IEEE Robotics & Automation Magazine - June 2018 - 89

TDFT
= k#

m # cos i
,
2
# tan a # tan b
(2)

t cm # r # d

where d, i, a, and b are the gun-target
distance, the inclination angle of the
spray gun, and the span angles, with
respect to the major-minor axis,
respectively. M, t cm, and k are the
weight of coat material, density, and
coefficient of spray, respectively. The
problem of loss of spray will be studied
in the "Field Experiments and Results"
section by evaluating the TE.
According to (2), all of the aspects of
the applicator, e.g., gun distance to the
target, the angle of application, and
traveling speed could affect the finish
quality. The film thickness is inversely
proportional to the square of the distance between the spray gun and surface. Therefore, variation in paint
thickness is a common problem in conventional spraying, particularly in highrise spraying due to the difficulties of
precisely controlling paint distribution
by a human painter. Inconsistent film
thickness contributes to various defects
such as runs, drips, sagging, mottling,
and striping.
The thickness variations in interior
finishing could be substantially avoided
by automated spraying if certain task
constraints are satisfied by accurate and
repeatable control of paint distribution
across the surface. Thus, coverage paint
planning is performed to generate the
trajectory of the spray gun by considering the 3-D layout of the as-built structure, characteristics of spray nozzle (i.e.,
spray angle, a, and spray pattern, w),
arm workspace, and geometric constraints [Figure 6(a)]. The following
constraints are considered and applied
to provide an even paint distribution by
using a flat fan nozzle.
● The spray gun, coupled to the arm, is
held and moved at an optimal and
constant spray distance to the surface, d = 30 cm. Otherwise, a portion of the paint droplets become
nearly dry before striking the surface,
resulting in significant paint dust.
● The nozzle is pointed straight and
perpendicular to the planar surfaces,

Lift Moves Up to the
Top-Most Work Cell

Patch

(m,1)

EndEffector
Path
Between
Paint
Strips
EndEffector
Path for
Painting
ph

(m,2)

Patch

Lift Moves
Down

Overlap
on Two
Horizontal
Paint
Strips
α

Patch

(m,3)

Lift Moves
Down

d
Trigger
Gun

I

Release
Trigger
End
Stroke

L
Start
Stroke

(m
Patch

,n)

w
w : Coverage
Width
α : Spray
Angle
d : Spray
Distance
l : Coverage
Length
L : Stroke
Length
ph

Move the Mobile Base to Adjacent Workstation
(a)
Patch

Constraint Plane
for End-Effector
Motion Planning:
Parallel to the
Wall Surface

)(1)

1
(m +

pv

Overlap on Two
Vertical Paint
Strips

(b)
Figure 6. The spraying sequence and spray-gun trajectory planning for (a) a single
vertical paint strip (the spraying sequence and geometry model of constrained path
planning) and (b) multiple vertical paint strips (the spraying sequence and geometry
model of constrained path planning).

june 2018

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IEEE ROBOTICS & AUTOMATION MAGAZINE

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89
IEEE Robotics & Automation Magazine - June 2018

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