Calibration Method for 2-Dimensional Laser Scanner Attached on a Robot Vehicle

Transcription

1 Proceedngs of the 17th World Congress The Internatonal Federaton of Automatc Control Seoul, Korea, July 6-11, 8 Calbraton Method for -Dmensonal Laser Scanner Attached on a Robot Vehcle Oscar C. Barawd, Jr.*, Kazunobu Ish**, Noboru Noguch*** * Ph.D. Canddate, Graduate School of Agrculture, Hokkado Unversty, Kta-9 Nsh-9, Kta-Ku, Sapporo, Japan ( TEL ; e-mal: oscar@bpe.agr.hokuda.ac.jp) * *Assocate Professor,, Graduate School of Agrculture, Hokkado Unversty, Kta-9, Nsh-9, Kta-Ku, Sapporo, Japan ( TEL ; e-mal: c@bpe.agr.hokuda.ac.jp) *** Professor, Graduate School of Agrculture, Hokkado Unversty, Kta-9, Nsh-9, Kta-Ku, Sapporo, Japan ( TEL ; e-mal: noguch@bpe.agr.hokuda.ac.jp) Abstract: The objectve of ths study was to develop a calbraton method to get the exact poston of the -dmensonal laser scanner mounted on the front of an automated vehcle from a reference coordnate system before the automatc navgaton n an orchard applcaton. The research was lmted only n calbratng a -dmensonal laser scanner that gathers dstance and angle data of the objects n front of t. The methods used n ths research were Hough transform, Euler rotaton theorem and LSM (least squares method). The calbraton results dentfed the exact attachment poston of the laser scanner wth respect to the vehcle coordnates. Fnally, feld test runs for autonomous gudance wth developed calbraton was conducted to confrm the travel accuracy mprovement. The accuracy of both lateral and headng error for calbrated sensor was hgher than run of subjected calbraton. 1. INTRODUCTION Calbraton of any sensors attached onto the vehcle or equpment s necessary to obtan envronment nformaton. After the nstallaton of the sensor, t s necessary to check f the sensor s algned or centered properly wth respect to the reference axes. For sensors such as a vdeo cameras, a laser range fnder, an ultrasonc sensor, a -d laser scanner and a GPS (global postonng system) etc., the poston and orentaton of the sensor affects the geometrc nterpretaton of ts measurements (Pless et al., 3). LMS (laser measurement sensors) are a popular method for acqurng optcal measurement data of the objects n any poston due to ther accuracy. In order to maxmze the range accuracy and to have correct data acquston, a proper calbraton method has to be appled. However, calbraton of sensors s a not an easy task. The determnaton of the fttng algorthm method alone s tme-consumng not to menton the choce of the approprate auxlary equpment that would ensure deal data. One thng to consder s the cost of engneerng equpment to be used n calbraton. Engneerng costs arse from both expensve components and dffcult calbraton requrements (Davs et al., 1). A laser range scanner desgned for mnmum calbraton complexty (Davs et al., 1) used a laser trangulaton scanners method for acqurng three-dmensonal geometry of the objects due to ther accuracy and robustness. In sad method, two-camera range scanner desgn was utlzed to mnmze calbraton complexty and cost, and elmnates all actuated components from the calbrated geometry. In ths research essental equpment were used to calbrate the laser scanner such as the RTK-GPS (real-tme knematc global postonng system), a FOG (fbre optc gyroscope), and total staton. Nowadays, these sensors are gettng nexpensve due to popular demand and due to ts effcency n yeldng optmal calbraton results. Usually, the choce of the engneerng equpment to use for the scanner calbraton s subject on the nsttutons' avalablty of the resources. In ths research, the developed method for the calbraton of laser scanner attachment poston dd not utlze a calbraton platform compared to other methods. Posture estmaton for autonomous weedng robots navgaton n nursery tree plantatons (Khot et al., 5) used a calbraton platform to calbrate the attachment poston of the sensor. Ths calbraton platform conssts of a fabrcated steel track where the calbraton method s performed for the prototype robot vehcle. The advantage of usng prototype robot vehcle s that the calbraton platform model s not bg enough to construct. But n ths research, t s not advsable to make a calbraton platform because the robot tractor s too bg and the constructon cost s expensve. A new calbraton method was developed and ntroduced n ths research usng a unque technque. The unque technque used n ths research s the use of the perpendcular wall. Ths perpendcular wall served as the reference lne for the laser scanner calbraton. The man thrust of the study s to develop a calbraton method to obtan the actual laser scanner attachment poston whch wll soon be used to correct the data outputs n an autonomous navgaton of the robot tractor. The attachment poston of the laser scanner s called offset poston values. These offset poston values of the laser scanner are mportant to know because t wll determne f the sensor attachment s properly algned or centered wth respect to reference axes /8/$. 8 IFAC /876-5-KR

2 17th IFAC World Congress (IFAC'8) Seoul, Korea, July 6-11, 8 The developed calbraton method for obtanng the laser scanner attachment poston used three essental sensors, FOG whch served as the headng sensor. The functon s to obtan the relatve headng drecton of the robot tractor. A RTK- GPS recever was used as the postonng sensor to get the absolute poston of the robot tractor. And, a total staton was used to obtan the relatve poston (x, y and z axes) of the perpendcular wall. A total staton s an optcal nstrument used n modern surveyng as well as by polce, crme scene nvestgators, prvate accdent reconstructonst and nsurance companes to take measurements of scenes (Wkpeda, The Free Encyclopeda). The perpendcular wall s wall perpendcular to the GPS antenna whch s mounted on the top of the cabn of the robot tractors' centre of gravty and the laser scanner whch s attached on the front of the robot tractor, served as the reference lne to obtan the exact attachment poston of the laser scanner wth respect to the reference axes. The methods used n ths research were Hough transform to recognze the perpendcular wall as straght lne, Euler rotaton theorem to transform the perpendcular wall relatve coordnates nto UTM (unversal transverse Mercator) coordnates, LSM (least square method) to get the scannng offset error of the laser scanner whch s the laser scanner exact attachment poston.. RESEARCH COMPONENTS Ths research used a 56-kW standard tractor, whch was modfed nto a robot tractor. The robot tractor controlled steerng, transmsson (forward, neutral and backward), PTO (power take-off), engne speed, brake system and three-pont htches (up and down). The LMS 91 s the laser scanner to be calbrated, (SICK AG, Dvson Auto Indent). Fgure 1a shows the LMS 91 and scannng basc prncples. The fgure shows the scannng angle drecton s counter clockwse and area montorng whch means that an nfrngement of a feld, e.g. by an object, leads to a swtchng sgnal at an output. The sensor was set to 8 m dstance range, 1 deg angle resoluton and 13 ms response tme. Fgure 1b shows the laser scanner attachment poston n front of the robot tractor. It has a dstance error of +/- 5 cm. The advantages of usng the laser scanner as the navgaton sensor are rapd scannng tmes thus measurement objects can move at hgh speeds, no specal target-object reflectve propertes necessary, no reflectors and no markng of the measurement objects necessary, backgrounds and surroundngs do not have any nfluence on the measurements, measurement data s avalable n real tme and can be used for further processng and completely weatherproof varants. Maxmum dstance = 8 m d ( d, φ ) 18 o counterclockwse Laser scanner scannng (a) Laser scanner (LMS 91) and scannng basc prncples φ Angle resoluton = 1 deg o Laser scanner (SICK LMS 91) 7 cm (b) Attachment poston of laser scanner Fg. 1. Laser scanner basc prncples and poston attachment The three essental sensors used to calbrate the laser scanner were the RTK-GPS recever (MS 75 dual frequency RTK recever, Trmble Navgaton Ltd.). The MS 75 GPS recever was preferred to use n ths research because t has the hghest level of accuracy and response avalable to receve nformaton and t s specally desgned to allow the easy ntegraton of relable-level postons to any gudance or control applcaton. In the experment run, the RTK-GPS recever nput was set to 1 Hz and the output was set to 1 Hz. It has a postonng accuracy of +/- cm. The FOG, (JG- 35FD, Japan Avaton Electroncs Industry, Ltd.) was used as the headng sensor. Ths sensor obtaned the headng angle necessary for the calbraton method durng the experment run. The sensor drft angle accuracy s +/-.5 deg/hour. And, the total staton (APL-1, TOPCON Ltd.) used as the postonng sensor to obtan the relatve poston (x, y, and z axes) of the perpendcular wall wth an accuracy of +/- 3 mm for fne mode and +/- 1 mm for course mode. The total staton was set to fne mode settng. All sensors are connected to the laptop PC usng RS-3 cable. 3.1 Hough transform samplng 3. METHODS The Hough transform used n ths research as the algorthm to recognze the perpendcular wall as a straght lne. It was patented by Paul V. C. Hough n 196. It used for lnear or crcular detecton. The man advantage of usng Hough transform compared to commonly used method lke least squared error method of fttng lnes to mage data, s that even f group ponts vares to some extent, askng for a straght lne s possble. Also, processng s collectvely possble even when there are two or more straght lnes n the mage data. The pont whch has the majorty of ntersecton served as the lne equaton. The dsadvantage, on the other hand, s that n order to plot curves (.e. snusods) for every observng pont (x, y ) n Cartesan mage space to r-θ polar Hough parameter space, the load of computatonal complexty s large. 1597

3 17th IFAC World Congress (IFAC'8) Seoul, Korea, July 6-11, 8 Consder the normal Cartesan equaton of a straght lne, whch s generally on an x-y plane, y = mx + c (1) where m s the slope and c s the y-ntercept. Consder some ponts of the mage data where a straght lne can be obtaned from ts edge. Transform the ponts nto r- θ normal representaton of a lne n Hough space (only ponts where the lne pass through) whch was shown n Fg. a. The shortest dstance from the orgn can be obtaned equvalent to () (Gonzales & Wood et al., 1993). r = xcosθ + y snθ () In Eqn (), the lne s defned n terms of r andθ, where r s shortest dstance from orgn to lne and θ s the orentaton angle wth respect to the x-axs. For any pont (x, y) on ths lne, r and θ has a constant value. Equaton () can be consdered a relaton between the coordnates (x, y) of some ponts n the edge mage, and the value of the parameters (r-θ) whch defnes the equaton of the lne. The ponts n Cartesan space correspond to a sne wave r- θ polar n Hough parameter space shown n Fg. b. In Fg. b, the ponts where the majorty of these snusods ntersect serve as the equaton of the lne. The value of dstance r s equvalent to.1 unt and the angle θ s equvalent to -4 deg. The equaton of the lne s y = x Perpendcular wall recognton as a straght lne usng Hough transform Applyng the Hough transform to the data obtaned by the laser scanner durng the calbraton experment run, the perpendcular wall was recognzed as a straght lne. The perpendcular wall wll serve as the base lne for the laser scanner calbraton. Fgure 3 shows the perpendcular wall and the total staton vsual representaton. r = d cos( φ θ ) ( 18, j 18) (3), j j In (3), r,j s the shortest dstance between the laser scanner and the perpendcular wall, d s the actual dstance between the perpendcular wall and the laser scanner, θ s the relatve angle of the perpendcular wall wth respect to laser scanner detecton, and φ j s the deflecton angle between the perpendcular wall and the vehcle drecton. The man advantage of the r-θ s that quantzaton s relatvely easy because not all the parameter space needs to be consdered. Lookng at Fg. b, the snusods all have the same perod, and therefore θ can be lmted to any angle range dependng on the applcaton wthout losng ts generalty. In ths research, the θ lmt was 18 and φ j lmt was j 18. y Estmated lne y Possble lne that wll r pass through the ponts θ Shortest dstance from orgn to the lne x Captured ponts of the laser scanner Pont (x, y) Perpendcular wall d r φ θ Total staton x Local coordnates (a) r-θ space normal representaton of a lne n Hough transform Intersecton pont estmate the 1 lne equaton θ, deg r, unt (b) Ponts transform to snusods n r-θ space Robot tractor Fg. 3. Outlne on how to recognze the perpendcular wall as straght lne usng the Hough transform Fgure 4a shows the actual captured ponts of the laser scanner on the surface of the perpendcular wall. The black ponts represent the wall and the black lne corresponds to the estmated lne. Transformng the data obtaned by the laser scanner nto a r-θ parameterzaton space shown n Fg. 4b usng the Hough transform, a cluster of ntersectons were ntersected. The majorty of ntersectons served as the equaton of a lne of the perpendcular wall. Fg.. Bascs of Hough transform 1598

4 17th IFAC World Congress (IFAC'8) Seoul, Korea, July 6-11, 8 Estmated lne Perpendcular wall scanned as ponts Centerlne to follow by the robot tractor dstance [cm] Laser scanner (scale 1:1,6) (a) Actual captured ponts by the laser scanner n a computer wndow r, cm r, majorty of the lnes ntersect θ, deg (b) Illustraton of the captured ponts of the laser scanner transform to snusods n r-θ space Fg. 4. Transformaton of the captured ponts usng Hough transform 3.3 Transformaton of local coordnates to UTM coordnates The perpendcular wall relatve poston (x, y and z axes) was measured by the total staton (surveyng nstrument) and then the startng edge pont absolute poston was measured by RTK-GPS. After determnng the perpendcular wall as a straght lne usng the laser scanner, next s to transform the relatve poston nto absolute poston by usng Euler rotaton theorem. In ths method, the rotaton s about the z-axs n counter clockwse drecton. Equaton (4) shows the rotaton matrx n z-axs. cos ρ sn ρ R z( ρ) = (4) sn ρ cos ρ In the equaton, ρ s the rotaton angle n deg, can be obtaned n the perpendcular wall angle n the UTM coordnates. Equaton (5) calculated absolute poston of the perpendcular wall. E N s s xs Eo = R z(ρ ) + (5) ys No Where the (E s, N s ) s the transformed poston n UTM coordnates, (x s, y s ) s the relatve poston of the perpendcular wall taken by the total staton, and (E o, N o ) s the startng edge pont of the perpendcular wall. 3.4 Determnaton of the offset poston of the laser scanner usng LSM The next method to be explaned s the determnaton of the offset poston values of the laser scanner attached on the front of the robot tractor. The offset poston values are between the laser scanner and the GPS antenna whch was shown n Fg. 5. In the fgure, a and b are the laser scanner offset values (x and y axes) n m and the δ s the offset angle of the laser scanner n deg at the vehcle coordnate system, respectvely. The center pont of the laser scanner from perpendcular wall s denoted by E n m. The value of E can be computed from the data obtaned by the laser scanner n dstance (d) and angle (θ) usng Hough transform usng (3). The values of the dstance (E) depend on the equaton of the perpendcular wall obtaned prevously by the laser scanner recognton as a straght lne. The dstance from the GPS antenna to the perpendcular wall s denoted by D n m. To solve the dstance (D), the straght lne equaton of the perpendcular wall s needed n UTM coordnates by usng (6). α x + βy + c = (6) Usng the perpendcular dstance relaton between the perpendcular wall and GPS antenna the dstance (D) can be solved by (7). N ν y s ψ Perpendcular wall D η E δ κ x a b Total staton- coordnate y y laser scanner center pont x UTM-Coordnate Fg. 5. Calbraton method outlne usng a perpendcular wall as the reference lne for gettng the laser scanner exact poston absαx + βy + c D = (7) α + β The angle (ψ ) between the perpendcular wall and vehcle coordnate system s gven by E x s 1599

5 17th IFAC World Congress (IFAC'8) Seoul, Korea, July 6-11, 8 ψ = η ν (8) Where η s the angle of the vehcle drecton n deg wth respect to the UTM coordnate and ν s the angle of the perpendcular wall n deg wth respect to the UTM coordnate. The equaton for solvng the offset angle δ of the laser scanner s shown n (9). δ = κ ψ (9) Usng the Hough transform, κ s the angle between the laser scanner s exact poston n deg and the perpendcular wall, computed from the data obtaned by the laser scanner durng the calbraton experment run. Snce dstance (E) and dstance (D) exsts on the straght lne, the poston of the laser scanner can be calculated usng (1) n vehcle's coordnate system. a cos ψ + bsnψ = E D (1) However, E-D values have measurement errors. Through usng the least squares method (Downe and Heath, 1984), the mnmum errors were obtaned. The error was acqured by n a straght lne n n value of observaton as a cos ψ bsnψ + D E = (11) + Assgnng the F as F = D E (1) Usng LSM, the mnmum error (E ) can be calculated n (13). ( a cos + b sn F E = ψ ψ + ) (13) Solvng for the least square estmates by summng of all observaton data: n E = Sε = (14) Usng partal dervatves, the mnmum error can be calculated n (16) and (17) whch are set to. n S ε = ( cos + cos sn + cos ) = a ψ b ψ ψ ψ F a (15) = n S ε = ( cos sn + sn + sn ) = b ψ ψ a ψ ψ F b (16) = The values of the offset poston of the laser scanner were a = -.56 m, b =.57 m and δ =.8 deg from the northng UTM coordnates. 4. RESULTS AND DISCUSSION 4.1 Determned offset poston values of the laser scanner Before the laser scanner was attached n front of the automated vehcle, a measurement was made to know the attachment poston of the laser scanner n front of the automated tractor. The purpose of ths measured poston was to nsure that the laser scanner was attached properly n front of the automated tractor. Ths attachment poston of the laser scanner s a subjectve calbraton because the nstallaton s only depended on the person who nstalled the laser scanner. In order to verfy whether t was attached properly/centered to the centrelne of the tractor the offset poston values should be obtaned. To obtan the offset poston values of the laser scanner dfferent algorthms-- Hough transform, Euler rotaton theorem, and LSM were used. A unque technque was also used to obtan the offset poston values. Ths technque was the utlzaton of the perpendcular wall as the reference lne to develop calbraton method for the laser scanner attachment poston. The developed calbraton method determned the offset poston values of the laser scanner. These values were the exact locaton on the robot tractor attachment poston and proved that the attachment poston of the laser scanner was not properly algned or centered wth the reference coordnate. Ths condton justfes the need for the calbraton of the laser scanner and t s very mportant to mplement because of the effect on the evaluaton accuracy on any system. In ths research, the offset poston values wll be used n the accuracy evaluaton to correct the data obtaned by the laser scanner n an autonomous navgaton orchard applcaton. Hough transform has possble errors durng the lnear and crcular detecton. In ths research, errors for lnear detecton were not consdered because the errors were mnmal and t wouldn't affect the accuracy of the calbraton. But n crcular detecton, the errors should be consdered. 4. Evaluaton of the autonomous run outputs wth developed calbraton and wth subjectve conjecture calbraton The laser scanner attachment poston n front of the automated vehcle was mounted by subjectve calbraton n whch the attachment poston was conjectured n the reference axes. In order to see the effect of the presence or the absence of the laser scanner calbraton n accuracy evaluaton of the autonomous navgaton, a seres of autonomous runs were conducted. The experment runs were conducted n the Hokkado Unversty, Sapporo, Japan. The selected test ste was approxmately 4 m by 3 m n length and wdth. The area whch resembled an orchard was spanned wth trees n two vertcal rows. Fgure 6 shows the accuracy evaluaton of autonomous navgaton wth developed calbraton and wth subjectve calbraton. In the fgure, the black lne represents the data wth subjectve calbraton and the broken lne represents the data wth developed calbraton. Ths research shows the effect of not calbratng the laser scanner was that the accuracy errors tend to ncrease and the subjectve 16

6 17th IFAC World Congress (IFAC'8) Seoul, Korea, July 6-11, 8 conjecture calbraton s not enough to do n attachment poston of the any sensor. lateral error, m.4 autonomous run wth developed calbraton.3 autonomous run wthout developed calbraton ` tme, s (a) Lateral error n autonomous run before the orchard autonomous applcaton. The developed calbraton method determned the poston of the laser scanner n robot tractor coordnates usng the reference coordnate. The reference coordnate was GPS antenna locaton. Hough transform recognzed the perpendcular wall as a straght lne and also obtaned the dstance between the perpendcular wall and the laser scanner centerpont, Euler rotaton theorem transformed the perpendcular wall relatve poston to UTM coordnates, and LSM determned the mnmum measurement errors n the laser scanner data acquston whch were the offset poston values. And also, the utlzaton of the perpendcular wall was the technque help n determnng the attachment poston of the laser scanner. The offset poston values of the laser scanner were a = -.56 m, b =.57 m and δ =.8 deg from the tractor's y axs. The developed calbraton method was used to correct data obtaned of the laser scanner n the autonomous navgaton on orchard applcaton. headng error, deg autonomous run wthout developed calbaraton autonomous run wth developed calbaraton tme, s (b) Headng error n autonomous run Fg. 6. Comparson of lateral and headng errors wth and wthout the developed calbraton The RMS (root mean squared) errors n terms of lateral and headng mean error that was calbrated usng the developed method s relatvely small compared to the data that was calbrated usng subjectve calbraton. Table 1 shows the RMS mean error results wth developed calbraton and wth subjectve calbraton. Also, the data that was calbrated by the developed method were the actual data taken by the laser scanner because t s algned wth the reference coordnate axes of the robot tractor. Table 1. Evaluated accuracy results of the autonomous run n orchard applcaton wth and wthout the developed calbraton REFERENCES Davs, J. and X. Chen (1). A laser range scanner desgned for mnmum calbraton complexty. In: Proceedngs of the Thrd Internatonal Conference on 3D Dgtal Imagng and Modellng, Downe, N. and R. Heath (1984). Basc statstcal method. Harper & Row, Publshers, Inc., New York. Gonzales, C. and E. Woods (1993). Dgtal Image Processng. Addson-Wesley Publshng, USA. Khot, L., L. Tang, S. Blackmore and M. Norremark (5). Posture estmaton for autonomous weedng robots navgaton n nursery tree plantatons. In: Proceedngs of the ASAE Annual Meetng. Paper number 539. Pless, P., Zhang, Q. 3. Extrnsc auto-calbraton of a camera and laser range fnder. Department of Computer Scence and Engneerng, Washngton Unversty, St. Lous. Wkpeda, The Free Encyclopeda. January 1, 8. Root mean squares (RMS) mean error wth calbraton wthout calbraton lateral error, m.1. headng error, deg CONCLUSION The research developed an attachment calbraton method for a -d laser scanner attached on the front of the robot tractor 161