BLENDING TOOL PATHS FOR G

-CONTINUITY IN ROBOTIC

FRICTION STIR WELDING

Mikael Soron and Ivan Kalaykov

Department of Technology,

Orebro University, Fakultetsgatan,

Orebro, Sweden

Keywords:

Robotics, friction stir welding, path planning.

Abstract:

In certain robot applications, path planning has to be viewed, not only from a motion perspective, but also

from a process perspective. In 3-dimensional Friction Stir Welding (FSW) a properly planned path is essential

for the outcome of the process, even though different control loops compensate for various deviations. One

such example is how sharp path intersection is handled, which is the emphasis in this paper. We propose a

strategy based on Hermite and Bezier curves, by which G

continuity is obtained. The blending operation

includes an optimization strategy in order to avoid high second order derivatives of the blending polynomials,

yet still to cover as much as possible of the original path.

1 INTRODUCTION

Being a quite recent welding process, Friction Stir

Welding (FSW), has been announced ’the next big

thing’ in the welding community since its release on

the market a decade ago. Since its invention at The

Welding Institute (TWI) in 1991 (patent ﬁled in 92

(Thomas et al., 1991)), it has been declared a supe-

rior welding technique, in term of quality and repeata-

bility, compared to traditional fusion welding tech-

niques, for joining aluminium alloys.

The high quality of the FS weld is a result from a

non-melting welding process without the use of ﬁller

material. And by the means of quality, it is deﬁned

through elimination (or close to) of shrinkage, poros-

ity and distortions, which are quality issues in tradi-

tional fusion welding (Chao et al., 2003; Lomolino

et al., 2005).

From an application point of view, the quality of

the weld and the robustness of the process, has ap-

pealed certain types of industries with extreme de-

mands on the results of the joining process. Two

examples are the aerospace industry and in nuclear

waste management (Cederqvist and Andrews, 2003),

which both has an obvious zero tolerance for error.

But the application does not necessarily have to be

extreme to beneﬁt from FSW, as a typical application

is joining extruded aluminium proﬁles.

But regardless of the application area, the process

is constrained by a few factors. One being the large

forces and torques needed to achieve a good result.

Depending on the type of material used and its thick-

ness, a certain amount of force is applied to produce

heat (by friction). These forces normally range from a

few kN up to 200 kN, which calls for heavy duty ma-

chinery to support the process. And as a result from

applying large forces, the object needs to be rigidly

clamped in a ﬁxture and supported by a backingbar. If

the object is capable of supporting the applied forces

using its internal structure, the backingbar may not be

needed.

The issue of self support can in some cases be

eliminated through engineering. That is, by design-

ing the pieces properly for FSW and selecting a loca-

tion of joining where it is most suited. The machinery

issue, on the other hand, can not be solved with one

single track. The extreme range in forces, calls for

multiple solutions. A machine capable of applying

200 kN, is most certainly oversized for application

in the lower region of FSW. And another issue is of

course ﬂexibility as well as the dextrous workspace of

the machine. A machine capable of applying 200 kN

in one direction does not necessarily have the power

to apply its forces in a arbitrary direction, if even the

Soron M. and Kalaykov I. (2007).

BLENDING TOOL PATHS FOR G1-CONTINUITY IN ROBOTIC FRICTION STIR WELDING.

In Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics, pages 92-97

DOI: 10.5220/0001624400920097

 SciTePress

possibility to reach it, which limits the application and

lowers the ﬂexibility.

As a complement in the lower region of FSW

(from a force perspective), industrial robots have been

introduced. The 3-dimensional workspace of the

robot as well as the relative low cost, are indeed ap-

pealing and several research project has aimed to de-

velop a robotic solution. One, using a parallel de-

signed robot (Strombeck et al., 2000), while the other

attempts made used a serial designed robot (Smith,

2000; Soron and Kalaykov, 2006).

Even though the robots used in these applications

were the ones having the greatest pay-load capabili-

ties, the robot applications are limited in terms of ma-

terial, thickness and speed due to the lack of capabil-

ity to produce forces greater than approximately 10

kN. Along with the ability to apply forces, comes ne-

cessity to handle positional errors due to compliance.

Both in the main direction (into the object) as well as

in the plane perpendicular to the main direction.

To handle the compliance issues (especially in

the main direction) force control is normally imple-

mented in all FSW machines, robot as well as stan-

dard machines. In robotics, a standard solution is

a force/position hybrid control (Raibert and Craig,

1981), enabling position based control in one or more

direction, while achieving a desired force value in the

other. A solution that ﬁts FSW, since a path may be

followed having a constant contact force with the ma-

terial.

2 PATH GENERATION FOR FSW

Path generation has for decades been a well investi-

gated topic for application areas such as milling (El-

ber and Cohen, 1993; Choy and Chan, 2003) and cut-

ting (Wings and J

utter, 2004). To create a high deﬁned

path in such applications without an off-line program-

ming (or CAM) tool, can be considered a time con-

suming operation, if not impossible in many cases.

The resemblance between mentioned processes

and FSW is in many areas high, where:

• In all processes a tool is in contact with an object.

• The tool must follow a pre-deﬁned path (or con-

tour) with high accuracy.

• The tool’s orientation must be deﬁned at all time

also often with high accuracy.

To achieve a satisfying result in such process, us-

ing an industrial robot as manipulator instead of an

NC machine, a set of new motion control algorithms

are essential. Typically, guidance by (3D) vision or

force/torque sensing is used to compensate for the

lack of positional accuracy or to gain robustness (Kim

et al., 2003; Motta et al., 2001).

As mentioned earlier, force control is often used

in robotic FSW applications to handle compliance is-

sues. But also when compliance is not in play, as with

traditional FSW machines, force control can increase

the success rate by handling the occurrence of small

deviations in the object’s surface as well as indirect

control the heat generation (Venable et al., 2004).

In FSW, one of the main reasons for implementing

a robot application is the support of a 3-dimensional

workspace. This implies that the main use of robots

in FSW should be in application containing complex

weld paths. At least, these are the application that

beneﬁts from a robotic solution. And as complex

weld paths are in focus, so becomes the need to create

those, preferably as simple as possible.

Another interesting aspect is the fact that one nor-

mally gains robustness, in force controlled motions,

by having an accurate reference path. Ill-deﬁned

paths obviously need a higher amount of corrections,

which the control system might be incapable of han-

dling. And as (more) errors are introduced, new ones

may arise as a result of the old.

The use of CAD objects in the path generation

process is a well known technology, especially in NC

applications. In robotics, on the other hand, the em-

phasis has been more in the area of factory modeling.

The ability to visualize the robot cell (and the robot’s

motion), measuring cycle times as well avoiding col-

lisions, are features supported in most of today’s off-

line programming (OLP) tools. But the features to

model and improve a path, based on underlying CAD

data and the application at hand, are often modest.

Simple features, such as path blending algorithms and

tool orientation control, are often hidden within more

general path planning algorithms, if included at all.

Even though, they are essential for many of today’s

robot applications, including FSW.

On most robotic systems, a path smoothing oper-

ation exists. Such operations may be deﬁned as zones

(Norrl

of, 2003) in which the control system is allowed

to re-author the path in order to reach motion con-

tinuity. Such implementation are deﬁnitely helpful,

e.g. when executing way-point motions, but gener-

ally not useful from a path planning perspective. Even

as the FSW process is bounded to the motion of the

robot, the process constraints are not accounted for

in the motion controller, leaving the operator to pure

guesses at the path designing stage.

BLENDING TOOL PATHS FOR G1-CONTINUITY IN ROBOTIC FRICTION STIR WELDING

3 PATH BLENDING

TECHNIQUES

Blending of curves or surfaces are well known tech-

niques when joining simple primitives to construct

complex shapes. Instead of using only one equation

to express a complex shape, which may lead to a high

degree polynomial, it becomes natural to use several,

less complex sub-shapes. And in order to maintain G

continuity, we apply blending techniques. In terms of

constructing a robot path, it becomes even more obvi-

ous since the continuity is directly linked to the ability

to execute the motion. Also, in order to generate mo-

tion commands for the robot, we are restricted to use

simple path primitives such as lines and arcs.

To represent a curve, with the lowest possible

complexity, still offering good enough ﬂexibility we

use cubic polynomials. Expressed on a parametric

form we get:

C(u) = (x(u),y(u),z(u)) (1)

where u ∈ [0,1] and

x(u) = a

+ b

+ c

u+ d

y(u) = a

+ b

+ c

u+ d

(2)

z(u) = a

+ b

+ c

u+ d

giving the compact form as:

C(u) = au

+ bu

+ cu+ d (3)

The tangent vector at u of the curve C is obtained by

differentiating C(u) as:

dC(u)



dx(u)

dy(u)

dz(u)



, (4)

or as in the case with a cubic polynomial:

dC(u)

= 3au

+ 2bu+ c (5)

which are the parametric derivatives.

3.1 Hermite Blending

A cubic Hermite curve is deﬁned based on the seg-

ments two end-points and the tangent vectors at those

points. Recalling the equations 3 and 5 we obtain the

following four equations:

C(0) = d

C(1) = a+ b+ c+ d (6)

′

(0) = c

′

(1) = 3a+ 2b+c

as we have substituted u for 0 and 1 respectively.

Solving the equation for the four unknowns we get:

a = 2C(0) − 2C(1) +C

′

(0) +C

′

(1)

b = −3C(0) + 3C(1) − 2C

′

(0) −C

′

(1) (7)

c = C

′

(0)

d = C(0)

And by substituting the algebraic coefﬁcients, we get:

C(u) = (2u

− 3u

+ 1)C(0)

+(−2u

+ 3u

)C(1) (8)

+(u

− 2u

+ u)C

′

(0)

+(u

− u

′

(1)

In a blending algorithm we may select C(0) and C(1)

from the two intersecting curves to join them with a

continuity. In such case, the only thing affecting

the output of the curve is the location of those end-

points. This may of course lead to unwanted phe-

nomena in the practical case due to high second or-

der derivatives. But if we release the C

continuity

in order to affect the blending curve by changing the

magnitude of the tangent vectors, we get another vari-

able, k. By doing so, we still have geometric ﬁrst or-

der continuity, G

, and a more ﬂexible algorithm for

blending. We then form the blending function as:

C(u) = F

(u)p

+ F

(u)p

(u)kt

+ F

(u)kt

(9)

where the F

are the Hermite basis functions

(Martens, 1990) substituted from equation 8, the p

are the intersecting control points and t

are the tan-

gent vector at p

3.2 Bezier Blending

Yet another type of Spline curve, often used in blend-

ing operation, is the Bezier curve(Bezier, 1986). In

difference to the Hermite curve, which interpolates

all its control points, Bezier curves only interpolate

the ﬁrst and last. The usage of the tangents at the end-

points is similar to the Hermite, but the basis functions

of a Bezier curve are based on a Bernstein polynomial

as:

C(u) =

∑

i=0

i!(n− i)!

(1− u)

n−i

(10)

for u ∈ [0,1].

In the case of smoothing a sharp intersection, we

now use three control points, giving the Bezier equa-

tion:

C(u) = (1− u)

+ 2u(1− u)p

+ u

(11)

ICINCO 2007 - International Conference on Informatics in Control, Automation and Robotics

Figure 1: On the left a Hermite smoothing using two control points and its tangents. On the right a Bezier smoothing based

on three control points.

As with the Hermite curve, the key to inﬂuence

the behavior of the curve is through the basis func-

tions. With Bezier curve we use the expression of

weights at the control points. The weight is general-

ized through specifying multiple-coincident points at

a vertex (control point), by which we pull the curve

closer to that control point. This feature is considered

desirable, due to its straight forward implementation,

making easier to predict the output of the curve, than

in e.g. the Hermite curve. Another important feature

of the Bezier curve is that it is contained within its

convex hull.

4 IMPLEMENTATION

In our path generation system we implement both

Hermite blending as well as Bezier blending, to allow

two different approaches towards the same goal. The

objective is of course to create G

continuous path for

the robot to execute, with only a limited interaction

with operator/programmer.

In both cases we allow the user to deﬁne a min-

imum and maximum distance from the intersection

point, where the blending function should be applied.

The idea behind having an interval in which the blend-

ing is performed is to allow the system to optimize its

blending performance. In the case with the Hermite

curve we also allow an interval for the magniﬁcation

of the tangent vector from [0, k], while the Bezier is al-

lowed to put weight on the intersecting control point,

Since neither Hermite or Bezier curves have any

corresponding motion implementation on the robot’s

control system, the blending motion needs to be ex-

ecuted as a circular motion (or rather as a sequence

of consecutive linear/circular motions). Therefore, at

each iteration of the blending optimization, the curve

is converted into circular path segments, which end-

points tangent’s are evaluated as well as the segments

second order derivative. To avoid a too time consum-

ing operation, we introduce discrete steps on which

we perform the optimization.

4.1 Blending Sequence

The following sequence is used in the Hermite blend-

ing operation:

1. Set initial variables for magniﬁcation (m = 1), er-

ror (ε

= ∞), optimization tolerance (µ) and dis-

tance interval (d ∈ [d

min

max

])

2. Deﬁne the intersection to blend through original

path segments, C

(u) and C

(u)

3. If d < d

max

exit

4. Extract control points at p

= C

(1−d) and p

(d)

5. Calculate the tangents, t

and t

, at p

and p

6. Create the blending curve, C, and calculate high-

est, |C

′′

7. If ε

< ε

i−1

increase m jump to 5.

8. If ε > µ reset m increase d and jump to 3.

9. Exit

By applying this strategy we iterate until the tangent

error is less than the optimization tolerance. If the

distance interval is zero, d

min

= d

max

we only optimize

locally on the magniﬁcation factor.

When using the Bezier method we end up with a

similar approach, namely:

1. Set initial variables for weight (w = 0), error (ε

∞), optimization tolerance (µ) and distance inter-

val (d ∈ [d

min

max

])

BLENDING TOOL PATHS FOR G1-CONTINUITY IN ROBOTIC FRICTION STIR WELDING

Figure 2: The resulting curves after blending.

2. Deﬁne the intersection to blend through original

path segments, C

(u) and C

(u)

3. If d < d

max

exit

4. Extract control points at p

= C

(1 − d), p

(0) and p

= C

(d)

5. Create the blending curve, C, and calculate high-

est, |C

′′

6. If ε

< ε

i−1

increase m jump to 4.

7. If ε > µ reset m increase d and jump to 3.

8. Exit

In this approach we still iterate through an inner and

an outer loop. But instead of evaluating the inner loop

on magniﬁcation we evaluate the weight, w.

One remark should be that the Bezier curve has

its convex hull property, which does not allow it to

expand outside volume of the control points. This is

however not the case with the Hermite, which might

exhibits undesirable characteristics, such as loops and

cusps (Mortenson, 2006).

5 SIMULATION

In this experiment we compare the output of our two

strategies in a path modeling environment. We will

not declare one better than the other, but simply vi-

sualize the output curves using the same input path

segments. By using the same input parameters for the

common variables, such as distance interval and tol-

erance level.

The two input segments are deﬁned in the xy plane

through three control points as:

= [0, 0,0]

= [0, 100,0]

= [100, 100,0]

where

= p

− p

and

= p

− p

. The two seg-

ments

and

correspond to two parameterized

curves, denoted C

(u) and C

(u) with u ∈ [0, 1].

As input parameters to our blending algorithm we

choose:

• A bending distance interval ranging from d

min

10 to d

max

= 50 .

• A tangent magniﬁcation factor of k

max

= 5 (for

Hermite).

• A weight of w

max

= 5 (for Bezier).

The resulting intersection blending of the two seg-

ments,

and

, is shown in Figure 2. Reviewing

the two operations, one may notice that the Bezier al-

gorithm, due to its convex hull property, deviates less

from the original path than the Hermite algorithm.

The limiting factor in the Bezier case is rather the

rapid increase of the second order derivative. In the

case of the Hermite operation, the change of the mag-

niﬁcation factor pulls the curve closer to (or further

away from) the intersecting control point. But in this

case, overexceeding the limits causes an overshot of

the curve. The visual feedback in such case, is a help-

ing factor in the path planning stage.

One may conclude the simulation with the follow-

ing remarks:

• The Bezier algorithm allows less deviation from

the original path, but the second order derivatives

needs to be monitored. One may also mention the

straight-forward solution to manipulate the curve

by adding weights at control points.

• The Hermite solution have a more complex ap-

proach to manipulation, but have on the other

hand a visual response when overexceeding lim-

its.

6 CONCLUSIONS

In this paper we have suggested two methods on how

to blend path segments to create G

continuous paths.

There certainly exists numerous of way to do this, but

the lack of implementations calls for such studies. In

our solution we provide the following:

• Two different implementations, Bezier or Hermite

blending.

• Allowing the user to deﬁne the location (or loca-

tion interval) of the blending function.

• A local optimization based on vector magnitude

(Hermite) or weight (Bezier).

• A global optimization on the interval (if existing).

ICINCO 2007 - International Conference on Informatics in Control, Automation and Robotics

One issue that occurs in this type of implementations

is that the blending function needs to be converted

into executable motion, since spline motions rarely

exists in the control system of the robot. One could

probably create better implementations through sub-

dividing the splines until a certain level of accuracy is

obtained, but this is, however, not within the scope of

this implementation.

The idea of intersection blending enlightens only a

portion of all issues involved in path generation. It is,

however, an essential issue in order to achieve good

weld result in 3-dimensional FSW, since the process

output is depending on a continuous motion of the

welding tool.

ACKNOWLEDGEMENTS

The ﬁrst author’s research is ﬁnanced by the KK-

foundation and ESAB AB Welding Equipment. Their

support is highly appreciated. The ﬁrst author is

grateful for the technical support provided by the

project members ESAB AB Welding Equipment,

ABB Robotics and the research centre for Applied

Autonomous Sensor System (AASS) at

Orebro Uni-

versity.

REFERENCES

Bezier, P. (1986). The Mathematical Basis of the UNISURF

CAD System. Butterworth-Heinemann, Newton, MA,

USA.

Cederqvist, L. and Andrews, R. E. (2003). A weld that

last for 100000 years:fsw of copper canisters. In CD-

ROM Proceedings of the 4th International Symposium

on Friction Stir Welding, Park City, Utah.

Chao, Y. J., Qi, X., and Tang, W. (2003). Heat transfer

in friction stir welding - experimental and numeri-

cal studies. Manufactoring Science and Engineering,

125:138–145.

Choy, H. and Chan, K. W. (2003). Modeling cutter swept

angle at cornering cut. International Journal of

CAD/CAM, 3(1):1–12.

Elber, G. and Cohen, E. (1993). Tool path generation for

freeform surface models. In SMA ’93: Proceedings of

the Second Symposium on Solid Modeling and Appli-

cations, pages 419–428.

Kim, S. I., Landers, R. G., and Ulsoy, A. G. (2003). Robust

machining force control with process compensation.

Manufacturing Science and Engineering, 125:423–

430.

Lomolino, S., Tovo, R., and Santos, J. D. (2005). On the fa-

tigue behaviour and design curves of friction stir butt-

welded al alloys. International Journal of Fatigue,

27(3):305–316.

Martens, J. B. (1990). The hermite transform-theory. IEEE

Trans ASSP, 38(9):1595–1606.

Mortenson, M. E. (2006). Geometric Modeling. Industrial

Press Inc., 200 Madison Avenue, New York 10016-

4078.

Motta, J. M. S. T., de Carvalhob, G. C., and McMaster, R. S.

(2001). Robot calibration using a 3d vision-based

measurement system with a single camera. Robotics

and Computer-Integrated Manufacturing, 17(6):487–

497.

Norrl

of, M. (2003). On path planning and optimization us-

ing splines. Technical report, Tekniska H

ogskolan.

Raibert, M. H. and Craig, J. J. (1981). Hybrid position/force

control of manipulators. ASME J. Dynamic Meas.

Control, (102):126–133.

Smith, C. B. (2000). Robotic friction stir welding using a

standard industrial robot. 2nd Friction Stir Welding

International Symposium.

Soron, M. and Kalaykov, I. (2006). A robot prototype for

friction stir welding. In CD-ROM Proceedings of the

IEEE International Conference on Robotics, Automa-

tion and Mechatronics, Bangkok, Thailand.

Strombeck, A. V., Shilling, C., and Santos, J. F. D. (2000).

Robotic friction stir welding - tool technology and ap-

plications. 2nd Friction Stir Welding International

Symposium.

Thomas, W. M., Nicholas, E. D., Needham, J. C., Church,

M. G., Templesmith, P., and Dawes, C. J. (1991). In-

ternational Patent Application no. PCT/GB92/02203

and GB Patent Application no. 9125978.9.

Venable, R., Colligan, K., and Knapp, A. (2004). Heat con-

trol via torque control in friction stir welding. Nasa

Tech Briefs.

Wings, E. and J

utter, B. (2004). Generating tool paths on

surfaces for a numerically controlled calotte cutting

system. Coputer-Aided Design, 36:325–331.

BLENDING TOOL PATHS FOR G1-CONTINUITY IN ROBOTIC FRICTION STIR WELDING