Airbrush robotic painting system: experimental

Airbrush robotic painting system: experimental validation of a colour spray model Lorenzo Scalera1 , Enrico Mazzon2 , Paolo Gallina2 and Alessandro Gasparetto1 1

University of Udine, via delle Scienze 206, 33100 Udine, Italy [email protected], [email protected] 2 University of Trieste, via Valerio 10, 34127 Trieste, Italy [email protected], [email protected]

Abstract. This research is focused on developing a robotic painting system for artistic and graphic applications by means of an anthropomorphic robot equipped with an airbrush. Firstly, we introduce a mathematical colour spray model, based on a radially symmetric Gaussian distribution of colour intensity within the spray cone. Then, we present an experimental characterization of colour intensity in a spot, by varying the distance between airbrush and target surface and the spraying time. The experimental results of this pilot study validate the paint intensity model and provide the basis for further investigations. Keywords: airbrush, robotic painting, spot characterization, paint intensity model, colour flow function

1

Introduction

Robotic painting is widely used in several different applications, not only in industry and manufacturing but also for artistic and decorative tasks [10]. Spray painting technique can be easily automated and, coupled with a robotic system, allows a high degree of repeatability and can be very efficient in terms of painting quality, cycle time and flexibility. Nowadays, the most common application of robotic painting in industry is certainly in automotive. In this field, the main target is the uniform coverage of the complex geometries of automotive surfaces and the thickness uniformity of painting coating. Several researches have been conducted in this context in order to optimize the tool trajectory planning of industrial robots. For example, Wei proposed a tool trajectory optimization using a parabolic deposition rate model [14], Zhou presented in [16] a off-line programming system which optimizes the coating distribution, based on a ellipsoid Gaussian spraying model. Atkar proposed a trajectory planning procedure that optimize the uniform coverage of automotive surfaces considering the use of electrostatic spraying [2]. Other contributions have been given by Sheng, who proposed a tool path planning approach which optimizes the motion performance and the thickness uniformity [11], and by Zeng, who optimized the parameters of zigzag path pattern [15].

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Lorenzo Scalera et al.

Painting robots are used also in artworks and graphics, as far as an automatic and accurate system for decoration tasks or image reproduction is required. An example can be found in [8], where eDavid, a painting machine able to reproduce images by means of brushes strokes in a very impressive way, is presented. Other examples are given by Paul the robot, a robotic arm that produces observational sketches of people [13], by the works of Aguilar, who studied a robotic system for interpreting images into brush painted artworks [1], and by Berio, who presented a compliant robot drawing graffiti strokes [4]. At present, no examples of painting robots using an airbrush in artworks can be found in literature. Spray painting for artistic tasks have been studied by Prevost, who developed a system that assists unskilled users in spray painting large-scale murals [9], and by Shilkrot, who proposed an augmented airbrush for computer aided painting [12]. Another contribution is given by Seriani, who developed an algorithm to reproduce grey-scale images on large surfaces using a spray painting robot [10]. Nowadays, the mechanics of spray painting has been widely studied and several mathematical models for the paint deposition and flux rate have been developed. For example, Balkan and Arikan utilized a beta distribution model [3], Chen a parabolic model [5], Conner a set of Gaussian functions [6]. Hertling proposes a mathematical model for the paint flux field, which matches experimental data assuming an elliptical cross section of the spray cone [7]. In this context, we present a robotic spray painting system for artistic and graphic applications. In particular, we use an anthropomorphic robot equipped with a single-effect automated airbrush. Firstly, we introduce a mathematical paint intensity model, which is based on a radially symmetric Gaussian distribution of colour intensity within the spray cone. With respect to other similar models, the one here presented is validated experimentally by means of an automated airbrush for decorative applications. Then, we provide a characterization scheme, which is needed for the fitting of the spray parameters of the Gaussian model. In this stage, we actuated the airbrush in stationary conditions for given intervals of spraying time and by varying the orthogonal distance between the airbrush and the target surface. Black colour and plain paper have been used in order to characterize the grey level for each spot sprayed by the airbrush. The paper is organized as follows: in Section 2 the paint deposition model is introduced and the main functions are defined. In Section 3 the experimental apparatus is described and the experimental validation of the colour spray model is presented. Finally, in Section 4 the conclusions of this research are given.

2

Paint intensity model

The colour intensity pattern generated by a single-effect airbrush is a function of the specific spray gun, the air flow and paint parameters, the environmental conditions, the shape of the target surface and the relative orientation of the airbrush. In this context, we consider the airbrush in stationary conditions and orthogonal to the canvas. Furthermore, for the sake of simplicity, we introduce

Airbrush robotic painting

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the hypothesis that the increasing of colour intensity in a point of a sprayed spot, for a fixed distance d between the airbrush and the canvas, is linear to time. Moreover, we assume that the colour intensity does not reach the saturation level. Over-saturation, or over-painting, indicates the phenomenon that occurs when a sprayed area has already reach the maximum intensity level, the support can not adsorb more paint but the airbrush keeps spraying. Over-saturation causes firstly the presence of high paint density in the centre of a sprayed spot and then the appearance of colour drops on the paper. For these reasons, the increasing of colour intensity within the spray cone can not be considered still linear to time. In Fig.1 a schematic diagram of our painting robot is reported. In particular, the spray cone ejected from the airbrush nozzle can be seen. The paint aerosol cone produces on the target surface a circular impact area S with radius r.

airbrush nozzle α

d

r

S ∆S

target surface

Fig. 1. Schematic diagram of painting robot and spray cone.

In order to develop our spraying model, we need to introduce the spray painting flow ϕ, which is the amount of colour that passes through an unitary surface during a unit of time. It turns out that ϕ is a function of the spray cone semi-aperture angle α: ϕ = ϕ(α) (1) [ mKg 2s ] In this context, we assume ϕ(α) constant with time. This assumption comes from the fact that, for the sake of simplicity, we consider the airbrush in stationary conditions and no transient effects, such as the opening or closing of the airbrush nozzle, are taken into account. During time T the airbrush sprays on the incremental area ∆S the incremental amount of colour ∆Mcolour defined as: Z ∆Mcolour = ∆S ϕ(α) dt [Kg] (2) T

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It is now possible to obtain the colour surface density δcolour as: Z ∆Mcolour Kg δcolour = lim = ϕ dt = ϕ T [m 2] ∆S→0 ∆S T

(3)

The relationship between colour surface density and the colour intensity icolour can be defined as follows: icolour = kc δcolour

[HSI]

(4)

For the colour intensity icolour we use, in this context, the HSI (Hue Saturation Intensity), a common cylindrical-coordinate representation of points in a RGB colour. kc is a proportional constant and it is measured in [HSI m2 /Kg]. By digitalizing sprayed spots (i.e. by means of a scanner), colour intensity has to be multiplied by a further constant ks in order to measure the new scanned intensity iscan as the grey level between 0 and 1. For a fixed nozzle opening time T , we obtain: iscan = ks kc δcolour = ks kc ϕ(α) T [0÷1] (5) We can now define the colour flow function Φ(α) as: Φ(α) = ks kc ϕ(α)

(6)

or, by using the scanned intensity definition, as: Φ(α) =

iscan (α) T

(7)

Since r = d tan(α), the flow function Φ(α) can be approximated, within the ˜ spray cone, with a radially symmetric Gaussian distribution Φ(r), characterized by coefficients A and B. The former represents the maximum colour intensity value in a sprayed spot, whereas the latter the width of the Gaussian curve. 2 ˜ Φ(r) = A e−B r

r < Rmax

(8)

For√the sake of simplicity, we truncate the flow function at a value of Rmax = 3/ 2B, which is 3 times the standard deviation of the normal distribution. The Gaussian function can be considered as function of α and d. The same relationship can be written as function of the distance d, between airbrush and canvas, and the opening angle α: ˜ d) = A e−B (d tan α)2 Φ(α,

(9)

Finally, the paint intensity model for the airbrush painting can be described as: ˜ d) T iscan (α, d) ' Φ(α,

(10)


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5

Experimental characterization

In this section, an experimental characterization of colour intensity is presented. First of all, the spray characterization is necessary to validate the paint intensity model presented in Section 2. In fact, we need accurate estimates of the parameters A and B of our spray model. This parameters can vary with air pressure and flow, environmental conditions and paint dilution. In order to take into account all these error sources, the experimental characterization is a procedure that can estimate spray features in a efficient way. In this research we used a UR 10 robot, by Universal Robots, equipped with a Iwata revolution HP-M2 airbrush. A single-effect airbrush has been chosen and it is actuated by means of a pneumatic actuator. A 50 L compressor provides the airflow for both pneumatic actuator (3 ÷ 6 bar pressure) and airbrush (1.5 bar fixed pressure, using a regulator and a filter). The painting robot is shown in Fig.2. The robotic painting system is controlled from computer via TCP/IP by means of MatlabTM environment.

Fig. 2. Painting robot equipped with airbrush and actuator system.

In order to characterize the spray painting, the airbrush is actuated in stationary conditions for given intervals of spraying time ∆t and by varying the orthogonal distance d between the airbrush and the target surface from 100 to 200 mm with a step ∆d = 25 mm. For each distance, we actuated the airbrush starting from t0 = 0.25 s, for the first spot, and then we increased the nozzle opening time by ∆t = 0.25 s, until the colour saturated. We used black colour diluted with water and plain paper (with a density of 80 g/m2 ) as support. All the spots were then acquired with a scanner (Epson Perfection V39) in order to fit the experimental distribution of colour intensity with the Gaussian function reported in Eq.(8). In Fig.3(a) an example of sprayed spot, executed at a distance d = 150 mm and with a opening time ∆t = 1.00 s, is reported. Fig.3(b) shows the corresponding intensity distribution plotted on a 3D graph, whereas the approximated intensity trend is reported in Fig.3(c).

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(a) Sprayed spot.

(b) Experimental intensity.

(c) Approximated intensity.

Fig. 3. Example of a sprayed spot and its intensity distribution (∆d = 150 mm, ∆t = 1.00 s). 1 0.25 s 0.5 s 0.75 s 1s 1.25 s 1.5 s 1.75 s 2s 2.25 s 2.5 s 2.75 s 3s 3.25 s 3.5 s

0.9 0.8

Intensity

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

5

10

15

20 25 30 Spot Radius [mm]

35

40

45

50

(a) 1 0.25 s 0.5 s 0.75 s 1s 1.25 s 1.5 s 1.75 s 2s 2.25 s 2.5 s 2.75 s 3s 3.25 s 3.5 s

0.9

Colour Flow Function

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

5

10

15

20 25 30 Spot Radius [mm]

35

40

45

50

(b) Fig. 4. Scanned intensity iscan (a) and colour flow function Φ (b) in function of spot radius r for different spraying times and a fixed distance d = 17.5 mm between the airbrush and the target surface.


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In Fig.4(a) the intensity distribution iscan in function of spot radius r for different spraying times and a fixed distance d = 17.5 mm between the airbrush and the target surface is reported. It can be seen as, by increasing the spraying time, the scanned colour intensity linearly increase. Each experimental distribution is then divided by its spraying time in order to obtain the colour flow function Φ(r), reported in Fig.4(b). As it can be seen, the distributions of Φ(r) for each different spraying time overlap in a very good manner. From the resulting curve it is then possible to extract the parameter A and B of the interpolating Gaussian distribution. For a low spraying time (∆t < 1 s), a transient effect caused by the opening of the airbrush nozzle can be seen. In fact, the actuation of a single-effect airbrush causes the simultaneous spraying of both colour and air. In this way, the immediate effect is a over-load of colour with respect to the normal behaviour. This undesirable effect can explain the non-perfect overlap of the distributions characterized by the lowest spraying time in Fig.4(b). In further studies, we will move to a double-effect airbrush, in which the colour can be sprayed when the compress air already flows, without any transient effect at the beginning of a spraying task. Finally, we can affirm that, within the spray cone of radius r, a linear trend of colour intensity with spraying time t before over-saturation has been found. Moreover, no linearity of intensity as function of distance has been measured. This can be explained by the fact that, by increasing the distance, not all the colour air-sole particles reach the target surface because of gravity force, air resistance and fluid-dynamics effects.

4

Conclusion

In this paper a robotic painting system for artistic applications by means of an anthropomorphic robot and a single-effect airbrush was presented. Firstly, a mathematical model based on a radially symmetric Gaussian distribution of colour intensity within the spray cone was presented. Then, an experimental characterization of airbrush spots was used to validate the model. A linear trend of colour intensity with time has been measured. In this way, a colour flow function, that can be used to describe the intensity behaviour for a fixed distance between the airbrush and the target surface, has been obtained. The mathematical model and the experimental results provide the basis for further investigations and developments of this robotic painting system.

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