1. INTRODUCTION
Industrial robots are used especially in sectors where the human
body is in danger or is working in extreme conditions. One of these
sectors is the forges sector where the manipulating objects are hot, and
the vibrations and noise are big. The problem of manipulation the hot
parts implies firstly the choosing of the right gripper mechanism in
order to obtain the best cooling of it and of the robot itself. But the
position of robot with respect to the application, by taken into
consideration as an objective function the accumulated heat from work
piece during the manipulation of it, it is also a very important
problem.
An empiric solution of determining the position of robot base by
computing only the three coordinates of the origin of the Cartesian
coordinate system assigned to the robot base is given in (Kovacs &
Cojocaru, 1982). This empiric solution is not taken into consideration
the way of moving of robot between the application points, but is taken
into consideration the weight of object that the robot is moving between
these.
In (Tian & Collins, 2005) an optimization problem of placement
of a simple two-link planar manipulator by using a genetic algorithm is
presented. Also in paper (Mitsi et al., 2008) a hybrid genetic algorithm
is used in order to determine the optimum location of the base of robot
with respect to imposed discrete positions of end-effector.
The location of robot base with respect to the application is so
that all the interest points of application to be situated in the
working space of robot. An optimization of this location by taken into
consideration the minimum time of movement was presented in papers
(Ciupitu & Simionescu, 2007). In paper (Ciupitu et al., 2008) an
optimum synthesis of motion law together with minimum time of motion was
performed.
The mechanical structure of the industrial robot chosen by the
manufacturers (Renault--France, Rahm--Italy), that are using it in
forges sector is of articulate kind with 6 DOF. Sometime the opening
area of forge makes difficult the inserting of hot part inside the forge
even with 6 DOF. But an industrial robot with a mechanical structure of
cylindrical type with at least 5 DOF may solve the problem too.
2. FORGING MANUFACTURING PROCESS
Usually the forged pieces are inserted from a bunker into a furnace
in order to be heated. The hot part comes out from a medium frequency
furnace (Fig. 1) with a random orientation or that can be fixed by using
special mechanisms, depending of the shape of part. But because of
temperature of part the individualization and orientation of part is
difficult to be made with a good accuracy. So, a vision system to
recognize the position of part and to communicate with the robot
controller in order to make the position and orientation corrections of
picking configuration, is necessary.
From delivering port of furnace the part is inserted by lateral
into the forge and left down inside the forging mold. The inserting
window is relatively small and requires a long final link of robot
mechanism or long gripper fingers.
Sometimes another task of spraying the parts of forge is done by
the same robot with the aid of a special dose fixed to the robot arm or
to the gripper. Anyway, the different planes in which the pick-and-place
operations are done, and the small window of forge where the robot arm
must be inserted, impose a 6 DOF spatial mechanism for robot mechanism.
An industrial robot with a mechanical structure of cylindrical type
with at least 5 DOF may solve the problem, but the prismatic joints are
pretentiously even in case of cold manufacturing processes.
The end-effector could be cooled by the aid of a fan or by pressure
air in some situations when the temperature of manipulating part is high
and the heat cannot be eliminated by the movement of the robot during
one cycle.
[FIGURE 1 OMITTED]
3. OPTIMISATION PROBLEM
In order to formulate the optimization problem 2 models must to be
known:
1) the mechanical structure model of robot with minimum and maximum
acceptable values for each joint independent parameter and
2) the forge application given by: coordinates of positions
(configurations) that the robot must reach, the trajectories and motion
laws between these points, the temperature of work pieces and the
weights of them.
Usual the mechanical structure model of a robot is implemented into
robot controller by using Denavit-Hartenberg formalism in order to find
a transformation from tool tip to the base of robot. By choosing the
axes systems in a special manner, the number of unknown parameters
between 2 Cartesian coordinates systems chosen anyway on each link is
reduced from six to four: [a.sub.i], [s.sub.i], [[alpha].sub.i] and
[[theta].sub.i], i = [bar.1, n], where n is the number of degrees of
freedom of robot.
The model of forge application is simplified composed only by the 5
points [P.sub.j], j = [bar.1, 5], that the robot must reach during the
motion, without any obstacles defined (Fig. 1): [P.sub.1]--in front of
forge (waiting point), [P.sub.2]--upper the picking position,
[P.sub.3]--picking position from the exit of furnace, [P.sub.4]--inside
forge and [P.sub.5]--extreme position of eliminating the piece from
forge to the cooling conveyer.
Also the order of reaching these 5 points in a complete cycle
(composed by l = 8 intervals of motion: [P.sub.1][right arrow]
[P.sub.2][right arrow] [P.sub.3] [right arrow] [P.sub.2] [right arrow]
[P.sub.1][right arrow] [P.sub.4][right arrow] [P.sub.1] [right arrow]
[P.sub.5] [right arrow] [P.sub.1]) and the motions laws between these
are supposed as known.
The heat accumulated by the robot during a cycle depends by the
temperature of work piece [T.sub.l], l = [bar.1, 8] and by the time when
the work piece is manipulated by the robot. Finally, especially for
optimization problems that is dealing with forces and energy or power
consumption, the weights [G.sub.jk], j = [bar.1, 5], k = [bar.1, 5], j
[not equal to] k, of objects moved by robots between application points,
must to be known.
The unknowns of optimization problem are the parameters that are
defining the position and the orientation of Cartesian coordinates
system assigned to the base of robot
[O.sub.1][X.sub.1][Y.sub.1][Z.sub.1] with respect to an inertial
Cartesian system assigned to the "world of robot" (or to the
application) denoted by [O.sub.0][X.sub.0][Y.sub.0][Z.sub.0]. These
parameters are composed by the 3 Cartesian coordinates of origin
[O.sub.1] expressed in Cartesian system
[O.sub.0][X.sub.0][Y.sub.0][Z.sub.0] ([X.sub.0O1], [Y.sub.0O1],
[Z.sub.0O1]) and the 3 independent angles that is giving the orientation
of Cartesian system assigned to the robot base
[O.sub.1][X.sub.1][Y.sub.1][Z.sub.1] with respect to fixed Cartesian
system O0X0Y0Z0 from the cosines directories matrix.
The number of unknown parameters could be reduced by choosing the
Cartesian system [O.sub.0][X.sub.0][Y.sub.0][Z.sub.0] in a Denavit-
Hartenberg manner. So, by choosing the [O.sub.0][Z.sub.0] axis
perpendicular to the [O.sub.1][X.sub.1] axis (chosen randomly
perpendicular to the [O.sub.1][Z.sub.1] axis), only 4 parameters are
enough: [a.sub.0], [s.sub.0], [[alpha].sub.0], [[theta].sub.0].
The objective function of optimization problem is a sum (or
integral) of minimized parameter:
O = [8.summation over (l=1)][Q.sub.l] (1)
where [Q.sub.i] is the heat accumulated by the robot in each
interval of motion from a cycle.
The process of finding the optimum set of parameters
{[a.sub.0.sup.*], [s.sub.0.sup.*], [[alpha].sub.0.sup.*],
[[theta].sub.0.sup.*]} is a numerical one. At the beginning of
computation, starting by an initial set {[a.sub.0.sup.(0)],
[s.sub.0.sup.(0)], [[alpha].sub.0.sup.(0)], [[theta].sub.0.sup.(0)]}, a
complete verification of application points [P.sub.j], j = [bar.1, 5] so
that to be into working space of robot is performed.
By inverse kinematics a set of joint independent variables
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is determined for
each point [P.sub.j], j = 1, 5 . A point [P.sub.j], j = 1, 5 is in
working space of robot if all independent variables values are between
minimum and maximum acceptable values for each joint:
[[theta].sub.imin] [less than or equal to] [[theta].sub.i,j] [less
than or equal to] [[theta].sub.imax], i = [bar.1,6], j = [bar.1,5]. (2)
The Lagrange method for solving of the minimization problems is
based on transforming a given constrained minimization problem into an
unconstrained minimization problem. Finally results an un-linear system
composed by 124 equations with 124 unknowns solved by numerical methods.
4. CONCLUSION
The optimum location of robot base depends to the robot structure
and to the application. With same robot but different application
positions and conditions results different locations for robot base.
The problem of finding the optimum location of robot base with
respect to the application points according to an objective function is
very important and could lead to major improvements (Ciupitu &
Simionescu, 2007), (Mitsi et al., 2008). Sometimes the conditions of
application impose special adjustments in order to protect the robot.
The placing of robot base in an optimum location from the very first
beginning is an essential initial task especially for large series
productions. The economy of time or/and energy (money finally) for each
product is decreasing it's price to almost a quarter (Feddema,
1996) but the protection of industrial robot parts is much more
important because without robot no production.
A multi-criteria optimization approach, by taken into consideration
the protection of industrial robot which is working in a hazardous
environment and the economy of time and energy, is the future work of
this research.
5. REFERENCES
Ciupitu, L. and Simionescu, I. (2007). Optimal Location of Robot
Base With Respect to the Application Positions, Proceedings of the 2nd
International Conference on "Optimization of the Robots and
Manipulators" OPTIROB 2007, Predeal, Romania, 27-29 May 2007, ISBN
978-973648-656-2, pp. 57-62.
Ciupitu, L., Simionescu, I. and Ivanescu, A. N. (2008). Optimum
Synthesis of Motion Laws Used By Robot Controllers, 0281-0282, Annals of
DAAAM for 2008 & Proceedings of the 19th International DAAAM
Symposium, ISBN 978-3-901509-68-1, ISSN 1726-9679, pp. 141, Editor B.
Katalinic, Published by DAAAM International, Vienna, Austria 2008.
Feddema, J. T. (1996). Kinematically optimal placement for minimum
time coordinated motion, In: Proceedings of the 1996 IEEE Int.
Conference on Robotics and Automation, Volume 4, 22-28 Apr 1996,
Minneapolis, pp. 3395-3400.
Kovacs, F. and Cojocaru, G. (1982). Manipulatoare, roboti si
aplicatiile lor industriale (Manipulators, Robots and their Industrial
Applications), Editura Facla, Timisoara. (in Romanian)
Mitsi, S., Bouzakis, K.-D., Sagris, D. and Mansour, G. (2008).
Determination of optimum robot base location considering discrete
end-effector positions by means of hybrid genetic algorithm, Robotics
and Computer-Integrated Manufacturing, 24 (2008) Elsevier Science, pp.
50-59.
Tian, L. and Collins, C. (2005). Optimal placement of a two-link
planar manipulator using a genetic algorithm, Robotica Journal,
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