Abstract—This paper focuses on the two-robot weldingcoordination of complex curve seam that one robot grasp theworkpiece, the other hold the torch, the two robots work on thesame workpiece coordinately. This paper builds the two-robotcoordinate system at the beginning. After that, the nonmaster/slave scheme is chosen for the path planning, the nonmaster/slave scheme sets the poses versus time function of thepoint u on the workpiece, and calculates the two robot endeffecter paths through the constrained relationshipautomatically. Moreover, Downhand welding is employedwhich can guarantee the torch and the seams keep in goodcontact condition all the time during the welding process.Besides, a Solidworks-SimMechanics simulation platform isestablished, and a simulation of Exhaust Manifold welding isconducted. Finally, the results of the simulation illustrate thewelding process can meet the requirements of predefined torchpose planning and the downhand welding. In addition, twoadvantages of two industrial robot coordinated welding aresummarized compared with arc-welding robot and positioningtable system.

I. INTRODUCTION

The research of multi-robot coordination started fromearly 1980s, represented by two-robot system, is a researchhotspot as it is a complicated system with nonlinearcharacteristics, motion constrains and kinematicsredundancy. Moreover, two-robot coordinated welding is atypical appliance of two-robot coordination. For thecoordination of arc-welding robot and positioning table,there are various research which include the path planning,analysis and avoidance of singularity, inverse kinematics,kinematics redundancy control and so on ([1]-[4]). For twoarc-welding robots execute different welding task on thesame object simultaneously, literature [5] and [6] haveanalyzed its path planning and control of welding condition.However, for two 6-degree-of-freedom (DoF) industrialrobot welding coordination that one robot holding theworkpiece, the other holds the torch and implements thewelding task, few research can be found. The arc-welding

This work was partly supported by the 863 Key Program(NO.2009AA043901-3)

Fan Ouyang. Author is a Ph.D. student of Mechanical & AutomotiveEngineering School, South China University of Technology, Guangzhou,China. Post Code: 510640 (oooyyyfff@hotmail.com)

Tie Zhang. Author is a professor and Ph.D. advisor of Mechanical &Automotive Engineering School, South China University of Technology,Guangzhou,China.( corresponding author, Phone.13660733192,merobot@scut.edu.cn)

Can Ying. Author is a student of M.E. of Mechanical & AutomotiveEngineering School, South China University of Technology,Guangzhou,China. (ying_can@foxmail.com)

robot and positioning table system generally has 6+3 DoF atmost while the DoF of two-robot coordinated weldingsystem can be up to 6+6 or more comparatively. Two 6-DoFrobot systems can meet the demand of advanced and morecomplex welding tasks which require better performance ofcoordination and flexibility, which can avoid designingspecialized welding equipment for special complex seams[7].

This paper studies two 6-DoF robots weldingcoordination, the non-mater/slave approach is employed forcoordinated motion planning. Moreover, a two-robotcoordinated welding Solidworks-SimMechanics simulationplatform is established. Finally, a coordinated weldingsimulation of a car’s exhaust manifold is given.

II.KINEMATICS ANALYSIS OF DUAL-ROBOT COORDINATION

A. Establishment of Dual-robot coordinate system

Fig. 1. Dual-robot coordinate system

As shown in Fig. 1, i=1 indicates the welding robot, i=2indicates the clamping robot. [Ri] represent the robot basecoordinate system, [Ei]represents the robot end-effectercoordinate system, [u]represents the workpiece coordinatesystem, [Ti]represents the tool end coordinate system.Ri

EiT indicates the transformation matrix from [Ei] to [Ri]Ei

TiT indicates the transformation matrix from [Ti] to [Ei]1

2R

RT indicates the transformation matrix from [R2] to [R1]Ti

uT indicates the transformation matrix from [u](point u on

the workpiece) to [Ti]

uT indicates the pose versus time function matrix of [u] in

the R1 coordinate systemAccording to the kinematics transformation relationship

indicated in figure 1, the coordinated constraint relationshipbetween Robot1 and Robot2 can be expressed as follow.

Offline Kinematics Analysis and Path Planning of Two-RobotCoordination in Exhaust Manifold Welding

Fan Ouyang, Tie Zhang, Can Ying, School of Mechanical & Automotive Engineering, South ChinaUniversity of Technology

978-1-4673-2126-6/12/$31.00 © 2012 IEEE

1 1 1 1 2 2 2

1 1 2 2 2

R E T R R E TE T u R E T u uT T T T T T T T× × = × × × = (1)

RiTEi is unknown that can be calculated by forwardkinematics of the 6 joint angular displacements. Moreover,EiTTi is decided by the assembly of the robot end-effecter andthe tool; Tu is specified by the robot operator; TiTu isobtained by the kinematic constraint relationship. Thesethree transformation matrixes are already known. Inaddition, matrix R1TR2 can be obtained through calibration,which is decided by the relative pose between the tworobots, assume it is known.

B. Inverse kinematics

For 6-DOF industrial robots similar to Puma560.when therobot end-effecter pose in Cartesian space is known, theprocess of analytical method for solving inverse kinematics

of six joint angular displacements（ 1θ , 2θ , 3θ , 4θ , 5θ , 6θ ）canrefer to [8]. This paper only makes use of the final analyticalinverse equations based on the parameters of the 6–DoFrobot used in the school’s laboratory. Among the six jointangular displacements, there are two solutions for 1θ , if 1θ is

specified, 2θ and 3θ may have two groups of solution. If 1θ ,

2θ , 3θ are specified, 4θ , 5θ , 6θ have two groups of solution.Therefore, the robot analytical inverse kinematics solutionmay have up to eight groups. There are mainly threeprinciples when choosing the best group. Firstly, it shouldensure that all joints did not exceed the maximum workingrange; for the second, is to avoid collision between robots orbetween robots and the environment; finally, due to theconsideration of minimum energy consumption and motionstabilization, the entire movement change of the six jointangular displacements should be weighted minimum.

III. NON MASTER/SLAVE PATH PLANNING AND TWO-ROBOT

COORDINATED SIMULATION PLATFORM

There are two types of path planning for two-robotcoordination. Which are master/slave mode and nonmaster/slave mode [9]. Since the spatial seam is complex,this paper chooses the non master/slave mode to ease theseam description. The non master/slave mode sets the poseversus time function of a point u on the object, the tool endpaths of welding robot (Robot1) and the clamping robot(Robot2) can be obtained by the constrained relationshipsbetween the object and each robot respectively. After that,the 6 joint angular displacement values of each robot can beresolved by inverse kinematics. As shown in figure 2, [T1Tu]-1, [T2Tu] -1 are the specified constrained relationshipmatrixes, R1TE1, R2TE2 can be obtained according to Eq. 2 and3.

1 1 1

1 1

1 1T

R T EE u uT T T T− −= × × (2)

2 1 2 2

2 2 2

1 1 1R R T EE R u u TT T T T T− − −= × × × (3)

Fig. 2 Coordinated path planning process

This paper use Solidworks-SimMechanics as the tool forestablishing the simulation platform. The origin robot modelis the 6-DoF robot used in the school’s laboratory. Theparameters of the robot are listed in table I.

TABLE IPARAMETERS OF ROBOT

The modeling process includes: 1) Establishing the 3D model of two-robot system inSolidworks. (Fig. 3); 2) Downloading the SimMechanics Link plug-in from theMathworks official website, and installing it to Solidworks; 3) Saving the Solidworks models established in step 1 as‘xml’ documents (SimMechanics Link documents). 4) Importing the ‘xml’ documents as a new model in matlab,the SimMechanics model can be generated automatically.The three strings of modules are Robot1, Robot2 and theconnection to the Ground. (Fig.4); 5) Adding S-functions, joint actuators, sensors and scopes tothe SimMechanics model, realize the actuation andsimulation of the model. System structure is shown in fig.5.

Fig. 3 3D model established in Solidworks

Fig. 4 SimMechanics model

Fig. 5 Solidworks-SimMechanics simulation platform structure

IV. PATH PLANNING OF EXHAUST MANIFOLD WELDING

COORDINATION

For the spatial curve seam, in order to achieve continuousseam tracing, the clamping robot must continuous move theseam point to the ideal position in order to fulfill therequirement of downhand welding [10]. The downhandwelding constraints means the normal direction of the seamshould against the direction of gravity in every moment.Besides, two-robot motion coordination and kinematicsanalysis are also needed in the welding process. This paperdeploys the X-Y-Z fixed-angle coordinate system. Use M1TM2

to express the pose transformation matrix from M1 to M2.

1

2

MM

x

Z( )*Y( )* ( ) y

z

0 0 0 1

p

p

p

XT

α ϕ γ⎛ ⎞⎜ ⎟⎜ ⎟= ⎜ ⎟⎜ ⎟⎝ ⎠

（4）

In matrix (4), Z( )*Y( )* ( )Xα ϕ γ indicates the 3×3

posture transformation matrix from M2 to M1 with rotatingsequence X axis, Y axis, and Z axis respectively. , ,α ϕ γare the rotating angle, xp, yp, zp. indicate the positiontransformation from M2 to M1. The subsequent matrixesused in this paper apply this from of pose transformation.

This paper selects a car’s Exhaust Manifold as theworkpiece for two-robot coordinated welding. Theappearance and Solidworks model is displayed in Fig.6.Fig.7 shows the dimensions. In Fig.7, T1 represents thetorch, T2 represents the clamping fixture. The pose versustime planning of torch is shown in Fig.8. Besides, during the

welding process, the torch not only needs to satisfy the poseconstrains, but also need to satisfy the downhand welding.The constrains of downhand welding can be achieved bysetting the pose matrix Tu1,Tu2,Tu3 of the circular center u1,u2, u3. The setting of Tu1, Tu2 and Tu3 can be found in Eq.10-12.

Fig. 6 Exhaust pipe and its Solidworks modeling

Fig. 7 Dimensions of exhaust pipe

Assume t is the time variable, T is the total simulationtime for each seam. As displayed in figure 7, the centers ofthe three circular seams are u1, u2, u3. Tu1, Tu2, Tu3 are set bythe operator according to the welding tasks, respectively.

1 11[ ]T

uT − 1 12[ ]T

uT − 1 13[ ]T

uT − represent the inverse matrixes of

the pose transformation matrixes from the torch terminal T1

to seam 1, 2, 3; 2 11[ ]T

uT − 2 12[ ]T

uT − 2 13[ ]T

uT − denote the inverse

matrixes of the pose transformation matrixes from thefixture end T2 to seam 1, 2, 3. Set the base coordinate systemof welding robot as the origin of the world coordinatesystem, the following matrix (5) - (10) can be obtained.

1

11 1 u11 1

R *sin(t*2 /T)

Z(-t* /T)*Y( /3)* ( ) R *cos(t*2 /T)[ ]

0

0 0 0 1

Tu T

XT T

ππ π π π−

⎛ ⎞⎜ ⎟⎜ ⎟= = ⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

（5）

1 12

2

0 1

Y( / 2 (2 * /T))* ( / 2) 0[ ]

0 0 0 1

Tu

t XT

R

π π π−

−⎛ ⎞⎜ ⎟− + −⎜ ⎟= ⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

（6）

3

31 1 33 1

R *cos(t*2 /T)

Z(-t*2 /T)*Y( /4)* ( ) R *sin(t*2 /T)[ ]

0

0 0 0 1

T uu T

XT T

ππ π π π−

⎛ ⎞⎜ ⎟⎜ ⎟= = ⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

（7）

221

0 1

1 0 0 0

0 1 0

0 0 1

0 0 0 1

Tu

LT

L L

⎛ ⎞⎜ ⎟−⎜ ⎟= ⎜ ⎟+⎜ ⎟⎜ ⎟⎝ ⎠

（8）

5

422

0 3

0 0 1

0 1 0

1 0 0

0 0 0 1

Tu

L

LT

L L

⎛ ⎞⎜ ⎟⎜ ⎟= ⎜ ⎟− +⎜ ⎟⎜ ⎟⎝ ⎠

（9）

6 7 2

1 2 4 7 2 123

0 3 7 2 1

*cos( )

( )* ( / 2 ) *sin( )*cos( )

*sin( )*sin( )

0 0 0 1

Tu

L L

X Y L LT

L L L

αα π α α α

α α

+⎛ ⎞⎜ ⎟+ +⎜ ⎟= ⎜ ⎟+ +⎜ ⎟⎜ ⎟⎝ ⎠

（10）

In order to meet the requirement of the downhandwelding, For seam2, keep the circular center u2 of seam 2static while rotate it along Y axis of the world coordinatesystem for 360 degrees. For seam3, keep the circular centeru3 of seam 3 static while rotate it along the X axis and Yaxis of the world coordinate system for sin(2 * / T)*( / 4)tπ π−

and cos(2 * / T)*( / 4)tπ π− radians simultaneously. However,due to the limitation of the workspace, the downhandwelding can not be applied to the seam 1. To facilitate thetorch to approach the seam 1, keep the circular center u1 ofseam 1 static while rotate it along the Y axis for ±60degrees. The settings of Tu1, Tu2 and Tu3 are shown in Eq. 11,Eq. 12 and Eq. 13 respectively.

1

11

1

x

Y( cos( * / ) *( / 3)) y

z

0 0 0 1

u

uu

u

t TT

π π⎛ ⎞⎜ ⎟−⎜ ⎟=⎜ ⎟⎜ ⎟⎝ ⎠

（11）

2

22

2

x

( / 2 2 * / )* ( / 2) y

z

0 0 0 1

u

uu

u

Y t T XT

π π π⎛ ⎞⎜ ⎟−⎜ ⎟=⎜ ⎟⎜ ⎟⎝ ⎠

（12）

3

33

3

x

Y( cos(2 * / )*( / 4))* ( sin(2 * / )*( / 4)) y

z

0 0 0 1

u

uu

u

t T X t TT

π π π π⎛ ⎞⎜ ⎟− −⎜ ⎟=⎜ ⎟⎜ ⎟⎝ ⎠

（13）

Fig. 8 Posture planning of torch

V. MOTION SIMULATION

During the welding process, the torch not only needs tosatisfy the pose constrains (Fig.8), but also needs to satisfythe downhand welding (Eq.11, 12, 13). The simulation timefor each seam is set to 20s. As illustrated in Fig.7,L0=100mm, L1=12 mm, L2=130 mm, L3=165 mm, L4=68

mm, L5=190 mm, L6=340 mm, L7=52. 11

ETT , 2

2E

TT , 12

RRT

are constant matrixes. (Eq.14-16). Tu1,Tu2,Tu3,1 1

1[ ]TuT − ,

1 12[ ]T

uT − , 1 13[ ]T

uT − , 2 11[ ]T

uT − , 2 12[ ]T

uT − , 2 13[ ]T

uT − can be

calculated according to matrix 5-13. The calculating resultsare displayed in matrix 14-25.

11

0.7071 0 0.7071 0

0 1 0 0

0.7071 0 0.7071 303

0 0 0 1

ETT

−⎛ ⎞⎜ ⎟⎜ ⎟=⎜ ⎟⎜ ⎟⎝ ⎠

（14）

22

1 0 0 0

0 1 0 0

0 0 1 210

0 0 0 1

ETT

⎛ ⎞⎜ ⎟⎜ ⎟=⎜ ⎟⎜ ⎟⎝ ⎠

（15） 12

0 1 0 1700

1 0 0 1650

0 0 1 0

0 0 0 1

RRT

⎛ ⎞⎜ ⎟−⎜ ⎟=⎜ ⎟⎜ ⎟⎝ ⎠

（16）

11

TuT =

0.5*cos( * / 20) sin( * / 20) 0.866*cos( * / 20) 22.5*sin( * /10)

0.5*sin( * / 20) cos( * / 20) 0.866*sin( * / 20) 22.5*cos( * /10)

0.866 0 0.5 0

0 0 0 1

t t t t

t t t t

π π π ππ π π π

− −⎛ ⎞⎜ ⎟− −⎜ ⎟⎜ ⎟− −⎜ ⎟⎜ ⎟⎝ ⎠

（17）

12

TuT =

sin( * /10) 0 cos( * /10) 57.5*cos( * /10)

cos( * /10) 0 sin( * /10) 57.5*sin( * /10)

0 1 0 0

0 0 0 1

t t t

t t t

π π ππ π π

−⎛ ⎞⎜ ⎟−⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

（18）

13

TuT =

0.7071*cos( * /10) sin( * /10) 0.7071*cos( * /10) 36.5*cos( * /10)

0.7071*sin( * /10) cos( * /10) 0.7071*sin( * /10) 36.5*sin( * /10)

0.7071 0 0.7071 0

0 0 0 1

t t t t

t t t t

π π π ππ π π π

− −⎛ ⎞⎜ ⎟− − −⎜ ⎟⎜ ⎟− −⎜ ⎟⎜ ⎟⎝ ⎠

（19）

21

1 0 0 0

0 1 0 130

0 0 1 112

0 0 0 1

TuT

⎛ ⎞⎜ ⎟−⎜ ⎟= ⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

（20） 22

0 0 1 190

0 1 0 68

1 0 0 265

0 0 0 1

TuT

⎛ ⎞⎜ ⎟⎜ ⎟= ⎜ ⎟−⎜ ⎟⎜ ⎟⎝ ⎠

（21）

23

0.6428 0 0.7660 379.83

0.3830 0.8660 0.3214 84.71

0.6634 0.5 0.5567 236.05

0 0 0 1

TuT

−⎛ ⎞⎜ ⎟⎜ ⎟= ⎜ ⎟− −⎜ ⎟⎜ ⎟⎝ ⎠

（22）

1uT =cos( cos( * / 20)*( / 3)) 0 sin( cos( * / 20)*( / 3)) 1400

0 1 0 400

sin( cos( * / 20)*( / 3)) 0 cos( cos( * / 20)*( / 3)) 200

0 0 0 1

t t

t t

π π π π

π π π π

− − −⎛ ⎞⎜ ⎟−⎜ ⎟⎜ ⎟− −⎜ ⎟⎝ ⎠

（23）

2

cos( / 2 * /10) sin( / 2 * /10) 0 1200

0 0 1 100

sin( / 2 * /10) cos( / 2 * /10) 0 600

0 0 0 1

u

t t

Tt t

π π π π

π π π π

− −⎛ ⎞⎜ ⎟− −⎜ ⎟= ⎜ ⎟− − −⎜ ⎟⎜ ⎟⎝ ⎠

（24）

When Eq.14-25 are obtained, the S-function matrixparameters of the two-robot model can be set according tothese matrixes, and then you can run the model for thesimulation. View from the motion animation (Fig. 9), thewelding process is uniform and stable, welding torch and theseam keep close fit at any time and keep a constant weldingangle, which can meet the requirements of downhandwelding, and there is no collision during the weldingprocess. As demonstrated in Fig.10, 11 and 12, for seam 1,the path of torch is a closed spatial curve, the path of fixtureend is an arc of 120 degrees; for seam 2, the path of fixtureend is a cycle while the torch keep still; for seam 3, the pathof torch is a cycle while the path of fixture end is a closedspatial curve. In summary, the Cartesian tool end paths ofthe three seams of both robots are continuous and smooth.Figure 13 and 14 show that the curves of six joint angulardisplacements are smooth and continuous, no joint angulardisplacement exceeds the working scope.

Fig. 10 Tool end trajectories of seam 1

Fig. 9 Two-robot coordinated welding simulation (Seam 1, 2, 3)

Fig. 11Tool end trajectories of seam 2

Fig. 12 Tool end trajectories of seam 3

3

cos(( / 4)*cos( * /10)) sin(( / 4)*cos( * /10))*sin(( / 4)*sin( * /10)) cos(( / 4)*sin( * /10)) 1400

0 cos(( / 4)*sin( * /10)) sin(( / 4)*sin( * /10)) 200

sin(( / 4)*cos( * /10)) cos(( / 4)*cos( * /10))*sin(( / 4u

t t t t

t tT

t t

π π π π π π π ππ π π π

π π π π π

−

=− )*sin( * /10)) cos(( / 4)*cos( * /10)) 0

0 0 0 1

t tπ π π

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

（25）

Fig. 13 Six joint displacement curves of Welding Robot of Seam 3welding

Fig. 14 Six joint displacement curves of Clamping Robot of Seam 3welding

VI. CONCLUCSION

This paper has investigated the two robot coordinatedwelding that one robot holds the workpiece, the other holdsthe torch and implements the welding task. The non-mater/slave path planning approach is employed whichspecifies the time versus pose function of a point u on thegiven workpiece and obtains the end effecter paths of bothrobots by the kinematics constrains respectively. After that,the Solidworks –SimMechanics platform is established for themotion simulation. Finally, the results of exhaust manifoldsimulation indicate the coordinated welding process can satisfyboth of the constrains of predefined torch posture and downhandwelding.

Since two 6 DoF robot coordinated welding, the DoF ofclamping robot is 6 which implies that the pose of the seamson the part can be adjusted arbitrarily. In contrast, thepositioning table generally has only 3 DOF which can notsatisfy the downhand welding constrains [10] of some seamson irregular part when the holding position is restricted (e.g.seam2 and seam 3 in Fig.7).

Therefore, two advantages of two 6 DoF robotcoordinated welding can be concluded after the success ofthe exhaust manifold coordinated welding simulationcompared with the arc-welding robot and positioning table. 1) For circular curve welding seam, there is hardly anyrestriction for the holding position of the clamping robotwhich is especially good for irregular part (e.g. exhaustmanifold) holding since there is few appropriate holdingposition compared with regular part.

2) Due to the holding position of clamping robot can bearbitrary, therefore, two 6 DoF robot coordinated weldingcan be suitable for continuous welding of multi-spatialseams without changing the holding position that decreasestime and improves efficiency.

The established simulation system for motion planningcan be helpful for two robot offline motion planning andprogramming. However, one limitation of the establishedtwo-robot simulation system is that the seam should beexpressed as accurate mathematical formula which might bedifficult in practice.

ACKNOWLEDGMENT

This work was partly supported by the 863 Key Program(NO.2009AA043901-3), Science and Technology PlanningProject of Guangdong Province, China (No.2012B010900076). Industry, University and ResearchProject of Guangdong Province (No. 2011B090400150).Strategic and Emerging Industrial project of GuangdongProvince (No. 2011A091101001). Science and TechnologyPlanning Project of Zhong Shan City, (2011CXY007)

REFERENCES

[1] HE Guang-zhong; GAO Hong-ming; ZHANG Guang-jun; WU Lin；Coordinated motion simulation in a robot arc off-line programmingsystem, Journal of Harbin Institute of Technology (Chinese), 2005(6):PP 813-815.

[2] Wu, L.,Cui, K.and Chen, S.B., “Redundancy coordination of multiplerobotic devices for welding through genetic algorithm[J],” Robotica, v18, n 6, p 669-676, Nov 2000

[3] KANG Yan-jun; ZHU Deng-lin; CHEN Jun-wei, Electric WeldingMachine(Chinese), Study on coordinative motion of arc-robot andpositioner, 2005(3),PP 46-49.

[4] Jouaneh, M.K.; Wang, Z.; Dornfeld, D.A., Trajectory planning forcoordinated motion of a robot and a positioning table. I. Pathspecification, Robotics and Automation, IEEE Transactions onVolume: 6 , Issue: 6, 1990 , PP 735 - 745.

[5] XIAO Jun; HE Jing-wen; ZHANG Guang-jun; GAO Hong-ming; WULin, Coordination Control for Dual Welding Robot of DifferentModel, Journal of Shanghai Jiaotong University(Chinese),2010(S1),PP 110-113+117.

[6] ZHANG Huajun; ZHANG Guangjun; CAI Chunbo; XIAO Jun; GAOHongming, Master-slave coordinated motion controlling of double-sided arc welding robots, Transactions of the China WeldingInstitution (Chinese),2011(1) Vol 32.NO.1 PP 25-28.

[7] Ren Fushen, Chen Shujun, Guan Xinyong et al. Special-purposewelding robot for intersection welding seam. Transactions of theChina Welding Institution, 2009, 30(6): PP 61-64.

[8] Craig,J.J,Introduction to Robotics: Mechanics and Control (3rdEdition), Prentice Hall, 2004-08-06,ISBN-10 / ASIN: 0201543613 ,ISBN-13 / EAN: 9780201543612

[9] M. Uchiyama and P. Dauchez, “A symmetric hybrid position/forcecontrol scheme for the coordination of two robots[J],” in Proc. IEEEInt.Conf. Robot. Automat., Philadelphia, PA, 1988, pp. 350–356.

[10] K. Fernandez and E. Cook, “A generalized method for automaticdownhand and wirefeed control of a welding robot and positioner,”NASA Tech. Paper 2807, Feb. 1988.