IEEE TRANSACTIONS ON ROBOTICS, VOL. 21, NO. 1, … Collection/TRO/2005/february/1.… · IEEE TRANSACTIONS ON ROBOTICS, VOL. 21, NO. 1, FEBRUARY 2005 1 Differential-Drive In-Pipe

IEEE TRANSACTIONS ON ROBOTICS, VOL. 21, NO. 1, FEBRUARY 2005 1

Differential-Drive In-Pipe Robot forMoving Inside Urban Gas Pipelines

Se-gon Roh and Hyouk Ryeol Choi, Member, IEEE

Abstract—Pipelines for the urban gas-supply system require arobot possessing outstanding mobility and advanced control algo-rithms, since they are configured with various pipeline elements,such as straight pipelines, elbows, and branches. In this paper,we present a comprehensive work for moving inside undergroundurban gas pipelines with a miniature differential-drive in-piperobot, called the Multifunctional Robot for IN-pipe inSPECTion(MRINSPECT) IV. MRINSPECT IV has been developed for theinspection of urban gas pipelines with a nominal 4-in inside diam-eter. The mechanism for steering with differential-drive wheels,arranged three-dimensionally, allows it to easily adapt to most ofthe existing configurations of pipelines, as well as providing excel-lent mobility during navigation. After carrying out analysis forfittings in pipelines, mathematical descriptions of their geometriesare presented, which make it possible to estimate the movementpatterns of the robot while passing through the fittings. Also, wepropose a method of controlling the robot by modulating speedsof driving wheels that is applicable without sophisticated sensoryinformation. To confirm the effectiveness of the proposed method,experiments are performed, and supplementary considerations onthe design of the in-pipe robot are discussed.

Index Terms—Branch, differential drive, elbow, in-pipe robot,steering mechanism.

I. INTRODUCTION

P IPELINES which are tools for transporting oils, gases, andother fluids, such as chemicals, have been employed as

major utilities in a number of countries for long time. Recently,many troubles have occured in pipelines, and most of them arecaused by aging, corrosion, cracks, and mechanical damagesfrom third parties. Even though lasting activities for mainte-nance are strongly demanded, they need enormous budgetsthat may not be easily handled by related industries. Currently,the applications of robots for the maintenance of the pipelineutilities are considered as one of the most attractive solutionsavailable.

In-pipe robots, which have a long history of developmentin robotics, can be classified into several elementary formsaccording to movement patterns, as shown in Fig. 1, although

Manuscript received August 26, 2003; revised May 28, 2004. This paperwas recommended for publication by Associate Editor K. Yoshida and EditorI. Walker upon evaluation of the reviewers’ comments. This work was supportedby a grant from the Safety and Structural Integrity Research Center at SungKyun Kwan University. This paper was presented in part at the IEEE Interna-tional Conference on Robotics and Automation, Seoul, Korea, 2001, in part atthe International Symposium on Robotics, Seoul, Korea, 2001, and in part at theIEEE International Conference on Robotics and Automation, Washington, DC,2002.

The authors are with the Intelligent Robotics and Mechatronic System Lab-oratory, School of Mechanical Engineering, Sungkyunkwan University, Suwon440-746, Korea (e-mail: [email protected]).

Digital Object Identifier 10.1109/TRO.2004.838000

Fig. 1. Classification of in-pipe robots. (a) Pig type. (b) Wheel type.(c) Caterpillar type. (d) Wall-press type. (e) Walking type. (f) Inchworm type.(g) Screw type.

most of them have been designed depending upon specificapplications. As shown in Fig. 1(a), for example, the pig typeis one of the most well-known commercial ones, which is pas-sively driven by the fluid pressure inside pipelines. It has beenemployed for the inspection of pipelines with large diameters[1]. The wheel type illustrated in Fig. 1(b) is similar to the plainmobile robot, and a number of commercialized robots havebeen reported up to now [2]–[19]. Fig. 1(c) shows the robotwith caterpillars instead of wheels [20]. As shown in Fig. 1(d),the wall-press type, which has a number of advantages inclimbing vertical pipelines, corresponds to the robot with aflexible mechanism for pressing the wall with whatever meansthey apply [13], [21]. As depicted in Fig. 1(e), the walking typepossessing articulated legs can produce highly sophisticatedmotions [22]–[25]. The inchworm type given in Fig. 1(f) isusually employed for pipelines with very small diameters[26]–[39]. The screw type (or helical-drive type) displaysthe motion of a screw when it advances in the pipelines, asdepicted in Fig. 1(g) [37]–[42]. Most in-pipe robots employ themechanism derived from one of the aforementioned basic typesof mechanisms or their combinations. In fact, the goals of thein-pipe robot have close relations with the taskspace of specificapplications, because the principal requirement of the in-pipe

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2 IEEE TRANSACTIONS ON ROBOTICS, VOL. 21, NO. 1, FEBRUARY 2005

Fig. 2. Typical methods of steering in branch. (a) Articulated activejoint type: straight drive. (b) Articulated active joint type: steering drive.(c) Differential-drive type: straight drive. (d) Differential-drive type: steeringdrive.

robot is that the robot should be able to explore wherever it hasto go within its taskspace. Existing robots generally travel alonghorizontal pipelines successfully, but only some of them cancope with complicated pipeline configurations, such as verticalpipelines, elbows (also called bends or L-shaped pipelines),etc. Furthermore, few of them can negotiate branches (alsocalled T-shaped pipelines). For successful navigation, however,in-pipe robots are strongly demanded to have the ability ofnegotiating elbows and branches, because urban gas pipelinesare configured with a number of special fittings, such as elbows,branches, and their combinations.

Up to now, several in-pipe robots with steering capabilityhave been reported. They are largely classified into two groups,an articulated type and a differential-drive one, as shown inFig. 2. The articulated type is the robot with active articulatedjoints physically similar to the snake or the annelid animal innature, which may be one of the most adequate mechanisms,although its steering mechanism becomes complicated, for ex-ample, steering joint [9], [17], [19], rubber gas-actuated joint[26], and double active universal joint [12], [13]. These robotscan move along branches. As an alternative approach, the dif-ferential-drive one that carries out steering by modulating thespeeds of driving wheels, as shown in Fig. 2(c) and (d), con-tains relatively simple mechanisms, whereas modeling and anal-ysis of its movements according to pipeline configurations areprerequisite.

Recently, we have proposed several prototypes ofin-pipe robots called the Multifunctional Robot for IN-pipeinSPECTion (MRINSPECT) series, whose designs have beenmainly focused on the capability of steering [12], [13]. ThoughMRINSPECT IV, the fourth prototype, shares a number ofaspects with the other robots in the MRINSPECT series, mostof the mechanism has been redesigned to be adequate for 4-inunderground gas pipelines, because the ideas for the previous

Fig. 3. Photo of MRINSPECT IV.

Fig. 4. Exploded view of MRINSPECT IV.

robots are not suitable for the pipeline with a smaller diameter.MRINSPECT IV is featured with a link construction capableof being folded forward and backward independently, and threeseparated driving modules, which provide high flexibility andmobility in a narrowly constrained space like pipelines. Itsmobility, however, not only depends upon the mechanism, butalso control strategies, proposed correspondingly.

This paper is organized as follows. After introducingits overall mechanical construction, the mechanism ofMRINSPECT IV and considerations on navigation in thepipelines are addressed. Then strategies for moving in thefittings, such as elbows and branches, are discussed, wheretheir geometrical features are described with mathematicalexpressions. Based on this, methods for controlling velocitiesare developed, which are evaluated experimentally in thetestbed. Finally, we conclude the paper with supplementaryconsiderations on the design of the differential-drive robot.

II. OVERVIEW OF MRINSPECT IV

As depicted in Figs. 3 and 4, MRINSPECT IV largelyconsists of three parts, called body frame, driving module, andcharge-coupled device (CCD) assembly. Three driving modulesare attached at the distal ends of foldable legs of the body frame,

ROH AND CHOI: DIFFERENTIAL-DRIVE IN-PIPE ROBOT FOR MOVING INSIDE URBAN GAS PIPELINES 3

Fig. 5. Maximum radial dimension of MRINSPECT IV.

Fig. 6. Minimum radial dimension of MRINSPECT IV.

and they are located circumferentially 120 apart from eachother. The CCD assembly is mounted on the front side of thebody frame. The radial dimension of the robot is changeablefrom 85 to 109 mm, while the axial one is a 150 mm constant,as illustrated in Figs. 5 and 6. Also, the robot can exert 9.8 Nof tractive force and 0.15 m/s of speed in maximum just with0.7 kg of its own weight.

A. Body Frame

As illustrated in Fig. 7(a), the body frame is a skeletal linkagemechanism the other components, such as driving modules andCCD assembly, are attached to. It is composed of two sets ofslider-crank mechanisms in the front and rear sides of the robot,respectively, where each set consists of three slider-crank mech-anisms located equidistantly along the circumferential direction.Couplers of slider-crank mechanisms in the front and the rearsides of the robot are connected to each other with driving mod-ules, as shown in Fig. 7(b). Radial motions of wheels are syn-chronized with a ringlike slider illustrated in Fig. 7(a), and itsaxial motion is limited with a stopper in the central shaft. Thefront wheels and the rear ones, called the front wheel set andrear wheel set, respectively, in this paper, are allowed to moveradially in an asymmetric fashion, as shown in Fig. 8. In the pro-posed mechanism, the distance between the central shaft and thewheel is determined according to the movement of the link, the

Fig. 7. Linkage mechanism. (a) Linkage configuration. (b) Wheeled leg.

Fig. 8. Asymmetric movement of MRINSPECT IV.

elastic restoration force of the spring at the central shaft, and re-action forces from the wall. From Fig. 9, the following equationcan be derived:

(1)

where and denote the radial and axial directions, respec-tively. means the length of the crank, and is the rota-tion angle of the linkage. and represent displacementsalong the and directions, respectively. Because the radialdisplacement can be uniquely calculated by using the axialdisplacement according to (1), the force pressing the wallcan be determined by adjusting the stiffness of the spring in theinitial design stage, and the tractive force of the robot is deter-mined accordingly. Kinematically, the asymmetric motion is not


Fig. 9. Model of link mechanism.

allowed when the front and rear wheels are constrained by themotor casing. In case of the MRINSPECT IV, however, the frontand rear wheel sets can move along a radial direction indepen-dently, because the axial displacement according to the radialone is not so large that the asymmetric motion is practically fea-sible, as shown in Fig. 8.

Since the proposed mechanism has been designed to makethe wheel have effective contact with the inside of pipelines andto cope with the variation of pipelines, the robot is adaptable tothe uncertain pipeline conditions, as well as providing sufficienttraction forces during movements.

B. Driving Module

Three driving modules are attached at the ends of the legs onthe body frame, as depicted in Fig. 4. The driving module largelyconsists of a geared DC motor (Maxon, 4.5 W) with an encoder,several wheels, gears, and casings, as shown in Fig. 10(a). Thefront wheel and the rear one are driven with a single motor viagear transmission, as shown in Fig. 10(b), where ’s denote thevectors for the rotating directions of the transmission units. Asthe driving module is designed to be easily disassembled fromthe body frame, the convenience in maintenance is ensured.Driving modules, since they are independently controlled, am-plify traction forces, which let the robot have sufficient tractiveforces on moving upward in the vertical pipelines.

C. CCD Assembly

As shown in Fig. 11, the CCD assembly is composed of aCCD camera, lamps for illumination, a frame, and an additionalmechanism, called the CCD wheel set. The CCD wheel set in-cludes a CCD wheel rotating along the circumferential direc-tion, and eight couples of the CCD subwheel located on CCDwheels and capable of rotating along their own axes. Becausethe CCD subwheels are capable of rotating circumferentially aswell as along its own axes, it helps the robot slide on the wallduring steering in the fittings and guides it in the desired di-rection, and prevents the body of the robot from having directcontact with the wall so that the robot may not be stuck in thepipeline.

III. PROBLEM STATEMENTS

The geometries of urban gas pipelines are relatively simple,because their dimensions and configurations are regulated bylaw. It is sure to be an advantageous aspect in developing an

Fig. 10. Driving module. (a) Outline of the driving module. (b) Details ofpower transmission mechanism.

Fig. 11. Construction and function of CCD assembly.

in-pipe robot, but there are several intrinsic problems to be con-sidered in the design of the in-pipe robot, especially its size.Since the inside of a pipeline is narrow and rigidly constrained,the size of the robot is not allowed to be excessively large or ex-tremely small, which is determined depending on the size of thepipelines. Hence, the selection of the differential-drive robot,because it provides simplicity and compactness in mechanism,assures advantages over the others. Nevertheless, moving insidepipelines with a differential-drive robot produces several diffi-cult problems in practical applications.


When mobile robots navigate on plain surfaces, such as in-door environments, steering is accomplished by modulating thespeeds of wheels according to the desired movement direction.It is not required to know the geometric configurations of theworkspace, and only internal states, such as position and ve-locity (visual or landmark information are used, too) are used.In the case of in-pipe navigation, the situations are quite dif-ferent from that of the plain surface. The inside of a pipelineis a three-dimensionally curved surface, even in the case of astraight pipe, and furthermore, the situations are getting morecomplicated in the fittings. For instance, it is almost impossibleto derive an analytical model on turning in the branch. In theelbow as well as the branch, the speeds of the wheels should bedifferent from each other, depending on the contact points withthe wall of the pipelines. In the case of a differential-drive robot,therefore, a sophisticated method of controlling the speeds of thewheels is required to prevent the slippage of the wheels. Thus,just knowing the internal states of the robot is not sufficient anymore, and relevant additional information, such as the geometryof the pipelines, as well as the locations of the contact points, isneeded. It is strongly demanded to sense internal states as wellas external environments simultaneously.

Up to now, these problems have not been discussed in depth,though there are several robots having a mechanism similar toMRINSPECT IV [10]. In this paper, we present a simple wayof controlling a differential-drive robot in lines composed ofstraight pipelines, elbows, and branches. Excluding complicatedmathematical analysis, a method capable of being implementedwith simple calculations is developed. Based on the geometricalmodel of the pipelines, we propose how to estimate the contactlocation of the wheels, and then a method for modulating thespeed of the wheels is proposed. After analyzing the movementpaths of MRINSPECT IV, a strategy for moving in the fittingsis proposed.

IV. CONTROL OF IN-PIPE ROBOT IN THE ELBOW

In this section, a method of moving the robot in the elbow ispresented. The method for the branch will be discussed in thenext section, because it is impossible to treat in a unified frame-work. We begin with representing the geometry of the elbowmathematically and describe the behavior of the robot in theelbow. Using this work, a method of controlling the robot isproposed.

A. Geometrical Analysis and Behavior of In-Pipe Robot inthe Elbow

As illustrated in Fig. 12, an elbow with its diameter , sinceit is similar to a part of a torus, is generated by rotating a circle

of the diameter around a given axis. Let us set a coordinateframe at the center of the torus such that the axis is alongthe axis of rotation of , and the other two orthogonal axes,

and , are set along the radial directions. The circle withthe radius of means the trace of the center of generatedby rotating along the axis. According to the regulation ofurban gas supply equipment, should be 1.5 times larger thanthe diameter of , such as . Thus, the mathematical

Fig. 12. Geometry of the elbow.

Fig. 13. Behavior of the robot entering the elbow.

representation of the elbow geometry can be writtenby

(2)

where is the parameter representing the polar location of thepipeline wall on from the axis, and denotes the latitudeangle of Circle A, as represented in Fig. 12. In Fig. 13, the move-ments of the robot in the elbow, simplified with wheels and link-ages, are simulated using a three-dimensional (3-D) graphicaltool. Section C-A is a transition region where the center of therobot moves from the straight pipeline to the elbow, while therobot completely enters into the elbow in the section A-B. CurveR represents the movement paths of the center of the robot rep-resented with , and Arc P corresponds to the section of theCircle B included in the elbow, as shown in Fig. 13. It can benoted that Curve R does not always coincide with Arc P, be-cause the wheels of the robot with finite width have 3-D contactwith the curved inner surface of the elbow. The difference be-tween Arc P and Curve R, designated with , changes whilethe robot goes through the elbow, and also, it depends on theaxial posture of the robot in the elbow. The location of the legswith wheels around the central axis of the elbow, represented by


Fig. 14. Analysis for movement of disk in elbow. (a) Perspective view.(b) Projected view on x � y plane.

Circle B, is called the axial-posture in this paper, and it plays asignificant role in controlling the steering direction of the robotin the branch.

In the elbow, since the traces of wheels have different cur-vatures depending upon the contact points of the wheels withthe walls, the largest velocity of wheels in the elbow may be re-quired to be 1.8 times faster than the smallest one in the extremecase. Thus, it is strongly demanded to accurately modulate thevelocities of wheels, or it may give quite detrimental effects onthe overall performance of the robot, because some of wheelsare inevitably forced to slip, and the driving system may be indanger of being overloaded during movement.

B. Computation of Wheel Velocities in the Elbow

First, let us assume that a disk with negligible thickness ismoving along the pipeline while its central rotating axis coin-cides with that of the pipeline. Then, since the geometry of theelbow is known, the contact points , , and with the pipelinecan be easily calculated, when the disk is assumed to have threewheels located equidistantly along the circumference. Consid-ering a circle containing contact points , , and shown inFig. 14, a polygon connecting , , and will be an equilat-eral triangle inscribed in , and the paths of wheels will be arcswith radii of , , and . Thus, the velocity ratios of threewheels are replaced with those of , , and such as

(3)

Fig. 15. Comparisons of velocities depending on .

Fig. 16. Graphical simulation of the robot in the elbow.

where , called the axial posture angle, designates the angularposition of the contact point . Since is able to be sensedwith the CCD camera (or can be estimated using the initial axialposture angle of the robot on entering the pipeline, assumingthat the robot does not experience spiral motions), velocities ofwheels can be easily controlled using (3). As shown in Fig. 15the velocities of wheels are quite different, depending on . Toaccurately modulate the velocities of the wheels in the elbow,the paths of the wheels should be computed based on the actualbehavior of the robot. However, as shown in Fig. 16, where thegraphical simulation of the movement of the robot in the elbowis illustrated, it may not be possible in reality, because of thegeometric complexity of the robot and contact conditions.

In this paper, as illustrated in Fig. 17, the robot is simplifiedas a form easily handled in the computation, such that the bodyand the frame of the robot are modeled as lines, while jointsand wheels are simplified as points. Based on this model, themethod for modulating the speed of the wheels is discussed. Inthe first, let us assume that , , and are the points of wheelshaving contact with the elbow. Curve W is on the inner surfaceof the pipeline connecting , , and . Based on the simpli-fication, the plane where , , and exist is parallel to the


Fig. 17. Modulation of velocities of wheels. (a) Trajectories of wheels.(b) Relations between the robot and the elbow.

one perpendicular to the central axis of the robot. Here, the pa-rameter , representing the axial posture of the robot, is intro-duced, which is quite similar to introduced previously. isthe angle between two planes, where the one includes the point

on Curve W closest to the axis and the central axis of robot,and the other is defined as the one including the point andthe central axis of the robot. Assuming that the whole body ofthe robot is located in the elbow, the distance between theplane and the plane including Curve W is , when the overalllength of the robot is represented as . Thus, the position vec-tors of , , and from the origin can be represented as

(4)

and the vectors from the axis will be

(5)

Here, all the components are zero, because the vectors areorthogonal to the axis. When Arc , Arc , and Arcrepresent the paths traveled by driving wheels, velocities of thewheels are proportional to , , and , and thus, wehave the velocity ratios as follows:

(6)

Fig. 18. Results of numerical computations. (a) Curve W and Curve Caccording to . (b) Changes in the length of wheeled legs. (c) Comparisons ofwheels’ velocities.

Unknown variables , , and in (6) can be computed ifthe equation for Curve W is obtained (calculation procedurescan be referred to in the Appendix).

As the results of calculations, we can get Curve W as shownin Fig. 18(a). Curve C is the trajectory of the point repre-sented in (33), depending on . The distance between the cen-tral axis of the robot and , as depicted in Fig. 18(b), varies with

because is not fixed. , , and are shown inFig. 18(c), as well. In Fig. 19, , , and are com-pared with velocities , , and calculated in Fig. 15.Especially, is compared with according to the axialposture angles and , as shown in Fig. 19(a), and their ra-tios are displayed in Fig. 19(b) after normalizing with and

, respectively. Comparing with , it isnoted that in the maximum of is not exactly equalto in the maximum . Also, the longer the overalllength of the robot becomes, the larger an inconsistency exists.When the overall length is zero, the maximum ratio of the ve-locity is 1.5, and the radio is 1.8 in the case of MRINSPECT IV,as shown in Fig. 19(b).

V. CONTROL OF IN-PIPE ROBOT IN THE BRANCH

Controlling the movements of the robot in the branch is moredifficult than in the elbow, because the geometry of the branchcan not be expressed as closed-form equations and additionalconsiderations are required, depending on the direction ofmovement. In this section, we propose an intuitive way of


Fig. 19. Comparisons of velocities according to the axial posture angle of therobot. (a) Velocities of wheels. (b) Velocity ratios of wheels.

Fig. 20. Geometrical analysis of the branch.

controlling the robot based on the geometric analysis of thebranch.

A. Geometric Analysis and Behavior of In-Pipe Robot in theBranch

As shown in Fig. 20, a branch can be considered to be built byputting together several patches with simple geometrical shapes,

Fig. 21. Constraint space in the branch.

Fig. 22. Characteristic features of movement in the branch.

Fig. 23. Movement path in the branch and corresponding regions.(a) Movement path. (b) Corresponding change of cross sections.

such as elbows, straight pipelines, and flat patches. The flatpatch, called the V-shaped area in this paper, is located betweenthe elbows, as shown in Fig. 20. It can be noted that it is toocomplicated to get a mathematical expression for the geometryof the branch. The characteristic situations the robot experienceson moving in the branch are briefly illustrated in Fig. 21. Thespace in the branch can be divided into four regions with bound-aries, such as , , , and . isthe end of the region with the regular diameter , meansthe intermediate one, and represents the region where thecross-section expands infinitely, as illustrated in Fig. 21.


Fig. 24. Paths of turning depending on the entrance.

Fig. 25. Paths of turning according to the axial posture.

is the center line of the branch. On entering the branch, the di-ameter of the pipeline initially does not change a lot until thefront wheel set reaches the line after passing through theline . The robot still cannot turn in this region, regardlessof the difference of wheel speeds. When the front wheel set ap-proaches the line , the diameter of the pipeline changesconsiderably, and the robot goes straight. However, it can notstill turn actively because the front wheel set has contact with theinner surface of the pipeline, and the rear wheel set is entirelyconstrained in the inner surface of the pipeline. In this situation,wheels just slip on the inner surfaces of the pipeline whenever ittries to turn with differences of the wheel velocities. This spaceis called the preliminary space, because the robot is ready toturn or drive forward. When the front wheel set is close to theline , either one or two wheels placed in the region, calledthe turn drive space, loses contact with the inner surface of thepipeline. This space is called the drive choice space because therobot is able to choose the direction of movement, e.g., turningor going forward. It can turn toward the designated direction ifthe speeds of the wheels are adequately modulated.

Though the method in the elbow may be partly employedon traveling through the branch, there are several characteristicfeatures requiring the method dedicated to the branch as follows.

1) As the robot proceeds to turn in the branch, the frontwheel set and the rear wheel set may be folded or un-folded, respectively, as shown in Fig. 22. Thus, light slipsin the contact points are inevitable, which are more se-vere in the V-shaped area.

2) As shown in Fig. 22, some of the wheels lose contactwith the wall, and the assumption that six wheels havecontact with the wall in the branch is not valid any more.

Fig. 26. Strategy for turning in the branch. (a) Basic idea. (b) Determinationof turning direction. (c) Relation between axial posture and rotational speed.

3) As shown in Fig. 23, the robot meets a wide variety ofcross-sections when it turns in the branch, which is notin the case of the elbow. Depending on the direction ofturning, the influence of gravity changes, and the pathsof turning change accordingly. In Fig. 23, the paths ofturning are simulated, where Curve and Curveare the paths according to the directions of gravity, suchas and , respectively.

4) The paths of turning are not deterministic, and changeconsiderably depending on the direction of entrance,as illustrated in Fig. 24. For example, Curve for


Fig. 27. Outline of experimental system setup.

entering from the side opening is much different fromCurve in the case of the middle one.

5) The paths of turning change depending on the axial pos-ture of the robot as well. Two typical paths, Curveand Curve , with different axial posture angles, aresimulated in Fig. 25.

The characteristic features aforementioned imply that therobot basically should be controlled according to the methoddifferent from that of the elbow when it travels in the branch.The paths of movement in the elbow are deterministic, becausethey are produced by the wheels of the robot while they keepcontact with the inner wall of the elbow. Those in the branch,however, are not deterministic, because the wheels not onlyslide, but some of them do not keep contact with the wall attimes.

B. Computation of Wheel Velocities in the Branch

Because it is impossible to find the deterministic paths ofturning in the branch, a strategy different from that of the elbowis required. As explained in Fig. 26, the proposed method, calledtriggering of turning method, modulates velocities just by usingthe direction of movement without calculating the paths of thewheels.

In Fig. 26(a), , , and denote the points of contacts. As-suming that the speed at the point is a finite speed of , andspeeds at and are zero, respectively, the robot turns aroundthe vector made by connecting the points and , as illustratedin Fig. 26(a). The triggering of turning method is the general-ization of this idea. Assuming that is the point closest to thedirection of turning among the three contact points on turningof the robot, the velocity of the wheel at the point is set tobe zero. Using a sensor such as the CCD camera, the anglebetween the axis and wheels is already known. If the desiredrotational speed of the robot is given, the velocities of wheelssuch as and are computed accordingly. In calculating thevelocities, as illustrated in Fig. 26(b), the rotational speed isderived as the summation of the rotational speeds and ,respectively, such as

(7)

Fig. 28. User interface. (a) CCD image for control. (b) Control software.

From trigonometric relations, when , we have

(8)

Rearranging it yields the magnitudes of and , such as

(9)

(10)

In the case where , the robot turns around the vectormade by connecting the points and , similar to the situationillustrated in Fig. 26(a), and in the case of , the robotgoes around the vector made by connecting the points and .Thus, as shown in Fig. 26(c), we can set or ,


Fig. 29. Testbeds. (a) Testbed for preliminary experiment. (b) Testbed foradvanced experiment.

respectively (Curve in Fig. 25 is the path of the robot whenor ). Consequently, (9) and (10) are the

equations comprehensively applicable in the range of, and the magnitude of linear velocities at contact points

and are computed as

(11)

(12)

Also, since and are the orthogonal vectors to the con-tact points and shown in Fig. 26, they are

(13)

Thus, the following equation is obtained:

(14)

Consequently, we have

(15)

Therefore, if the direction of turning represented with is spec-ified, the robot can turn by modulating the speeds of wheels ac-

Fig. 30. Navigation in the elbow. (a) Robot in the transparent elbow. (b) Testfor drive performance in the elbow.

Fig. 31. Comparison with straight drive and turn drive in the branch.

cording to (15), where only the ratio between speeds matters,not the absolute ones.

The speed modulation by the proposed method should be em-ployed only in the drive choice space, and does not work in thepreliminary space. Also, it is effective to set for turningsuccessfully, because the drive choice space is too narrow andthe robot easily passes over this region if , as shown inFig. 26.

When all the speeds of the wheels are the same, the robot goesstraight along the paths, such as Curve and Curve inFigs. 23 and 25, though a little difference exists, depending onthe direction of gravity and the axial posture of the robot.

VI. EXPERIMENTS

To confirm the effectiveness of the proposed method, sev-eral tests have been performed. In the first, the system setup isbriefly described, and experimental procedures are introducedwith results.


Fig. 32. Classification of turn drive according to the placement with respect to the direction of gravity. (a) Turn drive from the side entrance. (b) Turn drive fromthe middle entrance.

A. Outline of Experimental Setup

As shown in Fig. 27, MRINSPECT IV is controlled by apersonal computer and its power is supplied via a tether cableexternally. An operator controls the robot with a joystick and akeyboard using the images from the CCD camera transmittedthrough the tether cable. In most cases, the robot moves au-tonomously, and the operator chooses only the direction ofmovement in the branch by observing the CCD images onwhich the angle for choosing the direction of movement isdisplayed, as shown in Fig. 28(a). The left window of Fig. 28(b)is for steering, and it helps the operator choose the directionof steering in the branch according to the axial posture ofthe robot. The right window displays the data and the stateinformation of the robot in realtime. All the programs werecoded with C++.

The experiments were carried out in the test bed shown inFig. 29, where Fig. 29(a) was for the preliminary test, andFig. 29(b) was for the experiments in fittings. For ease ofobservation, pipelines were made of transparent plastics withseveral off-the-shelf parts, and various experiments could beperformed by reconfiguring the components of the testbed.

B. Experiments in Elbows

Fig. 30(a) represents the experimental scenes when the robotmoved along the elbow. Its maximum speed of movementwas 0.15 m/s while controlling velocities. Fig. 30(b) showsthe second experiment where the robot traveled in the specialpipelines composed of three elbows continuously welded. Toprove the effectiveness of the proposed method, the power con-sumption was measured when the control method was appliedor not, respectively. When the velocity was not controlled,about 10% more power was consumed, and it is because therobot was overloaded due to slippage of wheels. It can be

concluded that the speed modulation of the differential-driverobot is very important for moving in the elbow.

C. Experiments in Branches

Movements in the branch are largely classified into two cases,such as straight drive and turn drive, as depicted in Fig. 31. Thestraight drive is simple to realize, compared with the turn drive,since all the driving wheels just need to have the same speed.The turn drive in the branch is largely classified into two cases,as shown in Fig. 32, according to the entrance of the branch therobot approaches. Also, two cases in Fig. 32 are divided into tensubcases according to the relative placement of the branch withrespect to the direction of gravity. In fact, the turn drive is pos-sible without considering the direction of gravity in the Cases 1and 2, while the direction of gravity should be taken into consid-eration in the other cases. In Figs. 33 and 34, the experimentalscenes for these cases are shown. All the cases have been provento be successful. It has been shown that the turn drive could beaccomplished just by the triggering force generating the drivingmomentum along the commanded direction.

VII. SUPPLEMENTARY DISCUSSIONS

In this section, several additional considerations in the designare discussed.

A. Number of Driving Modules

In general, the differential-drive robot should have more thanthree driving modules in order to move in the pipelines, becausethe robot with two driving modules cannot turn in the branchunder the influence of gravity, and also cannot choose the di-rection for steering. The robot with four driving modules hascharacteristic features different from MRINSPECT IV. Usually,only three driving modules among four have contact with theinner wall, as illustrated in Fig. 35(b), in the elbow. As shown in


Fig. 33. Experiments on turning in the branch. (a) Case 1. (b) Case 3. (c) Case 5. (d) Case 7. (e) Case 9.

Fig. 35(c), all the modules have contact with the wall only when, , , and . Otherwise, three of the driving

modules give driving forces, while the other module idles orslips.

In the branch, although the driving force increases as thenumber of active modules having contact with the wall does,a critical aspect is not the force, but the triggering action,as mentioned in Section V. Therefore, the mechanism withthree driving modules is the configuration of the mecha-nism recommended.

B. Size of In-Pipe Robot

Pipeline configurations give geometric limitations, and thesize of a robot should be determined to satisfy the limitations. Inthe elbow, the robot can be modeled as a cylinder, and relationscan be derived between the diameter of the elbow, the curvature,

and the size of the robot. The worst placement of the robot iswhen it is inclined with , as illustrated in Fig. 36(a). In thissituation, two different cases can be considered: 1) the diameterof the robot is relatively smaller than the height , and bothends of the robot and are located on the region of thestraight pipeline and 2) both ends of the robot are included inthe elbow. Depending on the situation, constraint equations arederived to determine the size of the robot [12]. In the case of 1),

has the range of

(16)

The length of the robot is given by

(17)


Fig. 34. Experiments on turning in the branch. (a) Case 2. (b) Case 4. (c) Case 6. (d) Case 8. (e) Case 10.

Since is represented as in Fig. 36 ( is in the urbangas pipelines, but is set to be for comparing with thebranch), the length of the robot is rewritten by

(18)

In the case of 2), the range of is obtained by

(19)

Thus, the length of the robot becomes

(20)

and rewritten by

(21)

Equations (16), (18), (19), and (21) provide the basic constraintequation so that the robot can move in pipelines connected withelbows. The details can be referred to in [12].

In the branch, the size of the robot determines whether turningis possible or not. For example, when the length of the robot isa little longer in Fig. 36(b), the robot cannot turn in the branchalthough the robot has the proper size for moving in the elbow.When the front wheel set of the robot is placed in the branch andthe rear wheel set has contact with the inner side of the straightsection of the pipeline, the rear wheel set is confined absolutelyto the straight section of the pipeline. The rear wheel set is keptfrom steering, although the robot tries to turn. Thus, to turn in thebranch, the rear wheel set should pass over the line , fromwhich is the area of the branch. The robot should start turningbefore the front wheel set reaches the line . If the frontwheel set passes over the line and the robot tries turning,


Fig. 35. Features of four driving modules. (a) 3-D view. (b) Contact of threewheels. (c) Contact of four wheels.

Fig. 36. Size of the robot. (a) Size of the robot for negotiating the elbow.(b) Size of the robot for negotiating the branch.

then separation and isolation will occur. However, the robot canturn in the branch until the front wheel set reaches the lineif the body of the robot, except for the wheels, does not havecontact with the wall. It is because a supplementary device, such

as the CCD wheel set, extends the boundary of turning to the line. Therefore, the length of the robot should be shorter than. On the other hand, the robot could turn easily, but could

not drive straight because it would be isolated in the turn drivespace if the length of the robot is shorter than the diameterof the pipeline. Thus, the length of the robot for negotiatingbranches is given by

(22)

Consequently, to determine the useful length of the robot in theelbow and the branch, (18), (21), and (22) should be incorpo-rated. From (18), (21), and (22), can be determined with (22),since in Fig. 36 is flexible.

VIII. CONCLUSIONS

In this paper, the issues of the mechanical constructionof MRINSPECT IV and its control, mainly focused on themovement in fittings such as the elbow and the branch, werediscussed. According to the experiments, MRINSPECT IVcould navigate almost all kinds of pipeline configurations,regardless of the effect of gravity, its postures, and the directionof movement. Though the algorithms were described basedon MRINSPECT IV, the ideas can be generalized to otherrobots. However, according to our experiences on this work,the mechanism of the in-pipe robot should be adaptable tothe characteristic condition of the pipelines, and it is the pre-liminary requirement for successful movement. The use of ageneral-purpose robot may not be possible in in-pipe applica-tions. For that means, MRINSPECT IV has the possibility ofbeing used in practical applications, although it is still underimprovement through testing in field conditions.

APPENDIX

The equation of Curve W on which , , and exist, can beobtained by using (2), because Curve W means that the valueof the coordinate in (2) is . In advance, Curve W can beexpressed with parameters and as the following equation:

(23)According to (2), we get

(24)

Thus, the equation for Curve W is rewritten as follows:

(25)

According to (24), we have

(26)


Consequently, Curve W is expressed with a single parameter ,such as

(27)Thus, the positions of contact points , , and can be writtenby

(28)

(29)

(30)

where , , and are ’s for , , and , respectively.Also, the condition that the triangle made by , , and is anequilateral triangle yields

(31)

where , , . Thesolution of (31) makes it possible to represent and as thefunction of . Also, can be calculated from the parameters

, , and , where is the only parameter sensed during thenavigation, while and are known. The relation of , , ,and is obtained by solving the additional equation as follows:

(32)

where the position of the intersecting point between the cen-tral axis of the robot and the plane including Curve W is givenby

(33)

and the position on the Curve W is obtained as

(34)

Although it is not easy to solve the nonlinear simultaneous equa-tions of (31) and (30), the numerical calculation is applicable tothe case, as shown in Fig. 18.

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Se-gon Roh received the B.S. and M.S. degreesin mechanical engineering in 1997 and 1999, re-spectively, from Sungkyunkwan University, Suwon,Korea, where he is currently working toward thePh.D. degree in mechatronics engineering.

His research interests include robotic design andapplication of mobile robot.

Hyouk Ryeol Choi (M’96) received the B.S. degreefrom Seoul National University, Seoul, Korea, in1984, the M.S. degree from the Korea AdvancedTechnology of Science and Technology (KAIST),Taejon, Korea, in 1986, and the Ph.D. degree fromthe Pohang University of Science and Technology(POSTECH), Pohang, Korea, in 1994.

Since 1995, he has been with Sungkyunkwan Uni-versity, Suwon, Korea, where he is currently a Pro-fessor in the School of Mechanical Engineering. Hewas an Associate Engineer with LG Electronics Cen-

tral Research Laboratory, Seoul, Korea, from 1986 to 1989. From 1993 to 1995,he was with Kyoto University, Kyoto, Japan, as a grantee of scholarship fundsfrom the Japanese Educational Administry. He visited the Advanced Institute ofIndustrial Science Technology (AIST), Tsukuba, Japan, as a JSPS Fellow from1999 to 2000. His interests include dexterous mechanisms, field applications ofrobots, and artificial muscle actuators.

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IEEE TRANSACTIONS ON ROBOTICS, VOL. 21, NO. 1, … Collection/TRO/2005/february/1.… · IEEE TRANSACTIONS ON ROBOTICS, VOL. 21, NO. 1, FEBRUARY 2005 1 Differential-Drive In-Pipe