Verification of Selected Precision Parameters of the Trimble S8 DR Plus Robotic Total Station

Transcription

1 81 Verfcaton of Selected Precon Parameter of the Trmble S8 DR Plu Robotc Total Staton Sokol, Š., Bajtala, M. and Ježko, J. Slovak Unverty of Technology, Faculty of Cvl Engneerng, Radlnkého 11, Bratlava, Slovaka, Web te: E-mal: Abtract Prerequte for lable executon of urveyng work and acquton of relable reult uage of an ntrument whch meet the accuracy requred for the elected type of work. For th purpoe t poble to carry out tetng of the ntrument ung tandard from ISO 1713 tandard et or other tet method and procedure. In the preented paper reult from tetng the precon of the Trmble S8 DR Plu Robotc total taton by mean of elected tandard from the ISO 1713 et are publhed. Key word: ISO 1713, tetng, tablty of parameter, unveral meaurng taton 1 INTRODUCTION Market wth the urveyng technology currently offer a large number of devce from dfferent manufacturer. Th offer everal tme hgher than demand of urveyor for the new devce. Increang number of manufacture and model logcally lead to the lo of overvew of avalable technology for profeonal urveyor. Aumpton for relable executon of the urveyng actvte uage of an ntrument whch meet requred accuracy for executng work (Gašnec, 005) and (Gašnec, 010). For th purpoe t poble to carry out tetng of the ntrument ung the ISO 1713 tandard or by mean of own tetng procedure. Submtted paper deal wth the tetng of elected precon parameter of the Trmble S8 DR Plu Robotc total taton n term of the ISO 1713 tandard. 1.1 TRIMBLE S8 DR PLUS ROBOTIC The manufacturer of the Trmble S8 total taton clafe th ntrument nto the econd cla of accuracy. Regardng the dtance meaurement mode, the ntrument avalable n DR Plu or DR HP confguraton. The Trmble S8 total taton fnd t applcaton n prece takng out, control network etablhment, meaurement of dplacement and deformaton n tunnel contructon, automated control of contructon vehcle and other urveyng and related applcaton (Gašnec, 005) and (Gašnec, 010). The teted total taton erve for educatonal and centfc actvte at the Department of Surveyng SUT n Bratlava and avalable n the DR Plu ROBOTIC confguraton ncludng other Trmble technologe (MagDrve, Von, SurePont and Autolock). TS 8 Metrology, tetng and calbraton INGEO th Internatonal Conference on Engneerng Surveyng Prague, Czech republc, Aprl 3-4, 014

2 8 INGEO 014 General pecfcaton performance DR PLUS (Trmble, 011): Angle meaurement precon (DIN 1873): Standard devaton of angle..... " (6 cc ) Standard devaton of drecton.. 1,4" (4, cc ) Fgure 1 The bac control and feature Dtance meaurement precon Prm mode: Standard... mm + ppm Standard devaton accordng to ISO mm + ppm Trackng...4 mm + ppm DR mode: Standard... mm + ppm Trackng...4 mm + ppm TESTING THE PRECISION OF A TOTAL STATION One of the poble approach for tetng the precon of urveyng ntrument applcaton of the ISO 1713 tandard, Optc and optcal ntrument. Feld procedure for tetng the geodetc and urveyng ntrument. The tet procedure decrbed n the tandard have been developed pecfcally for n tu applcaton wthout the need for pecal ancllary equpment and are purpoefully degned to mnmze atmopherc nfluence (ISO , ISO and ISO ). The tandard contan clearly pecfed meaurement procedure, mathematcal proceng of the meaured data a well a practcal example of numercal calculaton. The tandard provde a mplfed and full tet procedure for mot of the teted charactertc. The mplfed tet procedure provde an etmate a to whether the precon of a gven total taton wthn the pecfed permtted devaton accordng to ISO The full tet procedure hall be adopted to determne the bet achevable meaure of precon of a total taton t ancllary equpment under feld condton. The tattcal tet hall be carred out to anwer the followng queton (ISO , ISO and ISO ): a) I the calculated expermental tandard devaton,, maller than or equal to correpondng value σ tated by the manufacturer or maller than another predetermned value σ? b) Do two expermental tandard devaton, and %, a determned from two dfferent ample of meaurement belong to the ame populaton, aumng that both ample have the ame degree of freedom, ν? The expermental tandard devaton, and %, may be obtaned from: two ample of meaurement by the ame ntrument but dfferent oberver, two ample of meaurement by the ame ntrument at dfferent tme, two ample of meaurement by dfferent ntrument.

3 Sokol, Š. et al.: Verfcaton of elected precon parameter TESTING THE PRECISION OF THE MEASUREMENT OF HORIONTAL DIRECTIONS AND VERTICAL ANGLES ACCORDING TO ISO The propoal for the tet feld, meaurement requrement, tetng procedure and proceng are tated n ISO The tandard provde mplfed tet procedure and full tet procedure. Full tet procedure, hould be adapted to determne the hghet attanable precon for meaurng wth a partcular theodolte or total taton and ther attachment n feld condton. Therefore, we carred out the full tet procedure. For tetng the precon of horzontal drecton 5 pont were tablzed ung the nal n the area of Freedom Square. For meaurng horzontal drecton trpod wth reflectve prm were et over the pont. Target were approxmately at the ame heght a the horzon of the devce and were evenly dtrbuted around the taton at dtance of about 100 m (Fg. ). For tet of vertcal angle, we ued 4 pont above each other at a dtance of about 50 m from the taton (Fg. ). Fgure Confguraton of the tet feld: left - horzontal drecton, rght - vertcal angle For the full tet procedure we carred out four ere of meaurement by manual targetng and four ere ung Autolock wth automatc meaurement of drecton. The ere were meaured on dfferent day and under dfferent weather condton. Each ere conted of meaurement of three rank on 5 target for the horzontal drecton and 4 target for vertcal angle. All target were meaured n two face of the telecope. The calculaton were carred out accordng to ISO and are preented n the followng table. Table 1 Standard devaton of Hz, V and Index-error accordng to ISO Manual targetng Average Automatc targetng Average No ( cc ) ( cc ) ( cc ) ( cc ) Hz V I-error Hz V I-error Hz V I-error Hz V I-error 1 5,9,3 1,4 4,0 4,3-36, 5,0, -8,5 4,0 3, -37,3 5,,0-4,7 3 4,6 1,7-6,5 5, 3,6-34, 4,4 3,7-36,7 4 5, 1,7-5,4 4,4 3,6-39,

4 84 INGEO 014 To anwer the queton 1, the null hypothe H0 formulated σ and not rejected f the followng condton fulflled (ISO ): χ1 α ( ) cc cc σ 4, 1, 5,04. (1) To anwer the queton, the null hypothe H0 formulated = and not rejected f the followng condton fulflled (ISO ): 1 F1 / (, ) 0,49,0. α () F, 1 α / ( ) Table Reult of tetng the precon of the horzontal drecton accordng to ISO Manual targetng Automatc targetng No ( cc ) Reult ( cc ) Reult 1 5,9 5,0 1,39 H 0 not rejected 4,0 4,0 1,00 H 0 not rejected 1 3 5,9 4,6 1,65 H 0 not rejected 4,0 5, 0,59 H 0 not rejected 1 4 5,9 5, 1,9 H 0 not rejected 4,0 4,4 0,83 H 0 not rejected 3 5,0 4,6 1,18 H 0 not rejected 4,0 5, 0,59 H 0 not rejected 4 5,0 5, 0,9 H 0 not rejected 4,0 4,4 0,83 H 0 not rejected 3 4 4,6 5, 0,78 H 0 not rejected 5, 4,4 1,40 H 0 not rejected Table 3 Reult of tetng the precon of the vertcal angle accordng to ISO Manual targetng Automatc targetng No ( cc ) Reult ( cc ) Reult 1,3, 1,09 H 0 not rejected 4,3 3, 1,81 H 0 not rejected 1 3,3 1,7 1,83 H 0 not rejected 4,3 3,6 1,43 H 0 not rejected 1 4,3 1,7 1,83 H 0 not rejected 4,3 3,6 1,43 H 0 not rejected 3, 1,7 1,67 H 0 not rejected 3, 3,6 0,79 H 0 not rejected 4, 1,7 1,67 H 0 not rejected 3, 3,6 0,79 H 0 not rejected 3 4 1,7 1,7 1,00 H 0 not rejected 3,6 3,6 1,00 H 0 not rejected Comparng the reult, we can conclude wth the uncertanty of 5% that the oberved tandard devaton obtaned from the meaurement of horzontal drecton by manual targetng greater than a pror tandard devaton σ declared by the manufacturer. Here hown probablty that the human factor poblty nfluenced the error of meaurement. Regard to Automatc meaurement the human factor uppreed, whch wa alo reflected n the reult, where the tandard devaton wa lower than pecfed by the manufacturer. Alo when meaured vertcal angle wth both way targetng there were obtaned favourable reult. When tetng the vertcal angle they are teted even to the null hypothe H0 (vertcal ndex error δ equal to zero), where ther acceptaton hall be n the followng condton (ISO ): δ δ t1 α / ( ) δ 0,3. (3) From the reult t een that the null hypothe rejected. It' alo logcal becaue the manufacturer do not eek the equpment to elmnate vertcal ndex error to zero, becaue th would be techncally dffcult, a the vertcal ndex error varable. Therefore, we would lke to tate that tetng of the vertcal ndex error n the relevant tandard ha no practcal jutfcaton when meaured n two poton of the telecope.

5 Sokol, Š. et al.: Verfcaton of elected precon parameter TESTING THE PRECISION OF THE DISTANCE MEASUREMENT ACCORDING TO ISO A n the prevou tet, we focued on the full tet procedure. In a flat terran we et the tet lne contanng 7 pont. Mutual dtance between end pont had value of d 0 = 453,61 m. Dervaton of the dtance between the ntermedate pont baed on the knowledge of the total dtance of the tet lne and the wavelength λ of the EDM unt embedded n the devce (n our cae λ = 0,74 m ). Procedure to calculate the dtance between the ntermedate pont gven n the relevant tandard. We menton only the reultng value (d 1 =30,69m, d =90,57m, d 3 =150,45m, d 4 =10,51m, d 5 =60,63m, d 6 =0,75m). Schedule of meaurng the dtance hown n fgure 3 (rght). Fgure 3 Confguraton of the tet lne and meaured dtance The Trmble reflectve prm wth degnaton PN and zero-pont correctonδ 0 = 35,0 mm wa ued for the meaurement. Durng the dtance meaurement we mplemented the correcton of the ar temperature and the atmopherc preure. We carred out two ere of meaurement n all combnaton ung tandard and trackng mode. The proceng wa made by mean of the leat quare method. Followng table how the reultng tandard devaton for once meaured dtance and zero-pont correcton of the prm for tandard mode and trackng mode. Table 4 Standard devaton of the dtance meaurement and zero-pont correcton accordng to ISO Standard mode Average Trackng mode Average No [mm] [mm] [mm] [mm] δ δ δ δ δ δ δ δ 1 0,7-35,6 0,3 0,7-35,5 0,3 0,7-35,6 0,3 0,7-35,5 0,3 0,6-35,5 0,3 0,7-35,5 0,3 To anwer the queton 1, the null hypothe H0 formulated σ and not rejected f the followng condton fulflled (ISO ): χ1 α ( ) 0 σ 0 σ 1,30. (4)

6 86 INGEO 014 To anwer the queton, the null hypothe H0 formulated = and not rejected f the followng condton fulflled (ISO ): (, ) 0,34, 98 (, ) F 1 α / (5) F1 α / 0 0 The am the 3 rd queton tetng the equalty of zero-pont correcton et by the manufacturer and obtaned from the proceng of meaurement. The null hypothe H0 formulated δ = δ0 and not rejected n the followng condton fulflled (ISO ): δ δ 0 δ,14. (6) Subttuton of the repectve value from table 4 to the above mentoned equaton (4), (5) and (6) confrmed the null hypothe for the tandard and trackng mode..3 TESTING THE PRECISION OF COORDINATES ACCORDING TO ISO The tet pont feld n the hape of a trangle wa located n the area of the Freedom Square n Bratlava. Trpod wth trbrach were et up at each corner of the trangle. The dtance between pont were approxmately 100 m. Confguraton of the tet feld wa elected n accordance wth the ISO tandard. Tet feld dtrbuton wthn the te hown n Fg. 4. Fg. 4 Confguraton of the tet feld The meaurement wa carred out twce n three ere n a day. The meaured et of reult obtaned by manual and automated targetng were ubject for tetng. ero rectangular coordnate were et at each ntrument taton. The value of temperature, preure and atmopherc moture were regtered to correct the dtance meaurement. Coordnate were alway determned n both telecope face. Reflectve prm from the producton of the Trmble Company wth the PN type degnaton wa ued. The meaurement procedure the ame n each ere, the meaurement tart at taton 1 wth targetng to pont and 3. Th followed by mlar meaurement from the econd and thrd taton. Proceng of meaured data realzed eparately for the potonal coordnate x, y and eparately for the z coordnate. Neceary condton for proceng of potonal coordnate x, y the tranformaton nto the one coordnate ytem. On pont 1, we chooe the zero heght pont. The proceng of the reultng coordnate and ther tandard devaton were determned by the leat quare method. Calculated tandard devaton once meaured of x, y, and z coordnate n two face of the telecope can be found n table 5.

7 Sokol, Š. et al.: Verfcaton of elected precon parameter Table 5 Standard devaton of once meaured x, y and z coordnate accordng to ISO Standard mode Trackng mode Set [mm] Average of et [mm] Average of et 1 1, 0,5 0,7 0,4 1,1 0,5 0,7 0,5 1,0 0,4 0,7 0,5 To anwer the queton 1, the null hypothe H0 formulated the followng condton fulflled (ISO ): χ ( ) 1 α σ σ 1,3, χ ( ) 1 α σ σ 1,9. σ and not rejected f (7) (8) To anwer the queton, the null hypothe H0 formulated the followng condton fulflled (ISO ): 1 F1 /, 0,44 α F, 1 α / ( ) ( ),7, = and not rejected f 1 (, ) 0,35,86, (, ) F1 α / (10) F1 α / The tandard devaton of the meaured coordnate not pecfed by the manufacturer of the ntrument, however t can be determned by applcaton of the error propagaton law. For th purpoe a knowledge about a pror tandard devaton of the meaured dtance σ d and the tandard devaton of the meaured horzontal (σ α ) and vertcal angle (σ β ) needed. The dervaton of tandard error baed on the formula for ndvdual rectangular coordnate x, y and z, whch are n the functonal relatonhp wth the dtance d, the horzontal angle α and the vertcal angle β. x = d coα co β; y = d nα co β; z = d n β. (11) The value of the horzontal angle, vertcal angle, lope dtance and the calculated tandard devaton are hown n table 6. Table 6 Calculated tandard devaton σ, σ, σ and σ X g α 118,55 Standard mode [mm] Trackng mode [mm] g β 1,91 σ σ X Y σ σ σ σ X Y σ σ d 99, 75m 0,7 1, 1,4 0,7 1,4 4,0 4,3 0,7 Y Takng nto account the value from table 5 and equaton (7), (8), (9), (10) we can aume that the tandard devaton and obtaned from proceng of the meaurement are maller than or equal to the calculated a pror tandard devaton hown n table 6 at 5 % gnfcance level. (9)

8 88 INGEO 014 Table 7 Stattcal tetng to the nd queton baed on ISO Set Standard mode, [mm] Trackng mode, [mm] Reult Reult 1 1, 1,0 1,44 H 0 for not reject. 0,7 0,7 1,00 H 0 for not reject. 1 0,5 0,4 1,56 H 0 for not reject. 0,4 0,5 0,64 H 0 for not reject. From table 7 we aume that the partal tandard devaton obtaned from ndvdual et of meaurement (for the tandard and trackng dtance meaurement mode) come from the ame populaton at 5% gnfcance level. 3 CONCLUSION In ubmtted paper decrbed tet of the precon of the Trmble S8 DR Plu Robotc total taton accordng to the ISO 1713 tandard. Precon of the horzontal drecton, the vertcal angle and gnfcance of the ndex error for manual and automatc targetng ung Autolock wa verfed accordng to the ISO tandard. Dtance meaurement precon and value of the zero-pont correcton wa teted n term of ISO tandard. Tetng the precon of plane rectangular coordnate x, y and heght coordnate z wa realzed by mean of the ISO tandard. Due to the fact that the manufacturer doe not pecfy precon of the coordnate determnaton, the relevant charactertc of precon were derved applyng the error propagaton law ung precon of the horzontal angle, the vertcal angle and the horzontal dtance declared by the manufacturer. Precon declared by the manufacturer wa not reached for manually meaured horzontal drecton and tetng the ndex error howed t gnfcant non-zero value. REFERENCES ISO : Optc and optcal ntrument. Feld procedure for tetng geodetc and urveyng ntrument: Part 3. Theodolte. SÚTN Bratlava, 010. ISO : Optc and optcal ntrument Feld procedure for tetng geodetc and urveyng ntrument: Part 4: Electro-optcal dtance meter (EDM meaurement to reflector). SÚTN Bratlava, 013. ISO : Optc and optcal ntrument Feld procedure for tetng geodetc and urveyng ntrument: Part 5: Total taton. SÚTN Bratlava, 01. Trmble, 011. Trmble S8 Total Staton Dataheet [onlne]. [ct ].:< ISO : Meaurement method for buldng. Settng-out and meaurement. Part 3: Checklt for the procurement of urvey and meaurement ervce. SUTN 00. GAŠINEC, J., GAŠINCOVÁ, S.: Subtardand practce of adjutment meaurement n local geodetc network. In: Acta Montantca Slovaca, 005. Volume 10, n., p ISSN GAŠINEC, J., GAŠINCOVÁ, S.: Adjutment of potonal geodetc network by unconventonal etmaton. In: Acta Montantca Slovaca 010. Volume 15, n. 1, p ISSN