Response surface method based robotic cells layout optimization in small part assembly liafan ZHANG, Member, IEEE, Xingyu FANG ABB Corporate Research, Shanghai 201319, China e-mail:
[email protected]@cn.abb.com (Tel: 86-21-61056488, Fax: 86-21-61056905)
Abstract--
Sman part assembly (SPA) in 3C industry is
considered as the next giant market for the industrial robots, which have proven to be more cost effective in terms of flexibility, repeatability, and with new functions offer improved accuracy. However, high product volume in a quite short product Iifecycle, short leading time for new product,
and
low
added
value
per
production
step
differentiates the robotic cens in 3C industry from those in the
established
normally
automotive
determines
the
industry.
The
fortune of
3C
productivity
manufacturing
enterprises. Therefore, how to maximize the throughput of a robotic cell in SPA with optimal cell layout
is highly
demanded. This present work puts forward a practical methodology
to
minimized
the
cycle
time
for
certain
patterned robotic cen layouts in SPA, by applying response surface method (RSM). The optimization is performed not only with 3-dimension translation, but also together with rotation. Additionally, an available solution can be provided to the cell with two workstations/tasks simultaneously. The validation
of
implemented
this with
methodology several
kinds
has of
been
carefully
practical cases,
by
achieving the optimum deployment of the workstations/ tasks in the cell, with an incensement in productivity up to
15%. This is not a considerate improvement, but will bring a significant benefit to SPA manufacturer's revenues.
Index Terms-- Robotic cell layout, small part assembly, response surface method, optimization. 1. INTRODUCTION Outside the established automotive industry, 3C industry of communication, computer and consumer electronics is regarded as the next highlighted market for the industrial robots, which has proven to be more cost effective in terms of flexibility, repeatability, and with new functions offer improved accuracy. However, high product volume in a quite short product lifecycle, short leading time for new product, and low added value per production step differentiates the robotic cells in 3C industry from other established industries. So how to achieve the maximum throughput, even a small improvement in throughput, is critical to these 3C manufacturing enterprises. Therefore, a very fast and efficient method to design an appropriate robotic cell layout for a particular manufacturing task with optimal cycle time is highly demanded. The general interest to optimize the cycle time performance, defined as the time during which the sequence of tasks are completed, is normally from these two main scopes: cell layout, and scheduling in robot
movement [1][2]. Many previous studies have taken step forward in both areas. Some data as far back as the late 1970s, but majorities have been performed in recently decades. Lueth optimized the cell layout fully automatically in three dimensions in the configuration space regarding the work-cell task, with the aim to minimize the cost of the layout [3]. With this automatic layout planning system (ALPS), the generated layouts with collision-free path were valid, without necessary final simulation. The work proposed in [4] was to answer two typical questions, including what type of robots is suitable to satisfy the existing working space, and where to place the base of this robot to efficiently serve the existing machines, in case of an existing robot working space occupied with a number of CNC machines. Nelson and Donath [5] also considered the relationship between specified robot motions in an assembly task and the locations of singularities in the workspace when they developed a gradient function based optimization method. The series work from Srskandarajah and Dawande [2][6] highlighted the problem on the global time-optimal sequencing and scheduling based on polynomial-time approximations for a robotic cell. Zacharia and Aspragathos [7] have solved the proble� of determining the optimum route of a manipulatorG end effector visiting a number of task points as a variation of Traveling Salesman Problem (TSP) using GA. The scheduling approach taken by Richardsson,Daneilsson et ai, is an event-driven approach with finite buffers [8]. The approach uses a modified A*-algorithm with heuristics developed from time-driven scheduling. But most of them are impractical in industrial engineering field because of the complex algorithm, heavy computational burden and long calculation time. On the other hand, these advanced functions normally require on-site engineers must have solid knowledge about robotics, programming, and cell layout planning. Unfortunately, it is not always possible to have qualified engineer even if he/she passed an intensive and expensive training. Wappling and Feng [9] were to determine the relative robot/prescri bed task position in the framework of time optimality by firstly applying response surface method on the concept of path translation and path rotation, and developed an add-in in RobotStudio™. It provides a very convenient and efficient method, without complicated algorithm for practical engineering. However in their demonstrated cases, there was only one workstation/task
existing in the whole robot cell, by translating the position,or rotating orientation of the path separately. The effort in this focuses on the first scope: cell layout, and retrieves the method from above study,but extends it to the case, where the optimization is performed not only with 3-dimension translations,but together with rotations. Additionally, the case of two workstations/tasks in one robotic cell is also available. After a short presentation of the development background in Section 2, the method used in this paper is outlined in Section 3. Section 4 introduces the validation of this method through several kinds of practical cases. The areas for the further research and conclusions are followed in Section 5. II. RESEARCH BACKGROUND A. Robot cycle time The sequence of the movements can be referred to as a robot task. The time duration during which the sequence of the movements is completed is normally referred to as cycle time [9]. Changing the relative positIOn or orientation of a cycle to the robot leads to different motion profiles, and hence to different cycle time performance. The cycle time can be considered as a continuous response function of the relative position and orientation of the reference coordinate.
Fig. l. Traditional pick-place cycle.
understood, normally depending on robot kinematics and kinetic sensitively and non-linearly. B. Response suiface method
A response surface model (RSM) is a mathematical model fitted to a response variable y as a function of n predictor variables, �J, �2' E , �Il' in order to provide a summary representation of the behavior of the response, as the predictor variables are changed [10]. The RSM not only involves just main effects and interactions, or also has quadratic and possibly cubic terms to account for curvature. It is almost always easy to use and sufficient for industrial applications, with a limited number of simulations,without convergence issue. To evaluate curvature, a second-order model must be introduced. Quadratic response surfaces are simple models that provide a maximum or minimum without making additional assumptions about the form of the response. It can be expressed as the polynomial function containing quadratic terms as the equation below: Y
_
-
{3 0
�k
i... i=l {3iXi
+
95
Original
.
065
055
�
3Iac/ol's Original locaction
X3!l
30
-0.2
Fig. 2. Corresponding cycle time for the pick-place cycle with different locations in XZ-plane. Fig.l illustrates a typical pick-place cycle, and Fig.2 gives its corresponding cycle time when deploying it in different locations in OXZ-plane, within the robot workspace. However, the nature of the true underlying relationship between the cycle time response surface and cycle relative pose is either unknown or poorly
tmalloop IT] C Opiq rm I ! .
bisection
. � L-y'
X,
0.5
.
IO':':iL 2Dzn
.85
75
E
(1) where {3o is the constant term, {3i represents the coefficients of the linear parameter, {3ij represents of the interaction parameter,Pii of the quadratic parameter,and f:: is the residual associated to the experiments. To estimate the parameters in above equation, the experimental design has to assure that all studied variables are carried out in at least three factor levels. One logical assumption is to add center point to a two level design, namely low-medium-high. As shown in Fig.3, the three-level factorial design with n factors can be regarded as the grid in n dimensional space, denoted by R/. The vector space R" comes with a standard basis: xl= [ I,O,E ,0], X2 = [0,1,E ,0], E Xn = [0,0,E ,1]. 2Iac/ol's
U16
",k 2 ",k + L i=l {3iiXi + L lsis j {3i jXiXj +
nlac/ol's Original
locaction
• nD bisection
.)g c) Xo
X,
Fig.
3.
Tlrree-level factorial design with n factors.
A so-called full factorial design is defined by a few simulations performed on the admissibility boundary in n dimensional space around the original point. Table I
summarizes the number of runs required for a 3k factorial designs. The last column in lists the number of terms present in a quadratic model for each case. TABLE I THREE-LEVEL FACTORIAL DESIGNS Number of coefficients Number of factors 3 k factorial quadratic empirical model 2
9
3
27
10
81
15
5
243
21
6
729
28
III. OPTIMIZATION METHODOLOGY Since the cycle time is sensitive to the workstation/task placement, the basic idea is to find this sweet point, where the robot could achieve the time optimality, by changing the relative pose of the workstations/tasks to the robot. In previous art [9],only 3-dimensional translations were involved in the optimization loop, by considering the rotation separately. But much work has proven that RSM can handle the optimization problem with more than 3 factors successfully. Technically, the pose of the workstation/task frame O"XwY,,'zw in the robot base frame OtXbY�b can be defined as the transformation matrix Ao: (2) in which P(x,y,z) represents the relative position: P(x,y,z)=
[�]
(3)
and R(e,
