Proceedings of the 7th Annual ISC Graduate Research Symposium
ISC-GRS 2013
April 24, 2013, Rolla, Missouri
Renwei Liu and Zhiyuan Wang
Department of Mechanical and Aerospace Manufacturing
Missouri University of Science and Technology, Rolla, MO 65409
REALIZATION OF ROBOT INK DEPOSITION ON CURVED SURFACES
ABSTRACT
A Robot Ink Deposition system is proposed in this article. The
method for generating ink deposition path is based on the
contour points information from 3D model, and an adaptive
compensation algorithm is developed for the robot to deposit
ink on a curved surface based on B-spline surface. This method
provides more flexibility for robot arm to print characters and
robot system could afford a larger working envelop for ink
deposition as well. Finally, an example of printing letters has
implemented by this method in our lab.
1. INTRODUCTION
Since robots can work continuously and tirelessly, the use of
robots is usually desirable in places where continuous operation
is required, such as at the assembly lines. Let the robot to
behave like human is always a research area of interesting.
Various researches have been done in studying the mechanism
and control of robot that can perform the task of writing letters.
A 4 DOF robot drawing platform which can write Chinese
character with brush and improved it with a vision system later
(K.W.Lo & K.W.Kwok [1, 2, 3]). A segmentation-based
algorithm is to store the character information, which is
concentrating on segmenting Latin character set, and the
segment information can then be used by the robots to write
(Salman [4]). The extraction of the trajectory of the writing
brush in character writing was proposed based on image and
curve processing techniques and the writing knowledge
([F.H.Yao 5]). The work so far, however, usually require
complicated programs to control robot and specific designed
devices, like dedicated movement mechanism and precise
drawing plane, what is more, the style of writing and the size of
character is limited as well.
The essence of writing is a process of ink deposition. In
this paper, a contour-points-based method is proposed to
generate ink deposition path and adopt surface measurement
technology to enable robot arm to print letters on a curved
white board. The core of this method is to decompose the shape
of characters into a set of contour points, then the robot can use
these information to reconstruct the characters with linear
tracks. The deposition movement of robot along the curved
surface can be adjusted by position compensation program.
This method is an easy way to realize robot to write different
style characters in large scale on a freeform surface.
2. GENERATION OF INK DEPOSITION PATH FOR
ROBOT
Characters in different language are consisted of various basic
segments. The Latin language is a simple example, which
mainly formed from two elements, the straight lines and the
curves. A complicated example is the Chinese language, there
are 28 strokes used to construct all characters and let alone the
different kinds of writing style. The process of extraction the
sequence of writing is an arduous task, it is a hard work of
algorithm designing and programming. From the view point of
geometry, a set of collinear points constitute a line and a set of
successive lines constitute a plane. The plane can be any graph
including the characters, since calligraphy could be considered
as a kind of plane art as well. In this way, if we could get the
contour points information of a character and connect these
points with tracks of reasonable width, the writing task can be
completed by just using linear movement of robot.
In order to get the graph information of the characters, we
adopt the concept of Layer Manufacturing, since the process of
writing is just like deposit one layer ink material. The 3D CAD
software on the market, such as Solidworks and NX, can build
3D model of characters easily. Another advantage of this
method is we can use the font library of 3D CAD software to
realize write different kinds of characters. The algorithm for
extract contour information of 3D model works in this way: use
a horizontal plane to slice the model into layers, a series
vertical plane been set to intersect with one of the sliced layer
to get the contour points. These work can be done by MAPS,
which is a software developed by our lab using for multi-axis
deposition. But the robot cannot directly implement these files,
therefore a postprocessor is needed to translate contour points
information into Robot Language Commands. According to
these commands, robot can reconstruct the character with ink
deposition process. Figure 1 explains the whole process of
generating robot deposition path.
Figure 1: Generation of robot deposition path
1
3. MEASUREMENT OF CURVED SURFACE AND
COMPENSATION ALGORITHM
To realize adaptive ink deposition, a matrix of points of the
board surface needed to be detected, and then the board surface
based on B-spline surface theory [6] could be reconstructed.
Therefore, the offset value for deposition path could be
calculated. The fundamental principle of reconstruction surface
from detected point matrix is as following [4]:
Suppose the detected points are pi, j (i  0,1,...r; j  0,1,..., s) ,
the expected surface can be expressed by Eq.(1). In this
equation, there are (m  1)  (n  1) control points d i , j
(i  0,1,..., m; j  0,1,..., n, m  r  k  1, n  s  l  1) , parameters
u , v and their times are k and l , knots vector are
U  [u0 , u1,..., umk 1 ] and V  [v0 , v1,..., vnl 1 ] .
m
p ( u, v ) 
The problem can be changed to the reconstructed calculation of
m  1 interpolation curves
n
d
i ,s N s ,l (vl  j )
 di , j , j  0,1,....r; i  0,1,..., m
(5)
s 0
Combine these equations, (m  1)  (n  1) control point d i , j
(i  0,1,..., m; j  0,1,..., n) of the surface can be calculated, and
then use B-spline surface equation can generate the surface. In
this paper, we use double 3 times B-spline interpolation surface
to reconstruct the robot writing surface. As shown in fig.2, (a)
is the white board which we use for the ink deposition, (b) is
the reconstruction surface by using the detected matrix points
based on B-spline surface theory explained above.
n
d
i, j
Ni ,k (u) N j,l (v), uk  u  um1, vl  v  vn 1 (1)
i 0 j 0
This equation can also be revised to Eq.(2):
m
p ( u, v ) 
n
 d
(
i 0
i, j
N j ,l (v ))N i ,k (u )
(2)
j 0
a) Curved white board
And then the Eq.(3) can be got, it is similar to B-spline
curve function:
m
p(u, v ) 
 c (v ) N
i
i ,k ( u )
(3)
i 0
n
In Eq.(3), ci (v ) 
d
i , j N j ,l (v ), i
 0,1,..., m , now control
j 0
curves instead of control points. Therefore, fix parameter v ,
m  1 points will be given in ci (v )(i  0,1,..., m) . Those points
are used as control points to define the equal parameter curve of
the surface in which u is parameter. When parameter v
sweeps its whole range, infinite equal parameter curves can
describe the whole surface. Obviously, there are n  1 curves
are given interpolation points in the infinite equal parameter
curves, it correspond to a column points of the value points
matrix. These n  1 equal parameter curves are called section
curve[7]. Therefore the control points d i , j (i  0,1,..., m; j 
0,1,..., s) of the section curve can be calculated by Eq. (4).
m
s j (uk i ) 
d
r 0
r , j N r ,k (uk i )
 Pi , j , i  0,1,..., m; j  0,1,..., n (4)
b) Surface reconstruction of white board
Figure 2: Curved white board and its reconstruction surface
After got the reconstructed surface, calculation will be
used to compensate the robot writing tool path. For a given
point [ x p , y p , z p ] from the writing path, project this point to
the reconstructed surface will get a correspond point
p(ui )  [ x p , y p , z p '] . Use the offset for compensation value for
the robot writing tool path when generate the NC code for
robot. The problem here is the reconstructed surface based on
B-spline surface was defined by parameters u and v , however,
the path data for robot writing on the surface is based on
Cartesian coordinate system. Therefore, in order to project a
given point from the tool path to the surface, the value
x p , y p of this given point must be transited to parameter
2
u, v correspond to the reconstructed surface and then calculate
the projected point on the surface.
For a given point, the calculation process is as following:
Firstly, use the control curve equations [6] ci (v), i  0,1,..., m to
calculate control curves of the surface. Suppose parameter u
along the y axis, parameter v along the x axis of robot
coordinate system. For each control curve, search the parameter
value vi to make the x value of the point ci ( vi ) equal to x p .
Use ci (vi ), i  0,1,..., m as control points calculate the section
curve of the surface p(u) . And then search the parameter value
ui , make y value of the point p(ui ) equal to y p . Therefore,
p(ui )  [ x p , y p , z p '] will be the projected point of given point
[xp , yp , zp ] .
has 6 joints and a moveable foundation, therefore it has great
flexibility and large working range (1.6m*3.4m). In our
experiment, the robot is going to write characters on a big white
board, it's worth noting that this board is not a flat surface,
especially at the four edges. In order to write on this board, the
first thing is get the curve information of it. For such a large
object, there is no coordinates measuring machine can do the
measurement. As fig.4 (b) shown, a touch probe installed on the
robot is used to collect the points coordinate matrix of the board
surface which shown in table 1. Then the compensation
algorithm which was mentioned in chapter 3 could calculate the
offset for each contour point on the curved surface and generate
the final writing commands. The writing result is shown in
Fig.5.
4. IMPLEMENT OF ROBOT INK DEPOSITION
In this paper, we use robot write characters as an implement
example of ink deposition. The first step is generate a character
model as step file with a 3D modeling software, we choose
Solidworks in this case. Secondly, path generating software can
slice this model into layers and generate file contour points, the
track width and overlap between each track can be controlled in
this step. Thirdly, post-processor translate the points
information into robot commands file. Figure 3 shows the
procedure of robot writing path generation.
a)
b)
Figure 4: Robot arm and touch probe
a) 3D model of characters
b) Contour points of characters c) Simulation of Robot writing path
[800 -1300 742.9] [480 -1300 741.8]
[160 -1300 741.0]
[800 -1500 752.0] [480 -1500 752.1]
[160 -1500 751.4]
[800 -1650 754.9]
[800 -1700 755.1]
[800 -1900 752.5]
[800 -2100 745.8]
[480 -1650 756.3]
[480 -1700 757.0]
[480 -1900 757.3]
[480 -2100 753.3]
[160 -1650 755.9]
[160 -1700 756.9]
[160 -1900 758.7]
[160 -2100 757.3]
[-160 -1300 739.8]
[-160 -1500 750.1]
[-160 -1650 754.5]
[-160 -1700 755.6]
[-160 -1900 757.6]
[-160 -2100 756.3]
[-480 -1300 738.6]
[-480 -1500 748.2]
[-480 -1650 752.0]
[-480 -1700 752.8]
[-480 -1900 753.6]
[-480 -2100 750.1]
[-800 -1300 737.5]
[-800 -1500 745.7]
[-800 -1650 747.5]
[-800 -1700 747.8]
[-800 -1900 745.8]
[-800 -2100 740.5]
Table 1: Points coordinate matrix of the board surface
Figure 3: Procedure of writing path generation
A mark pen was installed on the wrist of a 7-axis industry
robot arm as show in figure 4 (a) to do the writing task, which
3
[5].
[6].
[7].
Figure 5: Robot writing results
5. CONCLUSIONS
An adaptive robot ink deposition system aimed at writing larger
scale letters on curved surface has been developed in our lab.
Based on the contour points information of 3D model to
reconstruct the characters is an easier method than other control
algorithm for robot writing, and this process can also serving as
a test method for robot depositing. With curved surface
measurement method, the robot overcomes the limits of writing
only on a flat surface, especially for writing large scale
characters. In addition, the compensation control algorithm can
also apply to robot repair area, which is mainly focus on the
curved deposition.
6. ACKNOWLEDGEMENTS
This research was supported by National Science Foundation
Grants IIP-0822739 and IIP-1046492 and Intelligent Systems
Center at Missouri University of Science and Technology.
Their support is greatly appreciated.
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