1/22 1. Localization

Transcription

1 1/22 1 Localizaion Lecure 4 Thursday Ocober 20, 2016

2 2/22 2 Objecives When you have finished his lecure you should be able o: Ge familiar wih differen local, global and hybrid localizaion MUSES_SECRET: ORF-RE Projec - PAMI Research Group Universiy of Waerloo echniques of auonomous vehicles. Undersand he odomery of differenial drive. Recognize sysemaic and non-sysemaic odomery errors and learn how o measure hem using UMBmar and exended UMBmar.

3 3/22 3 Ouline Auonomous Vehicle Localizaion Local Relaive Localizaion Global Absolue Localizaion Hybrid Localizaion Odomery for Differenial Drive Sysemaic and Non-Sysemaic Odomery Errors Measuremen of Odomery Errors Summary

4 4/22 4 Ouline Auonomous Vehicle Localizaion Local Relaive Localizaion Global Absolue Localizaion Hybrid Localizaion Odomery for Differenial Drive Sysemaic and Non-Sysemaic Odomery Errors Measuremen of Odomery Errors Summary

5 Auonomous Vehicle Localizaion Auonomous vehicle localizaion provides answer for he quesion: Where am I? Overview of user requiremens in erms of accuracy and coverage [1] MUSES_SECRET: L4, SPC418: Auonomous ORF-RE Vehicles Projec Design - PAMI and Conrol- Research Zewail Group Ciy Universiy of Science of and Waerloo Technology - Fall 2016 Dr. Alaa Khamis 5/22 5

6 6/22 6 Auonomous Vehicle Localizaion Echolocaion in Naure

7 7/22 7 Auonomous Vehicle Localizaion Auonomous Vehicle Localizaion Indoor Localizaion The process of accuraely esimae he posiion and orienaion of a mobile vehicle moving inside building s environmens Oudoor Localizaion compared o indoor localizaion, oudoor localizaion is a more challenging process han indoor localizaion due o he lac of he abiliy o conrol he environmen nor o predic i

8 8/22 8 Auonomous Vehicle Localizaion Indoor Localizaion Indoor Localizaion echnologies Accuracy Vs. Coverage [1]

9 9/22 9 Auonomous Vehicle Localizaion Indoor Localizaion Indoor Localizaion echnologies Accuracy Vs. Carrier Wavelengh [1]

10 10/22 Auonomous Vehicle Localizaion Oudoor Localizaion Oudoor localizaion Local Relaive Localizaion/Dead Reconing Global Absolue Localizaion Hybrid Localizaion IMU-GPS, PPP-GPS, RTK-GPS,... Odomery Inerial Navigaion Acive Beacons Passive Beacons Opical encoders Hall-effec Doppler-effec Visual odomery Absolue Incremenal Ground based RF sysems Acive RF sysems Real-ime Locaing Sysems GPS Tradiional GPS Model Maching High-precision GPS Arificial Landmar Recogniion Naural Landmar Recogniion

11 11/22 Ouline Auonomous Vehicle Localizaion Local Relaive Localizaion Global Absolue Localizaion Hybrid Localizaion Odomery for Differenial Drive Sysemaic and Non-Sysemaic Odomery Errors Measuremen of Odomery Errors Summary

12 Local Relaive Localizaion Dead Reconing Dead reconing is a predicive calculaion based on inference o esimae he posiion of an aircraf or a ship wihou asronomical observaions, as by applying o a previously deermined posiion he course and disance raveled since. Source: Wiipedia and Answers.com Source: Wiipedia and Answers.com MUSES_SECRET: L4, SPC418: Auonomous ORF-RE Vehicles Projec Design - PAMI and Conrol- Research Zewail Group Ciy Universiy of Science of and Waerloo Technology - Fall 2016 Dr. Alaa Khamis 12/22

13 13/22 Local Relaive Localizaion Dead Reconing A disadvanage of dead reconing is ha since new posiions are calculaed solely from previous posiions, he errors of he process are cumulaive, so he error in he posiion fix grows wih ime. Accumulaed errors

14 14/22 Local Relaive Localizaion Dead Reconing Relaive Posiion Measuremens Dead Reconing Odomery Inerial Navigaion

15 15/22 Local Relaive Localizaion Odomery This mehod uses encoders o measure wheel roaion and/or seering orienaion. Odomery Opical Encoders Hall-Effec Sensors Doppler Sensors Visual Odomery See Lecure-3 Absolue Opical Encoders Incremenal Opical Encoders See Lecure-3

16 16/22 Local Relaive Localizaion Doppler Sensor The Doppler effec or Doppler shif, is he change in frequency of a wave or oher periodic even for an observer moving relaive o is source. The received frequency is higher compared o he emied frequency during he approach, i is idenical a he insan of passing by, and i is lower during he recession. Source: Wiipedia I is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from an observer.

17 Local Relaive Localizaion Doppler Sensor The microwave radar radio deecion and ranging sensor is aimed downward a a prescribed angle ypically 45 o o sense ground movemen. Acual ground speed V A is derived from he measured velociy V D according o he following equaion. V A = acual ground velociy along pah V D = measured Doppler velociy = angle of declinaion c = speed of ligh F D = observed Doppler shif frequency F 0 = ransmied frequency. MUSES_SECRET: L4, SPC418: Auonomous ORF-RE Vehicles Projec Design - PAMI and Conrol- Research Zewail Group Ciy Universiy of Science of and Waerloo Technology - Fall 2016 Dr. Alaa Khamis 17/22

18 18/22 Local Relaive Localizaion Visual Odomery Visual Odomery VO is he process of deermining he posiion and orienaion of a robo by analyzing he associaed camera images. This has been used in differen roboic applicaions, such as on he Mars Exploraion Rovers [2]. I is he process of incremenally esimaing he pose of he vehicle by examining he changes ha moion induces on he images of is onboard cameras.

19 19/22 Local Relaive Localizaion Visual Odomery In order o guaranee he reliabiliy of Visual Odomery esimaes, several assumpions are considered [3]: Sufficien illuminaion in he environmen. Dominance of saic scene over moving objecs. Enough exure o allow apparen moion o be exraced. Sufficien scene overlap beween consecuive frames.

20 20/22 Local Relaive Localizaion Odomery Advanages Odomery is oally selfconained, and i is always capable of providing he vehicle wih an esimae of is posiion. Disadvanages The posiion error grows wihou bound unless an independen reference is used periodically o reduce he error. Accumulaed odomery errors

21 Local Relaive Localizaion Inerial Navigaion Mechanical Gyroscopes Space-Sable Gyroscopes Gyrocompasses Heading Sensors Piezoelecric Gyroscopes Opical Gyroscopes Geomagneic Sensors Acive Ring Laser Gyros Resonan Fiber Opic Gyros Hall-Effec Compasses Magneoresisive Compasses Digial Compasses MUSES_SECRET: L4, SPC418: Auonomous ORF-RE Vehicles Projec Design - PAMI and Conrol- Research Zewail Group Ciy Universiy of Science of and Waerloo Technology - Fall 2016 Dr. Alaa Khamis 21/22

22 22/22 Local Relaive Localizaion Inerial Navigaion This mehod uses gyroscopes and someimes acceleromeers o measure rae of roaion and acceleraion. Advanages Measuremens are inegraed once or wice o yield posiion. Inerial navigaion sysems also have he advanage ha hey are self-conained.

23 23/22 Local Relaive Localizaion Inerial Navigaion Disadvanages Inerial sensor daa drifs wih ime because of he need o inegrae rae daa o yield posiion; any small consan error increases wihou bound afer inegraion. Inerial sensors are hus unsuiable for accurae posiioning over an exended period of ime.

24 24/22 Local Relaive Localizaion Inerial Navigaion Disadvanages Anoher problem wih inerial navigaion is he high equipmen cos. For example, highly accurae gyros, used in airplanes, are inhibiively expensive. Very recenly fiber-opic gyros also called laser gyros, which are said o be very accurae, have fallen dramaically in price and have become a very aracive soluion for mobile robo navigaion.

25 25/22 Ouline Auonomous Vehicle Localizaion Local Relaive Localizaion Global Absolue Localizaion Hybrid Localizaion Odomery for Differenial Drive Sysemaic and Non-Sysemaic Odomery Errors Measuremen of Odomery Errors Summary

26 26/22 Global Absolue Localizaion Acive Beacons This mehod compues he absolue posiion of he robo from measuring he direcion of incidence of hree or more acively ransmied beacons. The ransmiers, usually using ligh or radio frequencies, mus be locaed a nown sies in he environmen. Acive Beacons Ground based RF sysems Acive RF sysems Real-ime Locaing Sysems GPS Tradiional GPS High-precision GPS

27 27/22 Global Absolue Localizaion Acive Beacons: Ground-Based RF Sysems inerrogaor Moorola s Mini-Ranger Falcon 484 R posiion-locaion sysem provides 2 m accuracy over ranges of 100 m o 75 m. The acual disance beween he inerrogaor and a given ransponder/ransceiver is found by: Te Td c D 2 where D = separaion disance, T e = oal elapsed ime T d = ransponder urn-around delay, c = speed of ligh.

28 28/22 Global Absolue Localizaion Acive Beacons: Ground-Based RF Sysems Moorola s Mini-Ranger Falcon 484 R posiion-locaion sysem provides 2 m accuracy over ranges of 100 m o 75 m. An iniial calibraion is performed a a nown locaion o deermine he urn-around delay TAD for each ransponder i.e., he ime required o ransmi a response bac o he inerrogaor afer receip of inerrogaion.

29 29/22 Global Absolue Localizaion Acive Beacons: RFID-based Localizaion [4]

30 30/22 Global Absolue Localizaion Real Time Locaing Sysem RTLS Wireless RTLS ags are aached o objecs or worn by people, and fixed reference poins receive wireless signals from ags o deermine heir locaion. A pulse wih sharp edges is needed o accuraely locae an objec wih radio waves.

31 31/22 Global Absolue Localizaion Real Time Locaing Sysem RTLS UWB RTLS Advanages: o Precise localizaion of agged objecs from 10cm up o 300 m in Line-of-Sigh LOS mode o Cos effecive. o Localizaion of muliple devices using he same seup. o Low power consumpion. UWB RTLS Disadvanages: o Anennas should be insalled in he woring sie o Range limiaion 300m maximum.

32 32/22 Global Absolue Localizaion Acive Beacons: GPS GPS saellies broadcas he ime and daa abou heir locaions. a GPS receiver compares signals from a leas hree or four GPS saellies o deermine i s own locaion. A GPS receiver figures ou how far away i is from each saellie based on how much ime i aes a broadcas signal o ravel from he saellie o he receiver. Source: hp://

33 Global Absolue Localizaion Acive Beacons: GPS Since he locaion of each GPS saellie is nown, he receiver s locaion can be deermined by riangulaing he disances from several saellies. For perfecly synchronized saellies where c is he speed of ligh and B is he receiver cloc offse ime. The receiver cloc offse is he difference beween GPS ime and inernal receiver ime. B is he same, which means he all he saellies mus have perfecly synchronized clocs More info: hp:// MUSES_SECRET: L4, SPC418: Auonomous ORF-RE Vehicles Projec Design - PAMI and Conrol- Research Zewail Group Ciy Universiy of Science of and Waerloo Technology - Fall 2016 Dr. Alaa Khamis 33/22

34 34/22 Global Absolue Localizaion Acive Beacons: High-precision or Sub-meer GPS Saellie-based Augmenaion Sysem SBAS Precise Poin Posiioning PPP Real Time Kinemaic RTK

35 35/22 Global Absolue Localizaion Sub-meer GPS: SBAS Saellie-based augmenaion sysems SBAS, such as EGNOS, complemen exising global navigaion saellie sysems GNSS. SBAS compensae for cerain disadvanages of GNSS in erms of accuracy, inegriy, coninuiy and availabiliy. Exising Saellie based Augmenaion Sysems SBAS [5] For EGNOS, Egyp lies a around 2.5 meers in Verical, and 2.5 meers Horizonal. This means ha he 0.6 and 0.8 meers accuracies of EGNOS are inside Europe.

36 36/22 Global Absolue Localizaion Sub-meer GPS: PPP Terrasar-D is a precise poin posiioning PPP service which delivers posiion accuracy a beer han 10cm 95% globally. For more info, visi hp://

37 37/22 Global Absolue Localizaion Sub-meer GPS: RTK

38 38/22 Global Absolue Localizaion Sub-meer GPS Specificaion GPS PPP GPS RTK UWB Accuracy 10 cm > 10 cm 30 cm Updae Rae 20 Hz 20 Hz 3 Hz Power Consumpion 1.6 W - 3 W W 3 W Addiional Requiremen PPP subscripion ~ 2500 Euro/Year/ Module Single RTK Saion Insallaion ~ 5275 Euro Need anenna/s o be insalled in he field Source: Alaa Khamis, MineProbe projec: hp://

39 39/22 Global Absolue Localizaion Passive Beacon Passive Beacons Arificial Landmar Recogniion Naural Landmar Recogniion Model Maching

40 40/22 Global Absolue Localizaion Arificial Landmar Recogniion In his mehod disincive arificial landmars are placed a nown locaions in he environmen. The advanage of arificial landmars is ha hey can be designed for opimal deecabiliy even under adverse environmenal condiions. As wih acive beacons, hree or more landmars mus be in view o allow posiion esimaion. Landmar posiioning has he advanage ha he posiion errors are bounded, bu deecion of exernal landmars and real-ime posiion fixing may no always be possible.

41 41/22 Global Absolue Localizaion Naural Landmar Recogniion Here he landmars are disincive feaures in he environmen. There is no need for preparaion of he environmen, bu he environmen mus be nown in advance. The reliabiliy of his mehod is no as high as wih arificial landmars.

42 42/22 Global Absolue Localizaion Model Maching In his mehod informaion acquired from he robo s onboard sensors is compared o a map or world model of he environmen [6]. If feaures from he sensor-based map and he world model map mach, hen he vehicle s absolue locaion can be esimaed Sonar-based Environmen Map Esimaed Posiion Acual Posiion odomery Self Localizaion

43 43/22 Ouline Auonomous Vehicle Localizaion Local Relaive Localizaion Global Absolue Localizaion Hybrid Localizaion Odomery for Differenial Drive Sysemaic and Non-Sysemaic Odomery Errors Measuremen of Odomery Errors Summary

44 44/22 Hybrid Localizaion Source: Alaa Khamis, MineProbe projec: hp://

45 45/22 Hybrid Localizaion Localizaion Technique Complexiy Range Cos Reliabiliy Infrasrucure Req. Compuaional Cos Dead Reconing -- Inerial Navigaion -- Visual Odomery Ground based RF Acive RFID RTLS PPP GPS RTK GPS Source: Alaa Khamis, MineProbe projec: hp://

46 46/22 Ouline Auonomous Vehicle Localizaion Local Relaive Localizaion Global Absolue Localizaion Hybrid Localizaion Odomery for Differenial Drive Sysemaic and Non-Sysemaic Odomery Errors Measuremen of Odomery Errors Summary

47 Odomery for Differenial Drive y Given: Robo geomery Righ and lef wheels velociies or ravelled disances by each wheel. Iniial pose: x 0, y 0, 0 Odomery-based Posiioning Required: New pose: x, y, afer ime. New pose: x, y, duraion: Iniial pose: x 0, y 0, 0 MUSES_SECRET: L4, SPC418: Auonomous ORF-RE Vehicles Projec Design - PAMI and Conrol- Research Zewail Group Ciy Universiy of Science of and Waerloo Technology - Fall 2016 Dr. Alaa Khamis 47/22 x

48 48/22 Odomery for Differenial Drive Suppose ha a differenial drive robo is roaing around he poin ICC wih an angular velociy. During he infinie shor ime d he robo will ravel he disance from he poin P o P+d wih a linear velociy V. V has wo perpendicular componens, one along he X axis - V x, and he oher along he Y axis - V y. For infinie shor ime we can assume ha he robo is moving along a sraigh line angen in he poin P o he real rajecory of he robo.

49 49/22 Odomery for Differenial Drive Based on he wo componens of he velociy V, he raveled disance in each direcion can be calculaed: dx dy V V where V V x y x y. d. d V.cos V.sin Similarly, he angle of he roaion can be obained: d. d

50 Odomery for Differenial Drive dx V dy V x y. d. d d. d Inegraing he above equaions in he ime we obain: x y V V x y d d x d o o y o where x 0, y 0, 0 is he iniial pose. MUSES_SECRET: L4, SPC418: Auonomous ORF-RE Vehicles Projec Design - PAMI and Conrol- Research Zewail Group Ciy Universiy of Science of and Waerloo Technology - Fall 2016 Dr. Alaa Khamis 50/22

51 MUSES_SECRET: ORF-RE Projec - PAMI Research Group Universiy of Waerloo 51/22 51 L4, SPC418: Auonomous Vehicles Design and Conrol- Zewail Ciy of Science and Technology - Fall 2016 Dr. Alaa Khamis Odomery for Differenial Drive o x o o d y d V y x d V x sin.cos Since.sin.cos V V V V y x We can rewrien he previous equaions as follows: These formulas are valid for all robos capable of moving in a paricular direcion a a given velociy V.

52 MUSES_SECRET: ORF-RE Projec - PAMI Research Group Universiy of Waerloo 52/22 52 L4, SPC418: Auonomous Vehicles Design and Conrol- Zewail Ciy of Science and Technology - Fall 2016 Dr. Alaa Khamis Odomery for Differenial Drive o L R o R L o R L d v v D y d v v y x d v v x sin 2 1.cos 2 1 For he special case of differenial drive robo, we can infer: where D is he wheel separaion; v L and v R are he linear velociies of he lef and righ wheels respecively.

53 MUSES_SECRET: ORF-RE Projec - PAMI Research Group Universiy of Waerloo 53/22 53 L4, SPC418: Auonomous Vehicles Design and Conrol- Zewail Ciy of Science and Technology - Fall 2016 Dr. Alaa Khamis Odomery for Differenial Drive For a pracical realizaion, he previous formula can be rewrien for discree iming: o i L R o i R L o i R L i v i v D y i i v i v y x i i v i v x. 1..sin 2 1..cos where x, y, q are he componens of he pose a he sep of he movemen and is he inerval e.g. sampling period beween wo sampling imes. Depending on he expeced accuracy, should be properly seleced.

54 MUSES_SECRET: ORF-RE Projec - PAMI Research Group Universiy of Waerloo 54/22 54 L4, SPC418: Auonomous Vehicles Design and Conrol- Zewail Ciy of Science and Technology - Fall 2016 Dr. Alaa Khamis Odomery for Differenial Drive Easier o implemen on microconrollers is he recurren form: sin cos 2 1 v v D y v v y x v v x L R R L R L

55 55/22 Odomery for Differenial Drive The velociies v L i and v R i can be esimaed based on encoders, even hough i is easier and more precise wihou ime measuremen o use he disances obained direcly from he sensors, based on he following equaion: v v. d d L R L R where d L and d R are he disances raveled in las sampling period.

56 MUSES_SECRET: ORF-RE Projec - PAMI Research Group Universiy of Waerloo 56/22 56 L4, SPC418: Auonomous Vehicles Design and Conrol- Zewail Ciy of Science and Technology - Fall 2016 Dr. Alaa Khamis Odomery for Differenial Drive Finally he inemaics equaion of differenial drive can be rewrien as below: sin cos 2 1 d d D y d d y x d d x L R R L R L

57 57/22 Ouline Auonomous Vehicle Localizaion Local Relaive Localizaion Global Absolue Localizaion Hybrid Localizaion Odomery for Differenial Drive Sysemaic and Non-Sysemaic Odomery Errors Measuremen of Odomery Errors Summary

58 MUSES_SECRET: ORF-RE Projec - PAMI Research Group Universiy of Waerloo 58/22 58 L4, SPC418: Auonomous Vehicles Design and Conrol- Zewail Ciy of Science and Technology - Fall 2016 Dr. Alaa Khamis Odomery Errors Odomery is based on simple equaions ha are easily implemened and ha uilize daa from inexpensive incremenal wheel encoders sin cos 2 1 d d D y d d y x d d x L R R L R L However, odomery is also based on he assumpion ha wheel revoluions can be ranslaed ino linear displacemen relaive o he floor. This assumpion is only of limied validiy.

59 MUSES_SECRET: ORF-RE Projec - PAMI Research Group Universiy of Waerloo 59/22 59 L4, SPC418: Auonomous Vehicles Design and Conrol- Zewail Ciy of Science and Technology - Fall 2016 Dr. Alaa Khamis Odomery Errors Each compued robo posiion is surrounded by a characerisic error ellipse, which indicaes a region of uncerainy for he robo s acual posiion. Accumulaed odomery errors Growing error ellipses indicae he growing posiion uncerainy wih odomery sin cos 2 1 d d D y d d y x d d x L R R L R L

60 60/22 Odomery Errors Odomery Errors Sysemaic Errors Non-Sysemaic Errors

61 61/22 Odomery Errors Sysemaic Errors: Unequal wheel diameers. Average of acual wheel diameers differs from nominal wheel diameer. Acual wheelbase differs from nominal wheelbase. Misalignmen of wheels. Finie encoder resoluion. Finie encoder sampling rae.

62 62/22 Odomery Errors Non-Sysemaic Errors: Travel over uneven floors bumps or cracs. Travel over unexpeced objecs on he floor. Wheel-slippage due o: slippery floors overacceleraion fas urning sidding exernal forces ineracion wih exernal bodies inernal forces casor wheels non-poin wheel conac wih he floor.

63 63/22 Ouline Auonomous Vehicle Localizaion Local Relaive Localizaion Global Absolue Localizaion Hybrid Localizaion Odomery for Differenial Drive Sysemaic and Non-Sysemaic Odomery Errors Measuremen of Odomery Errors Summary

64 64/22 Measuremen of Odomery Errors Measuremen of Sysemaic Odomery Errors The error due o unequal wheel diameers, defined as: E D / d R D L where D R and D L are he acual wheel diameers of he righ and lef wheel, respecively. The error due o uncerainy abou he effecive wheelbase, defined as: E b b acual / b nominal where b is he wheelbase of he vehicle, ideally measured as he disance beween he wo conac poins beween he wheels and he floor.

65 Measuremen of Odomery Errors Measuremen of Sysemaic Odomery Errors Bidirecional square-pah experimen or Universiy of Michigan Benchmar UMBmar UMBmar requires ha he square pah experimen be performed in boh clocwise and counerclocwise direcion. The effec of he wo dominan sysemaic dead-reconing errors E b and E d. Noe how boh errors may cancel each oher ou when he es is performed in only one direcion. MUSES_SECRET: L4, SPC418: Auonomous ORF-RE Vehicles Projec Design - PAMI and Conrol- Research Zewail Group Ciy Universiy of Science of and Waerloo Technology - Fall 2016 Dr. Alaa Khamis 65/22

66 Measuremen of Odomery Errors Measuremen of Sysemaic Odomery Errors UMBmar Afer conducing he UMBmar experimen, one may wish o derive a single numeric value ha expresses he odomeric accuracy wih respec o sysemaic errors of he esed vehicle. wo dominan sysemaic dead-reconing errors E b and E d : when he square pah is performed in he opposie direcion one may find ha he errors add up. MUSES_SECRET: L4, SPC418: Auonomous ORF-RE Vehicles Projec Design - PAMI and Conrol- Research Zewail Group Ciy Universiy of Science of and Waerloo Technology - Fall 2016 Dr. Alaa Khamis 66/22

67 67/22 Measuremen of Odomery Errors Measuremen of Sysemaic Odomery Errors UMBmar Le x,y, represen he reurn posiion errors caused by odomery. x y x y abs abs abs x y calc calc calc x abs, y abs & abs = absolue posiion and orienaion of he robo; x calc, y calc & calc = posiion and orienaion of he robo as compued from odomery.

68 68/22 Measuremen of Odomery Errors Measuremen of Sysemaic Odomery Errors UMBmar Afer 5 runs, he coordinaes of he wo ceners of graviy are compued from he resuls: x y c. g., cw/ ccw c. g., cw/ ccw i1 5 i1 x y i, cw/ ccw i, cw/ ccw Typical resuls from running UMBmar a square pah run in boh cw and ccw direcions wih an uncalibraed vehicle.

69 69/22 Measuremen of Odomery Errors Measuremen of Sysemaic Odomery Errors UMBmar The absolue offses of he wo ceners of graviy from he origin are given by: r c. g., cw 2 x y c. g., cw c. g., cw 2 r c. g., ccw 2 x y 2 c. g., ccw c. g., ccw

70 70/22 Measuremen of Odomery Errors Measuremen of Sysemaic Odomery Errors UMBmar Finally, he measure of odomeric accuracy for sysemaic errors is: E max, sys max rc. g., cw; rc. g., ccw The reason for no using he average is ha for pracical applicaions one needs o worry abou he larges possible odomery error.

71 71/22 Measuremen of Odomery Errors Measuremen of Sysemaic Odomery Errors UMBmar E max, sys max rc. g., cw; rc. g., ccw One should also noe ha he final orienaion error is no considered explicily in he expression for E max,sys. This is because all sysemaic orienaion errors are implied by he final posiion errors. In oher words, since he square pah has fixed-lengh sides, sysemaic orienaion errors ranslae direcly ino posiion errors.

72 72/22 Measuremen of Odomery Errors Measuremen of Non-Sysemaic Odomery Errors Exended UMBmar Alhough i is more difficul o measure small angles, measuremen of is a more consisen quaniaive indicaor for comparing he performance of differen robos.

73 73/22 Measuremen of Odomery Errors Measuremen of Non-Sysemaic Odomery Errors Exended UMBmar One can measure and express he suscepibiliy of a vehicle o nonsysemaic errors in erms of is average absolue orienaion error defined as: nonsys averg i i1 nonsys i, cw nonsys i, ccw sys averg, cw sys averg, ccw

74 74/22 Ouline Auonomous Vehicle Localizaion Local Relaive Localizaion Global Absolue Localizaion Hybrid Localizaion Odomery for Differenial Drive Sysemaic and Non-Sysemaic Odomery Errors Measuremen of Odomery Errors Summary

75 75/22 Summary Odomery is he mos widely used navigaion mehod for mobile robo posiioning. I is well nown ha odomery provides good shor-erm accuracy, is inexpensive, and allows very high sampling raes. However, he fundamenal idea of odomery is he inegraion of incremenal moion informaion over ime, which leads ineviably o he accumulaion of errors. In some cases, odomery is he only navigaion informaion available; for example: when no exernal reference is available, when circumsances preclude he placing or selecion of landmars in he environmen, or when anoher sensor subsysem fails o provide usable daa.

76 76/22 References 1. Mauz, Rainer. Indoor posiioning echnologies. Diss. Habiliaionsschrif ETH Zürich, 2012, Available a: hp://ecollecion.library.ehz.ch/eserv/eh:5659/eh pdf Las accessed, Ocober 16, Maimone, Mar, Yang Cheng, and Larry Mahies. "Two years of visual odomery on he mars exploraion rovers." Journal of Field Roboics : Scaramuzza, F. Fraundorfer. Visual Odomery: Par I - The Firs 30 Years and Fundamenals,IEEE Roboics and Auomaion Magazine, Volume 18, issue 4, M. Suruz Miah and Wail Gueaieb, Indoor Robo Navigaion Through Inelligen Processing of RFID Signal Measuremens, 2010 Inernaional Conference on Auonomous and Inelligen Sysems AIS-2010, June 21-23, 2010, Povoa de Varzim, Porugal. 5. EGNOS poral hp://egnos-poral.gsa.europa.eu/discover-egnos/abouegnos/wha-sbas, las accessed: Augus, R. Brown y B. Donald, Mobile Robo Self-Localizaion wihou Explici Landmars, Algorihmica 26, pp , 2000.