Kinemaics of underwaer inspecion robo Mariusz Giergiel*, Krzyszof Kurc**, Pior Małka*, Tomasz Buraowski*, Dariusz Szybicki** *AGH Universiy of Science and Technology **Rzeszow Universiy of Technology Absrac: The aricle presens he issues associaed wih modeling and numerical verificaion of a kinemaics inspecion robo for diagnosic and mainenance anks wih liquid. The robo has been consruced a he Deparmen of Roboics and Mecharonics of AGH in frames of he gran financed by NBiR. The analysis of he kinemaic was drawn using available and described in he lieraure mahemaical mehods, as well as based on exising robos designs. Srucural soluions applied enable o conrol wo crawler racks, module cleaning he boom of ank and he diagnosic module. erificaion of he kinemaic model drawn up was carried ou wih use engineering mehods and developmen sofware MATAB. Received resuls were presened as mahemaical equaions and simulaions illusraed in he form of characerisics depicing kinemaic parameers of he robo s moion. The work also presens direcions of furher research on he consruced robo. Keywords: mobile robo, kinemaics, inspecion robo, underwaer robo Oher advanages of replacing radiional mehods of haw inspecion robo are: faser inspecion, greaer work securiy, and wider range of available inspecion mehods. The aricle presens one elemen of he srucural-research procedure ha is drawing he model of kinemaics along in wih numerical verificaion.. Descripion of he robo consrucion and working space The inspecion robo is consruced from ubular elemens allowing for he wheelbase change. rawler rack racks were used o he drive wih developed ransmission gears and propellers, heir srucure allows for works up o 3 m underwaer. Addiionally he robo is equipped wih he diagnosic-monioring module used for observaion he ank above he robo heigh. Equipped is wih 3 cameras ( for observaion, for he docking wih home saion), roaing drives and sensors laser.. Inroducion The projec of robo for inspecion and diagnosics of anks wih liquids is consruced a he Deparmen of Roboics and Mecharonic of AGH. I s creaed in cooperaion wih he Municipal Enerprise MPWiK SA of waer supply sysems and sewage sysem. Is aim is o develop he original consrucion of inspecion machine enabling o deermine he echnical condiion of concree consrucion of sorage liquid anks (mos ofen waer). The design fundamenal assumpion: work in condiions of souse in liquid a dephs up o several. Fulfilling his assumpion will have a fundamenal influence on he reducion coss of he inspecion procedure because exising mehods require mos ofen empying anks, wha carries behind long (abou one monh) soppages. I nex burdens he company budge, which is forced o urn off he ank/s from use. Fig.. Tanks for soring waer MPWiK racow Rys.. Zbiorniki do magazynowania wody pinej MPWiK SA Kraków The inspecion robo is inended for diagnosics and observaion of anks wih liquids. ooperaion wih MPWiK SA in racow [7] enables verificaions and esing he consruced robo in real erms. racow waer supply sysems have a dozen of anks for soring waer (among ohers he bigges in Europe abou diameer of 34 m). They require repeaed reviews and exper opinions, applying he consruced robo will enable o sreamline hese aciviies, and will reduce he coss of hese ype acions. 3. Modeling he kinemaics of inspecion robo Fig.. Inspecion robo wih he diagnosic-monioring module Rys.. Robo inspekcyjny z modułem diagnosyczno-obserwacyjnym rawler rack driving sysems are arrangemens, o which involves a differen ype of variables in ime. Descripion of he crawler rack movemen in real condiions wih uneven ground on changeable parameers, is very complex. The deailed mahemaical descripion of he move of
For he descripion of moion poins on he crawler rack circumference for he simplified model (fig. 6) wo sysems of coordinaes were acceped. Arrangemens y, z is he moionless arrangemen associaed wih he ground, arrangemen y, z is movable arrangemen associaed wih vehicle [,, 5, 6]. Fig. 3. a) AD Model, b) Simplified Model Rys. 3. a) Model AD, b) Model uproszczony individual crawler rack poins is so compound ha i is necessary o apply simplified models. rawler racks (fig. 3a) in he very simplificaion i is possible o model, as he non-srech ape abou deermined shape by he drive wheel, sreching wheel and no deformable ground (fig. 3b) [ 4]. Apar from widely applied crawler racks consruced from links, appear also crawler racks made from he elasomer bel. They consiue one elemen along wih cluches. Driving arrangemen of he analyzed crawler rack robo are wo driving modules (fig. 4). Specificaions: heigh: mm, widh: 9 mm, lengh: 38 mm, speed up o 9.75 m/min, maximum load: 45 kg, waer resisance o he deph 3 m, mass: sainless seel.5 kg. Fig. 6. Simplified model of he crawler rack rack Rys. 6. Uproszczony model gąsienicy The movemen of any crawler rack poin is composiion of wo movemens (fig. 6): relaive move, of he agreemen y, z, ransporaion move relaive o he immovable arrangemen y, z. The absolue speed of any poin on he crawler rack circumference is equal o he sum of geomerical ransporaion speed and relaive speed. by = u +cosϕ () = sinϕ () bz b= by+ bz = u + +u cosϕ (3) Fig. 4. rawler racks model AD Rys. 4. Gąsienice model AD where: u speed of ransporaion, relaive speed of any poin on he crawler rack circumference, b absolue speed of he poin on crawler rack circumference, j angle beween vecors and u. In case when j = p, ha is when poins of he crawler rack circumference conac wih he ground, i is possible o wrie. b= u+ (4) Basic inside sub-assemblies (fig. 5) of each module: driving engine planeary ransmission conical ransmission leading ransmission Individual raio of hese ransmissions: i = 66 : ransferring he planeary ransmission, i = : ransferring he conical ransmission, i 3 = : ransferring he leading ransmission. Toal raio he driving module: i = 64 :. Fig. 5. Driverain Rys. 5. Układ przeniesienia napędu 3.. Slide crawler rack When ransferring of he loadbearing crawler rack segmen appears relaive o ground, hen he effec of slip occurs [, 5, 6]. Mainly for he crawler rack slide affecs he following facors: ownerships of he ground, appearing driving force, ype and placing cluches on he crawler rack rack. Appearing in he crawler rack arrangemen, he driving force causes appear of cuing powers in he ground. The re- Pomiary Auomayka Roboyka nr / 3
laionship beween appearing facors i is possible o deermine relaions by: 6 Pn b τxdx = (5) where: P n driving force, b widh of he crawler rack, lengh of he load-bearing of he crawler rack segmen, x sresses cuing in he sof ground. Assuming ha he course of parallel deformaions o he ground is linear, i is possible o express hese deformaions by: l = xs (6) x where: s b slip, x disance of he place, for which he slip is calculaed from he poin of crawler rack conac wih ground, he greaes slip appears for x =. Therefore, i is possible o express he slip by: l x b l x max b = = (7) s 3.. Kinemaics of urning I is possible o define he urn of crawler rack vehicle as he fla movemen, which is a sequence of urns around nex momenary axes of roaion. The cener of urn creaes racks on he plain of nex roaion axes and i can be fixed poin for he movemen abou consan radius or line. Turn in crawler rack vehicles depending on he direcion and value of driving forces and braking (P and P ) can be carried ou in few ways. When he speed of running crawler rack is reduced in he relaionship o run (fig. 8a) by braking, a urn appears abou he small radius R. On running crawler racks hen operae oblong angen forces abou direcion opposie direcion o he movemen of he crawler rack vehicle. In ha kind of urn on he vehicle operae wo forces, brake force P in he running crawler rack and driving force P abou he direcion of vehicle movemen in he running crawler rack. In case of disconnecion he running crawler rack drive (fig. 8b) appears urn abou he grea radius. Then only P force of he running crawler rack appears. Fig. 8. Possible varians of he crawler rack vehicle urn Rys. 8. Możliwe wariany skręu pojazdu gąsienicowego A appearance of grea resisances progressive move and low resisances of he urn, may appear case ha P force of he running crawler rack have direcion in accordance wih direcion of he ride (fig. 8c). 3.3. Kinemaics equaion Prędkość punku, znajdującego się na osi symerii pojazdu gąsienicowego, przyjęego jako środek masy pojazdu [ 3, 5, 6], wynosi: ( s ) + r α ( + s ) = (8) Nie uwzględniając poślizgu: + = (9) omponens of he speed poin i is possible o wrie as: x = cos b () y = sin b () Afer aking ino accoun he relaion (8) received he equaion of simple kinemaic ask: ( s ) + ( s ) = cos x b () Fig. 7. Kinemaic diagram of he crawler rack vehicle urn wihou a slip Rys. 7. Schema kinemayczny skręu pojazdu gąsienicowego bez poślizgu Fig. 9. Diagram of he frame robo urn for he angle b Rys. 9. Schema obrou ramy roboa o ką b 4
( s ) + ( s ) = sin ( s) ( s) b = (4) H y b (3) Based on he relaion () and (3) i is possible o wrie as he equaion of reverse kinemaics asks: = x + y (5) H a (6) -,5 b = r ( -s ) H a (7) +,5 b = r ( -s ) onsidering correlaions of he ransmission crawler rack arrangemen: s= 64 a a (8) 64 a a s= (9) where: ȧ s angular speed on he shaf of driving engine running crawler rack, ȧ s angular speed on he shaf of driving engine running crawler rack Subsiuing (6) and (7) o (8) and (9) received relaions on he angular speeds of driving engines: s ( ) r( -s ) 64 -,5 H ȧ = () s ( ) r( -s ) 64 +,5 H ȧ = () 4. Numerical verificaion of he kinemaics model In many cases during he inspecion work he zone of robo acion isn limied o horizonal planes. Many imes he robo mus defea differen heighs and herefore in order o obain more comprehensive analysis of he kinemaics robo mus carry i also in case of he move afer he hill. For he numerical verificaion he following assumpions were made. The robo moves on he segmen abou g gradien, a equal angular speeds of driving wheels u = u, slip s = s = s hen he equaions of movemen will adop he form: 64( -,5 H) 64( +,5 H) a s =, a ' s = ' ( n-) Dl ( n-) Dl r - r - Assuming ha is poin moves on he rajecory (fig. a), wih he speed course (fig. b). Received courses for he se rajecory and speed of he poin. Fig.. a) Se moion rack of he poin, b) se speed course of he poin Rys.. a) Założony or ruchu punku, b) założony przebieg prędkości punku c [m/s].6.4...8.6.4. 5 5 Fig.. Se speed of he poin Rys.. Prędkość zadana punku alfa*, alfa* [rad/s] 3.5 3.5.5.5 5 5 Fig. 3. Angular speed of crawler racks Rys. 3. Prędkość kąowa kół napędzających gąsienice alfa*s, alfa*s [rad/s] 8 6 4 5 5 Fig.. Angular speed on shafs of driving engines Rys.. Prędkość kąowa na wałach silników napędowych co [m/s].6.4...8.6.4. 5 5 Fig. 4. Received speed driving wheels Rys.4. Prędkość orzymana Pomiary Auomayka Roboyka nr / 5
5. Summary Equaions of he kinemaics inspecion robo were drawn up correcly, simulaion examinaions confirmed i. The numerical verificaion showed influence of he slip on behavior of he robo. As can be observed for increasingly larger se disposable horizonal deforming ground or cluch, he speed of slip increases is value. More considerable value assumes also received speed of he poin in order o ensure he se speed. However, he increase speed in fac is limied by parameers of he driving arrangemen (roaion speed, engine power driving) wha leads o siuaion ha he robo sars o move wih smaller los speed in aid of he slip speed. Bibliography. Burdziński Z., Teoria ruchu pojazdu gąsienicowego, Wydawnicwa Komunikacji i Łączności, Warszawa 97.. Dajniak H., iągniki eoria ruchu i konsruowanie, Wydawnicwa Komunikacji i Łączności, Warszawa 985. 3. Żylski W., Kinemayka i dynamika mobilnych roboów kołowych, Oficyna Wydawnicza Poliechniki Rzeszowskiej, Rzeszów 996. 4. Trojnacki M.: Modelowanie i symulacja ruchu mobilnego roboa rzykołowego z napędem na przednie koła z uwzględnieniem poślizgu kół jezdnych, Modelowanie Inżynierskie, Tom, Nr 4, 4 4, ISSN 896-77X, Gliwice. 5. hodkowski A.W., Badania modelowe pojazdów gąsienicowych i kołowych, Wydawnicwa Komunikacji i Łączności, Warszawa 98. 6. hodkowski A.W., Konsrukcja i obliczanie szybkobieżnych pojazdów gąsienicowych, Wydawnicwa Komunikacji i Łączności, Warszawa 99. 7. Documenaion made available by MPWiK SA Krakow [www.wodociagi.krakow.pl]. Kinemayka podwodnego roboa inspekcyjnego Sreszczenie: W arykule przedsawiono zagadnienia związane z modelowaniem i weryfikacją numeryczną kinemayki roboa inspekcyjnego do diagnosyki i konserwacji zbiorników z cieczą. Robo zbudowany zosał w Kaedrze Roboyki i Mecharoniki AGH w ramach granu finansowanego przez NBiR. Analizę kinemayczną przeprowadzono przy użyciu dosępnych i opisanych w lieraurze meod maemaycznych oraz na podsawie isniejących konsrukcji roboów. Zasosowane rozwiązania konsrukcyjne pozwalają serować dwoma gąsienicami, modułem czyszczenia dna zbiornika i modułem diagnosycznym. Weryfikację kinemayki przeprowadzono przy użyciu meod inżynierskich oraz oprogramowania MATAB. Orzymane wyniki przedsawiono w posaci równań maemaycznych oraz charakerysyk pokazujących kinemayczne paramery ruchu roboa. Praca przedsawia również kierunki dalszych badań nad zaprojekowanym i skonsruowanym roboem. Słowa kluczowe: mobilne roboy, kinemayka, roboy inspekcyjne, roboy podwodne Prof. Mariusz Giergiel, PhD He was born in 96 in racow, Poland. He was graduaed in 985 a AGH Universiy of Science and Technology in field of elecronics auomaics. In 99 earned his docoral degree in field of mechanics a he same Universiy. Since 5 he is professor a AGH UST a Faculy of Mechanical Engineering and Roboics. Works in filed of auomaics and roboics, applied mechanics and mecharonics. urrenly is research manager of group working on projec of underwaer ank inspecion robos. Member of local and inernaional scienific socieies, auhor of many publicaions, paens, developed researches and applied soluions. e-mail: giergiel@agh.edu.pl Krzyszof Kurc, PhD In 999 graduaed from echnical school in elecronics Krosno, in 4, graduaed from he Faculy of Mechanical Engineering and Aeronauics, Rzeszow Universiy of Technology. Since 4, working in he Deparmen of Applied Mechanics and Roboics, Rzeszow Universiy of Technology. Research ineress include mecharonics, roboics, mechanics, design. e-mail: kkurc@prz.edu.pl Pior Małka, PhD He received MSc degree in Roboics and Auomaics from he Faculy of Mechanical Engineering and Roboics, AGH Universiy of Science and Technology in, he PhD degree in 8 also a AGH Universiy. He is currenly employed a Municipal Waerworks and Sewer Enerprise, holds he posiion of manager for he auomaion. His main research area is conneced wih indusrial and mobile robos, fuzzy logic applicaions, modelling and idenificaion of mecharonic sysems. e-mail: malka@agh.edu.pl Tomasz Buraowski, PhD He received MSc degree in Roboics and Auomaics from he Faculy of Mechanical Engineering and Roboics, AGH Universiy of Science and Technology in 999, he PhD degree in 3 also a AGH Universiy. He is currenly employed a AGH universiy as an assisan professor. His main research area is conneced wih indusrial and mobile robos and also human-robo ineracion, fuzzy logic applicaions, modelling and idenificaion of mecharonic sysems. e-mail: buraow@agh.edu.pl Dariusz Szybicki, MSc He was born in Przeworsk. He graduaed from he Universiy of Rzeszów, where in 9 he sared engineering docoral sudies a he Faculy of Mechanical Engineering and Aeronauics. He works as an assisan in he Deparmen of Applied Mechanics and Roboics a he Technical Universiy of Rzeszów. His research ineress relae o roboics, programming, and modeling of mecharonic sysems. e-mail: dszybicki@prz.edu.pl 6