Sukhatme, and G.A. Bekey. Circumventing dynamic modeling: Evaluation of the error-state kalmanlter applied to mobile robot localization. In Proceedings ofthe 1999 IEEE International Conference in Robotics and Automation, May 1999.[9] S.I. Roumeliotis, G.S. Sukhatme, and G.A. Bekey. Smootherbased 3-d attitude estimation for mobile robot localization. InProceedings of the 1999 IEEE International Conference inRobotics and Automation, May 1999.[10] S. Thrun. Bayesian landmark learning for mobile robot localization. Machine Learning, 33(1), 1998.[11] S. Thrun. Learning maps for indoor mobile robot navigation.Arti cial Intelligence, 1999.
odom.calib.KF8007006005004003002001000 600 400 0 800 600 400 2000200odom.calib.KF25002000150010005000 2000 1500 1000 5000500100010005000 500odom.calib.KF 100005001000150020002500Figure 4: Each gure above shows three traces. The traces are from un-calibrated odometry(- -), calibrated odometry(-.)and from the Kalman lter using information from calibrated odometry and gyroscope (solid line). Measurements are incentimeters.
hnique, dead rec k oning, emplo ys simple geometric equations (a kinematic mo del of the rob ot) on o dometric data to compute the p osition of the rob ot relativ e to its start p osition. Dead rec k on-ing cannot b e used for long distances b ecause it su ers from v arious dra wbac ks. The
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