BASIC STUDY ON THE REAL-TIME THREE-DIMENSIONAL POSITION MEASUREMENT OF GROUND MOVING OBJECTS USING AN ACCELEROMETER AND GYROS

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1 BASIC STUDY ON THE REAL-TIME THREE-DIMENSIONAL POSITION MEASUREMENT OF GROUND MOVING OBJECTS USING AN ACCELEROMETER AND GYROS Yoshiwo OKAMOTO*, Toshio KOIZUMI**, Yasuyuki SIRAI*** *Dep. Electrical, Electroics ad Computer egieerig, Professor, Chiba Istitute of Techology, -7-, Tsudauma, Narashio-shi, Chiba 75-6, Japa - okamoto@ec.it-chiba.ac.jp **Dep. Architecture ad Civil Eg., Professor, Chiba Istitute of Techology, -7-, Tsudauma, Narashio-shi, Chiba 75-6, Japa - koizumi@pf.it-chiba.ac.jp ***Dep. Desig, Associate Professor, Chiba Istitute of Techology, -7-, Tsudauma, Narashio-shi, Chiba 75-6, Japa - shirai@pf.it-chiba.ac.jp Commissio I, WG I/ Keywords: Surveyig, Developmet, Measuremet, Navigatio, Platforms, Mobile, Three-dimesioal ABSTRACT I recet years, electroics ad computer techology have bee applied to the developmet of survey istrumets, ad the methods of measuremet have widely chaged. We make use of sophisticated systems i daily base such as Total- Statio, GPS ad Laser-scaer, to ame a few. However, a system based o light wave ad/or radio wave has a weakess that it would ot work if the waves were itercepted. A iertial survey system, o the other had, fuctios idepedetly of those waves, ad it must be coveiet uder such circumstaces. Therefore the authors are developig a portable ad low-priced strap-dow iertial avigatio system. I this paper, the results from the field tests are preseted, which have bee performed o the equipmet made o a experimetal basis i order to ivestigate how the accuracy depeds o the measuremet strategy, amely the ostop or the stop-ad-go strategy. INTRODUCTION For mobile mappig ad various other purposes, it is a importat research subject to measure accurately the three-dimesioal positio of a platform o real-time basis. GPS has bee commoly used for these purposes. However, GPS sometimes does ot work i urba areas with a umber of towerig buildigs ad/or moutaious rural areas because of the electromagetic iterferece or blockage. By makig use of the techique kow as iertial survey, the authors had developed a system capable of measurig three-dimesioal positio of a groud-movig object o a real-time basis usig accelerometers ad gyros eve i a area where GPS does ot work. I the iertial survey system, positios are determied by itegratig acceleratios ad agular velocities obtaied from sesors. Therefore, the accuracy decreases as the measurig time becomes loger because of the accumulatio of errors. I order to overcome these difficulties, the authors propose a modified method i which stop-ad-go procedures are repeated durig oe sequece of measuremet, ad the itegrated value of acceleratio (velocity) is forced to be zero at every stoppage by subtractig liear drift so that errors do ot accumulate ay more. They also performed experimetal measuremets so as to evaluate the effectiveess of this method. Their results are show i this paper. I this study, servo-type accelerometers ad two types of gyros were used: oe is the vibratio gyro that is iexpesive but has somewhat lower performace, ad the other is the fiber optical gyro with moderate performace. By attachig a accelerometer ad a gyro to each of three mutually orthogoal axes, a strap-dow iertial survey system was costructed. As a platform, a bicycle trailer was used. Experimets were performed o a asphalt-paved road with horizotal distace of about 6 meters ad level differece of about 6 meters. Resultat time courses of the platform locatio were compared with the actual oes i both the horizotal plae ad vertical aligmets of the road. Two kids of measuremet strategy were tested: the covetioal oe i which the equipmet moves without ay stoppage ad the oe with repeated stop-ad-go, which had bee proposed by the authors. They shall be called the ostop strategy ad the stop-ad-go strategy, respectively, hereafter i this paper.

EQUIPMENT USED IN THE PRESENT STUDY Table. Specificatio of accelerometer JA-5V As metioed i the previous sectio, servo-type accelerometers ad two types of gyros were used i the preset study.

2 EQUIPMENT USED IN THE PRESENT STUDY Table. Specificatio of accelerometer JA-5V As metioed i the previous sectio, servo-type accelerometers ad two types of gyros were used i the preset study. Their specificatios are listed i table through table 3. As show i figure, a strap-dow iertial avigatio system was costructed by attachig a accelerometer ad a gyro to each of three mutually orthogoal axes. Figure shows the equipmet made o a experimetal basis, which was used i the preset study. Item Resolutio Sesitivity Zero poit ubalace Largest measurig rage Lateral sesitivity Voltage Power sup. Curret Weight Axis-Z Table. Specificatio of Vibratio gyro ENV-5A Item Resolutio Detectio rage Resposibility Voltage Power sup. Curret Weight Accelerometer Gyro Axis-X Specificatio < 4 (with LP filter) 5V G ± 3% < ±.% ±G <.% ± ~ ± 8V DC < ma < 8gf Table 3. Specificatio of fiber optical gyro JG-35FD Axis-Y Item Resolutio Detectio rage Resposibility Voltage Power sup. Curret Figure. Coordiate system ad sesors Figure. Experimetal equipmet Specificatio. s ±9 s DC ~ 7Hz +8 ~ + 3.5V DC < 5mA < 45gf Specificatio.6 s ±9 s DC ~ Hz V DC < A Figure 4. Ruig through chart of the experimet place Figure 3. Pla of experimet place 3 MEASURMENT STRATEGY SUITABLE FOR INERTIAL SURVEY 3. Route aligmet Experimets were performed o the asphalt-paved road with about 5.5 m elevatio differece ad 64 m iclied legth. Aligmet of the road was measured i detail usig a total statio ad a digital level, ad the result was cosidered as the true aligmet i the followig experimets cocered with our iertial survey system. Figure 3 ad 4 show the plae ad the vertical aligmet, respectively, used i the experimets. Figure 4. Ruig through chart

3 3. Fixed ad movig coordiate systems Two kids of coordiate system are used i the experimets: the oe deoted by Σ ( XYZ ) is fixed to the groud such that X-Y plae is horizotal ad X-axis directs toward magetic orth, ad the other oe deoted by Σ ( xyz) moves with the equipmet. They shall be called the fixed coordiate system ad the movig coordiate system, respectively. Both systems coicide with each other at the begiig of the experimet, but the system Σ ( xyz) traslates ad rotates as the iertial avigatio system goes alog the route. Acceleratios ad agular velocities obtaied from the sesors are the vector compoets i the movig coordiate system Σ ( xyz). Therefore, they are trasformed ito those i the fixed coordiate system Σ ( XYZ ) before itegratio, ad the rest of the computatios (e.g. positioig ad error evaluatio) are performed i Σ ( XYZ ) True value.9[m/s].4[m/s].7[m/s] Vibratio gyro True value.9[m/s].4[m/s].7[m/s] Figure 5. Estimated trajectories projected oto a horizotal plae (ostop strategy) 3.3 Effects of the movig speed I iertial survey, the distace is obtaied by itegratig the acceleratio twice, ad the agular chage is obtaied by itegratig the agular velocity oce. The error accumulates ad icreases with the lapse of time, ad hece it seems desirable to fiish the measuremet i shorter time to make the positioig more accurate. I order to ascertai whether this iferece is correct or ot, experimets were repeated chagig the movig speed of the equipmet. The ostop strategy is adopted i this experimet with three kids of movig speed: slow (approximately 3 mi. to go aroud whole the route, approximately.9 m/s), medium ( mi.,.4 m/s) ad fast ( mi.,.7 m/s). Horizotal Discrepacy[m] Horizotal Discrepacy[m] Movig speed[m/s].9[m/s].4[m/s].7[m/s] Approximate curve Vibratio gyro 3 Movig speed[m/s].9[m/s].4[m/s].7[m/s] Approximate curve Figure 6. Depedece of the horizotal discrepacy o the movig speed (ostop strategy) Figure 5(a) shows the estimated trajectories by the iertial avigatio system equipped with fiber optical gyros. They are projected oto a horizotal plae. Thick solid curve represets the true trajectory metioed i sectio 3., ad other three curves stad for the estimated trajectories i cases that the movig speed is slow, medium ad fast, respectively. As has bee expected, the discrepacy betwee the true ad the estimated trajectories decreases as the movig speed icreases. If 3

4 the fiber optical gyros are replaced with the vibratio gyros, we get the results show i figure 5(b). Sice the resolutio of the vibratio gyro is lower tha that of the fiber optical gyro, the discrepacy is larger i figure 5(b) tha that i 5(a). I order to evaluate the discrepacy quatitatively, the horizotal discrepacy ε h is defied as the horizotal distace betwee the true positio ad the estimated oe at the ed poit of the route, amely ε h = (( X e X t ) + ( Ye Yt ) ) where the subscripts e ad t refer to the estimated ad the true coordiates of the ed poit, respectively. The depedece of the horizotal discrepacy o the movig speed is plotted i figure 6. The experimets were repeated three times for each movig speed, ad hece three poits are plotted for each movig speed i both paels of figure Effects of the stop-ad-go strategy The stop-ad-go strategy was proposed i order to suppress accumulatio of itegratio errors due to radom drift of the accelerometers ad gyros. I this strategy, the equipmet moves from the startig poit R ad halts at a poit R o the route, the it moves from R ad halts at the ext poit R o the route, ad so o. These procedures are repeated util the equipmet reaches the ed poit R N. Suppose that the equipmet leaves from R at time poit t ad gets to R at T, which meas that the equipmet moves durig the time iterval [ t, T ] for = ~ N ad stays still durig [ T, t + ] for = ~ N. Suppose more that the itegratio of the acceleratio ( t) measured by the accelerometers over the iterval [ t, T ] is v, which would be if the measured acceleratio were free from oise. The, i order to make the velocity at T zero, ( t) is replaced with ( t) v ( T t ) i the iterval [ t, T ]. This method of compesatio is kow as ZUPT (Zero-velocity Up Dates). Ayway, i order to make this method effective, it is crucial to record the timigs t, T accurately. I the actual experimet performed this time, the stoppig poits R ( = ~ N) are arraged uiformly over the route with the distace betwee the adjacet poits, or the stoppage iterval, about 3, 5,,, 3, ad 5m. This meas that the experimet was repeated 6 times with these 6 choices of stoppage iterval. The velocity of the equipmet was kept as costat as possible to about.4 m/s that is referred as medium speed i the previous sectio, ad the legth of the time iterval [ T, t + ] or the stay time is chose to be 5s. I each pael of figure 7, the true trajectory is plotted with a thick solid lie as the same i figure 5, while a thi solid curve represets the estimated oe by meas of the stop-ad-go strategy i the case that the stoppage iterval is m. Moreover, the estimated trajectory by meas of the ostop strategy with medium movig speed is also plotted with a thi dotted lie as a compariso. It is clear that the estimatio error is reduced drastically by meas of the stop-ad-go strategy Figure 7. Trajectories estimated by meas of stop-ad-go ad ostop strategies 4 BIAS CORRECTION True value Stop&Go No-Stop 5 Vibratio gyro True value Stop&Go No-Stop Whe the accelerometers ad gyros stay still, their outputs should be zero. However, i reality, some ozero output called the bias error is observed eve form a sesor at a stadstill as described i figure 8. The bias error α B i the acceleratio yields the positioig error α t B where t is the elapsed time, while the bias error ω B i the agular velocity causes the agle error ω t B. The magitudes of bias errors observed from the sesors used i the preset experimets are listed i table 4. The positioig ad agle errors due to these bias errors are plotted i figure 9 as fuctios of the elapsed time. As ca be see i this figure, the positioig errors become 6, 7 ad 6m alog X, Y ad Z axes, respectively, whe the elapsed time is 6s. I the case of fiber optical gyros, the agle errors 6s after the oset are 3.,. ad.3 degrees aroud X, Y ad Z axes, respectively, while they are as large as 47, 38 ad 5 degrees i the case of vibratio gyros. 4

5 Output Figure 8. Bias error Table 4. Bias errors cotaied i the sesors Item X-axis Y-axis Z-axis Accelerometer [m s ].5.. [ s] Vibratio gyro [ s] Error i distace[m] Error i agle[deg] Error i agle[deg] Accelerometer Y-axis 7m X-axis 6m Z-axis -6m 4 6 Time[s] X-axis 3.deg Y-axis.deg Z-axis.3deg 4 6 Time[s] Vibratio gyro X-axis 47deg Y-axis 38deg Z-axis 5deg ( c) 4 6 Time[s] The bias errors are estimated at each stoppig poit R ( ~ ) = N as the averages of 5 cosecutive outputs from the sesors sampled at every ms durig the time iterval [ t, t ]. As metioed before, the equipmet leaves from R at time poit t, so the averages are take over the oe-secod itervals just before leavig times. The, the bias errors thus estimated are subtracted from the measured values of acceleratios ad agular velocities durig the time iterval [ t, T ] so as to elimiate their effects. This method of bias elimiatio should be called the bias correctio. I figure (a) shows the trajectories projected o a horizotal plae estimated by meas of the stop-ad-go strategy with ad without the bias correctio i the case that the stoppage iterval is m. I figure (b), the elevatios or z-coordiates are plotted as fuctios of the horizotal distace that is defied as the legth from the startig poit alog the route projected o a horizotal plae. As ca be see from this figure, the discrepacy betwee the estimated trajectory ad the true oe is otably reduced by correctig the bias errors. X(North-South)[m] Elevatio Discrepacy[m] Plae aligmet Y(East-West)[m] True value Before correctio After correctio Vertical aligmet Horizotal distace[m] True value Before correctio After correctio Figure. Effects of the bias correctio applied to the iertial survey together with the stopad-go strategy Figure 9. Positioig ad agle error due to bias error 5

6 5 CONCLUSIONS Coclusios are as follows: () The stop-ad-go strategy proposed by the authors makes the iertial survey more accurate tha the covetioal ostop strategy. () The accuracy icreases as the speed of the equipmet icreases. (3) The accuracy is strogly iflueced by the performace of gyros. (4) The accuracy is improved by the stop-ad-go strategy eve with low-performace gyros. (5) The bias correctio is quite effective, especially whe it is used together with the stop-ad-go strategy, to improve the accuracy. REFERENCES ) Ies J.: Iertial platform techiques for rapid surveys of hilliess ad bediess, Sesors Highway ad Civil Egieerig; Lodo, p.43-54, 98 ) Chapma W. H.: Proposed specificatios for iertial surveyig, Tech. Paper Au. Meetig America Cogr. Survey Mappig, No.43, p.87-93, 983 3) Roof E. F.: Iertial survey systems, J. Surv. Eg Vol.9, No., p.6-35, 983 4) Cross P. A.: Iertial surveyig, It. J. Remote Sesig, Vol.6, No., p , 985 5) Suzuki H. et al.: Real-time measuremet of altitude data usig the accelerometer, Iteratioal Archives of Photogrammetry ad Remote Sesig, Hakodate, Vol. XXXII, Part 5, p.78-83, 998 6) Koizumi T. et al.: Fudametal study o developmet ad applicatio of the local positioig system usig accelerometer ad gyroscope, Proc. It. Workshop o Mobile Mappig Techology, Bagkok 6B B- 5-6, 999 7) Shirai Y. et al.: Fudametal study o real time measuremet of altitude data with accelerometer ad vehicle speed sesor, Iteratioal Archives of Photogrammetry ad Remote Sesig, Amsterdam, Vol. XXXIII, Part B, p.3-36, 6

577. Estimation of surface roughness using high frequency vibrations

577. Estimation of surface roughness using high frequency vibrations 577. Estimatio of surface roughess usig high frequecy vibratios V. Augutis, M. Sauoris, Kauas Uiversity of Techology Electroics ad Measuremets Systems Departmet Studetu str. 5-443, LT-5368 Kauas, Lithuaia