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O-line compensation of the tool path deviations on
robotic machining : Application to incremental sheet
forming
Jérémy Belchior, Mario Guillo, Eric Courteille, Patrick Maurine, Lionel
Leotoing, Dominique Guines
To cite this version:
Jérémy Belchior, Mario Guillo, Eric Courteille, Patrick Maurine, Lionel Leotoing, et al.. O-
line compensation of the tool path deviations on robotic machining : Application to incremental
sheet forming. Robotics and Computer-Integrated Manufacturing, Elsevier, 2013, 29 (4), pp.58-69.
�10.1016/j.rcim.2012.10.008�. �hal-00926215�
Off-line compensation of the tool path deviations on robotic
machining: Application to Incremental Sheet Forming
J. Belchior
a,∗
, M. Guillo
b
, E. Courteille
a
, P. Maurine
a
, L. Leotoing
a
, D. Guines
a
a
Université Européenne de Bretagne, INSA-LGCGM EA-3913, 20 Avenue des Buttes de Coësmes, 35043,
Rennes Cedex, France
b
Institut Maupertuis, Contour Antoine de St-Exupéry Campus de Ker Lann, 35170, Bruz, France
Abstract
In this paper, a coupling methodology is involved and improved to correct the tool
path deviations induced by the compliance of industrial robots during an incremental
sheet forming task. For that purpose, a robust and systematic method is rst proposed to
derive the elastic model of their structure and an ef cient FE simulation of the process
is then used to predict accurately the forming forces. Their values are then de ned
as the inputs of the proposed elastic model to calculate the robot TCP pose errors
induced by the elastic deformations. This avoid thus a rst step of measurement of
the forces required to form a test part with a stiff machine. An intensive experimental
investigation is performed by forming a classical frustum cone and a non-symetrical
twisted pyramid. It validates the robustness of both the FE analysis and the proposed
elastic modeling allowing the nal geometry of the formed parts to converge towards
their nominal speci cations in a context of prototyping applications.
Keywords: robot machining, elastic modeling, robot calibration, stiffness
identi cation, off-line compensation, incremental sheet forming
1. Introduction
In order to reduce manufacturing costs and to improve production !exibility, the
industrial robot manipulators are nowadays involved for processes such as machining,
assembly or forming [1], [2]. Robots can be used for Incremental Sheet Forming (ISF)
which is an interesting process for small series production and prototyping [3]. In ISF
the sheet is deformed locally by successive paths of a simple tool. It means that lower
forming forces than stamping are needed to form a part. These forming forces are fun-
damental data to predict the tool pose deviations of the robot [1]. These deviations are
mainly due to the elastic deformations of the robot structure which lack of stiffness in
comparison to dedicated machines [4], [5]. The resulting Tool Center Point (TCP) pose
✩
The present work is supported in part by the European Union (EU). EU is committed in Brittany via
FEDER founds.
∗
Corresponding author
Email addresses: jeremy.belchior@insa-rennes.fr (J. Belchior),
mario.guillo@institutmaupertuis.fr (M. Guillo),
eric.courteille@insa-rennes.fr (E. Courteille), patrick.maurine@insa-rennes.fr
(P. Maurine), lionel.leotoing@insa-rennes.fr (L. Leotoing),
dominique.guines@insa-rennes.fr (D. Guines)
Preprint submitted to Robotics and Computer-Integrated Manufacturing September 21, 2012
.tex file
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errors degrade the process results in terms of geometry, surface, etc. In past decades,
much of the work in the area of robot calibration including studies on the modeling
of their structure, the measurement data collection and the model error identi•cation
has been done [6], [7], [8]. For that purpose two main approaches are available in the
literature.
The •rst approach is to perform the dynamic elastic modeling of the robot structure
in order to compensate by a linear or non linear feedback control the elastic deforma-
tions of the structure that degrade the TCP pose accuracy [9], [10], [11]. Outputs of
such control consist in modifying the actuator torques. Therefore its implementation is
dif•cult in actual industrial robots where only the TCP pose is controlled [12]. More-
over, the dynamic parameters (inertia, center of gravity, gear ratio) must be identi•ed
by dedicated methodologies [8], [13].
The second approach is based on realistic parametric models of the robots to predict
the elastic deformations. The methodologies proposed in the literature are based either
on Lumped-parameter [14], [15], [16] or more realistic Finite Element models [17],
[18], [19]. Since outputs of these models are TCP pose errors, the term elastic model is
used. As a result, a correction of the tool path deviations in the programming language
of the controller (real-time or off-line programming) is possible. This method has
already been applied on a Two Point Incremental Forming (TPIF) process (a supporting
tool is used to hold the sheet on the backside) [20], [1]. In these works, the tool path
deviations are computed with a Multy Body System modeling (MBS) of the robot
structure coupled to a Finite Element analysis (FE). In the MBS model, the links are
assumed rigid and the elastic behavior of the robot structure is described considering
the joint stiffness only. The ISF FE simulation computes the estimated forming forces
required to form the part assuming an ideal stiff robot. These values are then used
to estimate with the MBS model the TCP pose errors that are due to the robot elastic
deformations.
The main objective of our paper is to bring consistent contributions to these last
works. For that purpose, our work focussed on the following points:
1. The TCP pose errors induced by the elastic deformations are calculated with a para-
metrical modeling method based on a new notation instead of a MBS modeling. The
main advantage of this approach is that a realistic and complete 3D elastic model
can be derived automatically for any industrial robot manipulators including open-
and closed-loop structures. Thereby the robot structure can be described consider-
ing the joint and the link stiffness.
2. Thanks to an ef•cient FE simulation of the process, the predicted forming forces
are calculated and then used as inputs of the proposed elastic model. The advantage
of this approach is to avoid the measuring of the forming forces during a •rst run
without any compensations as in [20]. Actually in the case of really compliant
robots, the measuring forces might be really lower as those exerted by an assuming
stiff structure and this can lead to inaccurate corrections of the tool path.
3. In order to validate the coupling approach an intensive experimental investigation
is performed by considering on one hand a classical frustum cone as in [20] and
on the other hand a twisted pyramid. The non-symetrical geometry of this last one
allows to validate the robustness of both the FE analysis and the elasto geometrical-
modeling.
The paper is organized as follows. First the ISF process requirements are given
and the TCP pose accuracy abilities of a FANUC S420iF are veri•ed according to
2
ISO-9283 standard. Next sections describe respectively the new proposed systematic
elastic modeling and its application to the FANUC S420iF. The resulting elastic model
of its structure is next identi•ed and then involved to compensate both the geometrical
errors and elastic deformations during the ISF of a frustum cone and a twisted pyramid
on an aluminium sheet. For each shape, experimental results are deeply analyzed and
discussed.
2. Incremental Forming process requirements
To be as ef•cient as dedicated machines the serial robots have to verify the process
requirements. For example, to form a frustum cone of 40 m m depth and 50° wall an-
gle with a 1.2 mm thick aluminium sheet, a maximum force of 600 N is needed. Feed
rates usually programmed are included between 1 m/min and 2 m/min so the pro-
cess can be considered as quasi-static [21]. The forces required to form thin aluminium
parts are compatible with the FANUC robot S420iF. It is a typical robot used for me-
chanical assembly with six degrees of freedom and a payload capacity of 1200 N. It
has a kinematic closed loop that increases the global stiffness of the structure. In order
to verify the robot capabilities versus the process, a diagnostic of the robot has been
made according the ISO-9283 standard [22]. Results obtained with ROBOSCOP E
©
software and the Nikon Metrology K600-10 photogrammetric measurement system are
presented in TABLE 1. The system has a pose measuring accuracy up to 37 µm for
a single point. As one can see in TABLE 1, the maximum compliance and accuracy
errors respectively of 3.3 and 1.6 mm clearly show that this robot cannot achieve ISF
parts with an acceptable level of accuracy (±0.5 mm [23]). Therefore an ef•cient
off-line compensation of the robot tool path deviations has to be performed.
Table 1: Certi•cations’s results based on ISO-9283 standard
Position (mm) Orientation (mdeg)
Mean Repeatability error 0.134 15.271
Max Repeatability error 0.176 20.059
Mean Accuracy error 0.914 137.239
Max Accuracy error 1.644 165.346
Max Compliance error (650 N) 3.253 -
3. Elastic modeling
Denavit-Hartenberg or Khalil-Klein•nger notations are usually used for the geo-
metrical modeling of industrial robots [6], [8]. Finite Element theory [24] is involved
to derive the elastic model by discretizing the robot structure into a set of nodes and
beams. Nodes can represent the start or the end of a link, an intermediate frame or a
characteristic point on the real structure. However, the de•nition of the frames used for
the geometrical modeling is not really appropriated for the elastic modeling one [17]
since in the classical beam theory x axis has to be along the neutral axis [24]. In this pa-
per, the de•nition of a new parameter table is proposed to make mutually coherent the
notation of both geometrical and elastic models in order to describe with a minimum
set of parameters open- (Figure 1) and closed-loop structure robots (Figure 2). For that
purpose, the systematic modeling is performed by the de•nition of two speci•c frames:
3
• Joint frames R
j
: Khalil-Klein•nger notation is used and allows to have the geo-
metrical situation of frames R
j
in the base frame R
0
.
• Link frames R
u,v
: links can be considered either rigid nor deformable. If a link
is considered deformable, the classical beam theory is then used to described its
mechanical behaviour. x axis has to be along the neutral axis [24]. A notation
based on three parameters allows to have the geometrical description of the link
frame R
u,v
in the base frame R
0
.
3.1. Open-loop robots
The system is composed of n joints and n + 1 links. The link C
0
is the base of the
robot and C
n
the link holding the tool.
3.1.1. Joint frames R
j
Joint j de•ned between two nodes l and u, connects link C
j−1
with link C
j
. C
j−1
is the precedent link of C
j
. The frame R
j
, which is •xed with link C
j
and connected
to the node l, is de•ned such that:
• z
j
is along the axis of joint j.
• x
j
is taken along the common normal between z
j
and z
j+1
. If z
j
and z
j+1
are parallel, the choice of x
j
is not unique. In order to minimize the number of
parameters, x
j
will be placed if possible along the neutral axis of the link C
j
.
3.1.2. Link frames R
u,v
It is necessary to de•ne a speci•c frame when a link C
j
is considered deformable.
This is de•ned between two nodes u and v. A link frame R
u,v
is associated to the node
u and de•ned such that:
• x
u,v
is along the neutral axis of the link C
j
.
• z
u,v
is along the main inertia axis of the link C
j
.
Figure 1: Modeling of open loop structures
4
