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Determining robot process capability using Taguchi methods
Robotics & Computer-Integrated Manufacturing, Vol. 6, No. 1. pp. 55-66, 1989
0736 5845/89 $3.00 + 0.00 ~:, 1989 Maxwell Pergamon Macmillan plc
Printed in Great Britain
•
Paper D E T E R M I N I N G R O B O T PROCESS CAPABILITY U S I N G TAGUCHI METHODS B E R N A R D C. J I A N G , J T. B L A C K , JAMES N . H O O L a n d C. M . W u Industrial Engineering Department, Auburn University, AL 36849, U.S.A. The robot process capability problem is outlined and terms are defined. Recent efforts to measure robot capability are reviewed. Two methods were used to analyze robot process capability data: the randomized complete block design method and Taguchi statistical experimental design methods. The purpose of the study was to compare the results obtained by these two methods and determine which method was better for analyzing the data to be used in determining]optimizing a robot's process capability. Three-dimensional (3-D) coordinate data were obtained using a WATSMART vision system to determine a robot's process capability. Three levels of four independent variables--load, X-, Y- and Z- coordinates--were chosen for the study. Both analysis methods yielded similar results in determining a robot's process capability (within 10.4 %). The Taguchi methods required significantly fewer data than the randomized complete block design used. Taguchi methods also optimized a robot's process capability.
In a process capability study of a machine tool, the parts made on the machine are measured to determine the machine tool's process accuracy and precision and the effect of varying input parameters on the process capability. For example, in lathe turning, precision decreases (variability increases) as the diameter of the workpiece increases. However, in robot material handling or material assembly, no product or output can be examined (measured) directly to determine the process capability. Therefore, a different method must be developed to determine the process capability of a robot. To do that, a means must be provided to independently measure the robot end effector's spatial location, three-dimensionally, at any specific time. A review of the measurement techniques and the testing methods, conditions and specifications is given in Ref. 15. A sound experimental design is necessary because of the many variables which influence a robot's process capability interactively. 14 The randomized complete full factorial design method is used to obtain the most complete information. However, this method requires the collection of a large amount of data and extensive data analysis, yet does not optimize the process capability for the factors considered. Although other types of experimental designs (e.g. Latin square design) require significantly fewer data, they usually lose certain information and still have the same shortcoming as the randomized complete design. A major concern of the robot user is how to determine the best operating characteristics for
INTRODUCTION Robot use is increasing in industries worldwide. Robot installations in the United States increased from a few hundred in 1970 to 4200 in 1984.1'2s The electronics and precision equipment industry is expected to double its market share from 8 % in 1985 to 16% in 1995. 25 Process capability data are vital in designing and implementing robots for manufacturing and assembly applications. Most manufacturers provide specifications for their robots. However, most of the current specifications are for a static condition or a range of extreme conditions of performance, e.g. the capacity of weight handled (0-20 kg), the velocity of movement (1-20 cm/sec) and the positioning tolerance ( + 0.5 mm). However, when a robot performs a task (during a process), neither the manufacturer nor the users know its process capability characteristics. The manufacturer lacks an acceptable methodology and measuring technique to determine a robot's process capability, and companies using robots often do not have the personnel to determine a robot's process capability. Furthermore, quality control objectives cannot be accomplished if the robot process capability is unknown. Acknowledegment--This project was supported by National Science Foundation Grant No. DMC-8519778 and the Advanced Manufacturing Technology Center at Auburn University. Special thanks to Ms. A. H. Honnell and Ms. P. S. Flick of the A M T C Information Resources Laboratory for the preparation of this manuscript.
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Robotics & Computer-IntegratedManufacturing • Volume 6, Number 1, 1989
optimizing process capability. This information is required when placing a robot in the workplace, particularly in an unmanned manufacturing cell. Therefore, not only the determination of a robot's process capability but also the optimization of its operational parameters is important. Using statistical Taguchi experimental design methods to determine and optimize a robot's process capability 14 is also possible. To evaluate the applicability of Taguchi methods for determining a robot's process capability, a comparative study was conducted of two types of experimental design methods--the randomized complete block design method and Taguchi methods.
OBJECTIVES The objective of this study was to compare the results obtained by two methods of experimental design and analysis. Method 1 used the randomized complete block design method and method 2 used Taguchi statistical experimental design methods. When supplied with sufficient information for process capability determination, method 2 not only required significantly fewer data, but also provided a means to optimize the experiment parameters in the study.
D E F I N I T I O N OF T E R M S The concept of process capability for a manufacturing process has been known for a long time. However, robot process capability is new. Although the terms "accuracy", "repeatability", "reproducibility" and "stability" seem intuitively clear, disagreement exists about their proper meanings. For the purpose of communication, the following definitions will apply. Although the given generic definitions apply to both point-to-point and continuous-path motions of a robot, only the point-to-point case is studied in this paper. • Robot process capability: Refers to the ability of a robot to perform consistently a job with a certain degree of accuracy, repeatability, reproducibility and stability. It is a function of task variables such as move speed, spatial position and load. • Accuracy: Refers to the ability to hit what is aimed at. It is the degree of agreement between independent ineasurements and the target value being measured. • Repeatability: Refers to the process variability. It is the degree of mutual agreement between independent measurements under specified conditions. This term is also called "precision". • Reproducibility: Refers to the deviation from or difference between the means of measurements
taken from repeated tests that hit the same target but developed from different starting points. • Stability: Refers to the difference in the average o f at least two sets of measurements obtained with the same target from the same starting point at different times. This term is also called "drift". BACKGROUND Process capability has been referred to as the positional accuracy, repeatability, reproducibility and stability when a robot performs a task. Most research has been with the control device 7-9'28 or path determination 2'7 to enhance the robot's capability to locate a point in space and to repetitively perform a job. The traditional methods-time-measurement (MTM) technique has been used to determine the required time for a certain job. 2' This technique is called robot time and motion (RTM). The factors considered in the RTM technique were a robot's mechanical design and work patterns. Some other process characteristics considered include arm movement velocity and reach distance. However, the study did not examine the interaction of these process characteristics and the consequent process capability. Some work has been done on the robot calibration method. 22'35 Whitney e t aL 35 discussed a calibration procedure for serial link manipulators. The procedure used a model whose parameters represented link lengths, joint encoder offsets, the relative orientations of consecutive axes, and the observed effects of joint compliance, backlash, and gear transmission errors. They used a least squares numerical search algorithm with theodolite measurements of tool positions and the robot's joint encoder readings to estimate all of the model's parameters. The study proved that a robot's positioning errors could be reduced significantly. However, the difference between a calibration study and a process capability study is that the latter is done to determine operational (during usage) characteristics, while the former is done to develop a method to adjust positioning errors (which seldom consider the process parameters). Furthermore, the measurement system for determining a robot's process capability must be independent of the robot. The calibration system can be part of the robot, which can cause intrinsic errors. However, robot calibration is a valuable technique for robot manufacturers to use in verifying the design of a robot. Warnecke e t al. 34 reported several methods for measuring a robot's spatial location, such as using contact sensors (e.g. a touch-trigger probe, a 3-D measuring head) and noncontact sensors (e.g. a theodolite, an optoelectronic system and a laser system). In
Determining robot process capability • B. C. JIANGet al. most cases, inductive sensors were superior to ultrasound, laser and photogrammetry because of data processing, distance, resolution, linearity and price. Test results were reported based on the studies done at the Institute for Production Automation (IPA), F . R . G . 3x-33 In general, data specified were positioning accuracy, path accuracy, and overshooting. One way to measure robot process capability is to use appropriate contact-sensing devices (touch-trigger probes) with feedback capability. 34 For example, Lembke and Jones 17 designed a Latin square threedimensional ball plate (LSBP) to characterize a robot's accuracy and repeatability. To design the LSBP, they used the Latin square design concept and used 16 different height poles, with 4 on each row and 4 on each column. The touch-trigger probe generated a signal upon contact from any direction. The probe was interfaced to the robot through an input channel. A program was written to move the probe slowly into the vicinity of a ball and to stop upon contact with it. Each ball was approached from the top and four sides to permit estimation of the bali's center location. Vira and Lau 3° at the National Bureau of Standards used a 1-D extensible ball bar to measure the positioning accuracy and repeatability of industrial robots. The extensible ball bar had a 5-cm travel radius and was monitored by a built-in electronic transducer which had 2.5-/~m resolution. At each end of the bar was a precision steel sphere. One sphere was magnetically attached to a socket which was firmly located within the robot's work zone. The center of the sphere becomes the origin of the measurement system. The other sphere was mounted on a universal joint which was attached to the robot end effector. A probe installed in the ball bar measured the radial displacement between the two spheres. Tests conducted to quantify errors of a commercially available robot were: point-to-point teach mode, wrist rotation, circular movement, and drift (for the robot's thermal stability). They stated that although an extensible ball bar is a reliable and economical instrument, application of it is limited to only 1-D measurement. Another way to measure a robot's spatial location is to use appropriate noncontact-sensing devices with position sensing capability. These systems can be acoustic -6"2° video-, 7'24'29 and laser-based. 3 As an example, the Robotics and Automation Applications Consulting Center (RAACC) 24 developed a procedure to test a robot's accuracy and precision before the robot was put into a workplace. Tests included the verification of manufacturer's specification: accuracy of repeatable placement, accuracy of playback to commanded position, stabilization and others. The positioning measurement was determined with non-
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contact eddy current measurement system equipment (Kaman Sciences Corporation model KD-4358 with model 15U1 sensors) arranged in three planes. Two levels (max. and 50 %) of payload, arm reach and speed were reported and analyzed (e.g. statistical characteristics) for robot process capability information. In 1986, RAACC reported a modified robot-testing procedure which included point-to-point, path control, continuous path and cycling tests. The setup was also changed to use the Selspine Robot Check System (Selcom Selective Electronic, Inc.). This vision system included two cameras, a micro-PDP 11/23 computer, LEDs and control unit, calibration fixture and plotter. This optoelectronic motion-analysis system used active light sources to determine actual positions of moving objects in space. These positions can be presented in Cartesian coordinates and can be calculated into speed and acceleration. The Industrial Technology Institute 11 reported a similar testing procedure. The Robotic Industries Association (RIA) formed a committee in 1985 to develop standards for the methods used in the testing procedure for evaluating industrial robotic systems. In a revised RIA draft for robot performance testing standards, 23 a standard test plane and standard test path were proposed. The standard test plane is "one which is orthogonal to the (1, 1 , - 1) vector or the base coordinate system'. 23 This plane is at a 45 ° angle to the horizontal plane. The standard path is a zigzag path passing through the center of the standard test plane. The length of each zigzag segment is either 200, 500, or 1000 ram, depending on the type of robot being tested. The robot is commanded to go from the first segment to the last segment and then to swing back from the end point to the starting point. Eight performance factors are determined by a series of tests: accuracy, repeatability, overshoot, settling time, segment cycle time, deviation from standard test path, warm-up drift, and static compliance. Test payload should be 50 % or more of the manufacturer's rated payload and must be in one of the 12 categories ranging from 0 to 140 kg as listed in the standards. The International Organization for Standardization (ISO) is another organization involved in the standard development effort. The subcommittee on performance testing is composed of delegates from the Federal Republic of Germany, France, Japan, Sweden, the United Kingdom, and the United States. 4 Their draft standards, as of August 1987,12 defined a test cube as the largest volume that can be covered in the working envelope. Four optional testing planes (i.e. the center X Y , YZ, and X Z planes, and the plane that is at a 45 ° angle to the center X Y plane) are defined.
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Robotics & Computer-Integrated Manufacturing • Volume 6, Number 1, 1989
Four corner points plus the center point make the five testing points. The payload and speed used in a test should generally be at 100 ~o of the rated payload and 100 ~ of the rated speed, respectively. A 50 ~ payload and a 50~o or 10~o speed may be used as alternative testing conditions. In Japan, Makino and his colleagues 18'~9 proposed "standard performance test methods for planar positioning assembly robots". The proposed tests for a planar positioning robot consist of six point-to-point tasks (swinging 300 ram, time vs. distance characteristics, base-running, pick-and-place, palletizing and peg insertion), and three continuous-path tasks (linear interpolation, circular interpolation and spline interpolation. Both standard working area and maximum working area were considered. The proposal followed Japan Industries Standards and specified the points of measurement at the four corners of the standard working area. Thirty measurements were taken at each point, and the spread of the distribution __+3s (where s is the standard deviation) was given. In summary, many factors can affect robot process capability, such as gravity, acceleration, backlash error, temperature, bearing plan and windup play. 5 These factors are categorized into task, human and environmental attributes (see Table 1). To isolate one factor from another is not easy; however, the overall improvement of robot process capability is feasible. Jiang and Black 13 reported on four techniques for measuring and improving robot process capability: changing the robot design; using work holders; positioning with contact sensing devices; and positioning with noncontact sensing devices.
EXPERIMENT To compare the results from two methods for determining/optimizing a robot's process capability, the following experimental conditions were chosen: three load levels (0, 0.227 and0.454 kg), X-coordinate (left/right, 65, 175 and 285 mm), Y-coordinate (in/out, - 1 3 , 97 and 207 mm), and Z-coordinate (up/down, - 2 5 3 , - 1 1 3 and 27 mm).
Method 1. Using the randomized complete block design A randomized complete block design was used, with each load level treated as a block to facilitate data collection. Twenty-seven spatial locations and 10 replications were randomized within each block. The design layout is shown in Table 2. The 27 points covered, approximately two-thirds of the maximum of the X- and Y-reaches in the first quadrant, and onehalf of the maximum Z-reach (Fig. 1). The robot was commanded to move from the home position (0, 0, 0~ to each of the 27 spatial locations in random order.
Table 1. Factors associated with a robot's process capability Attributes Robot Design
Control
Specification
Task
Human
Environmental
Factors Type: servo point-to-point, non-servo pointto-point, servo continuous-path Work envelope: cylindrical, spherical,jointed arm, rectangular Arm: number of joints, degree of freedom, weight, shape, length, material, tolerance End effector: material, size, shape, mobility, compliance, strength, sensor Type: air logic, stepping drum Memory type and capacity: standard (single program, multiple program), optional (expansion of standard different controller) Software: main program, subprogram, degree of intelligence Power supply: electric, hydraulic, pneumatic Movement range, velocityrange, repeatability, cycle time, reliability, number of years used, frequency of use, mobility, commonality, training and maintenance requirements Object: load, shape, size, material, load distribution, location, distance, direction Accuracy requirements Repeatability requirements Force requirements Frequency of task performance requirements Task type: process materials (painting, welding, grinding), material handling, assembly (pick up and place, insertion), loose registration, inspection (finding burrs) Operator skill, programmer skill, operator variations Psychological factors: mood, motivation, coordination Temperature, air velocity, humidity, stability, dust, floor loading, peripheral equipment, safety, electrical noise
For each movement, 3-D coordinate data were collected for the starting point (i.e. home position) and the ending point (i.e. a certain spatial point) by using a 3-D vision system called WATSMART.
Method 2.
Using the Taguchi statistical experimental
design Taguchi methods 1°'16'27 are quick and efficient methods for optimizing the design and performance of processes and products. They concentrate on finetuning products and processes by selecting the best combination of relevant controllable factors so that process or product performance is least sensitive to factors (noise) that are difficult, expensive or impossible to control. Taguchi methods have been used very effectively in Japan for many years. They have only recently been introduced in the United States where they are used primarily in the automotive industry.
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Determining robot process capability • B. C. JIANG et al. Table 2. Completely randomized block design layout X
Load
R
1
1 2
2
1 2
3
1 2
1
Y
1
Z
123
2
2
3
12 3
12 3
1
2
123
123
3 3 1 2 3
1 123
2
3
1 2 3
12 3
io
io
io Load levels: 0, 0.227 and 0.454 kg. X levels: 65, 175 and 285 mm. Y levels: - 13, 97 and 207 mm. Z levels: - 2 5 3 , - 1 1 3 and 27 mm. R levels: Replications (10).
Taguchi methods allow us to: • Examine m a n y variables in a simple design (orthogonal array). Significantly fewer tests are required than with m a n y other experimental designs. • Determine quickly the optimal or near-optimal operating conditions by employing a signal-tonoise ratio (S/N) that simultaneously measures process accuracy and repeatability. This condition can be further examined by changing the tolerance of each parameter (called tolerance design). • Combine on- and off-line quality engineering efforts into an overall system. An L27(313) orthogonal array was used for this study. The design layout and the variable assignments are shown in Table 3. Notice that method 2 had only one-third the data that method 1 had. To make the comparison, the subset data from method 1 were used for the method 2 analysis.
Equipment The noncontact 3-D coordinate measuring system (WATSMART) used to collect data in this experiment consisted of two high-resolution infrared cameras (positioning sensors), an IBM PC/AT, and data collection and analysis software. An active infrared lightemitting diode (IRED) was attached to the robot arm as a marker. The X- and Y-coordinates of the marker were detected by both cameras. Then a direct linear transformation (DLT) technique was used to convert data to 3-D coordinates. This equipment was chosen because it can measure the characteristics of robot
motion, i.e. it can continuously measure a robot's point-to-point and continuous-path motions to obtain a robot's kinematic data, and perhaps to control a robot in real time. A R H I N O robotic arm, a five-motor-controlled educational robot, was used in this experiment. The robot controller was interfaced with an IBM PC. The robot could be commanded to move by either controlling each joint m o t o r or by entering spatial point coordinates. The latter method was used in this experiment.
Results The objective of this study was to compare two methods of obtaining/analyzing data for use in determining/optimizing a robot's process capability. Reproducibility and repeatability data can be expressed as the spread (3s) of the measurements. In the spatial sense, this 3s value represents the radius of a sphere that covers the measured data points. These overall indicators can be broken into the spread of each of the X-, Y- and Z-coordinate components (i.e. 3sx, 3Sy and 3Sz). The three axes components provide valuable directional information while the overall reproducibility/repeatability is a simple integrated indicator. Only the home point could be analyzed for reproducibility because this was the only location tested. In method 1, a total of 810 measurement data were used under three load levels and 27 spatial locations with 10 replications under each condition. In method 2, a
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Robotics & Computer-Integrated Manufacturing • Volume 6, Number 1, 1989 Y (mm)
Z (mm)
= ,
~
a
-- y tmrrO
Selected Points
(X) in the Study
Calibration Frame
RHINO Robo!
Camera # 2
Camera #1
illlllll
Prinler
IBM PC/AT
WATSMART Conlroller
Holler
Fig. 1. Experimental layout.
subset of 270 m e a s u r e m e n t d a t a was used u n d e r t h e s a m e c o n d i t i o n s as in m e t h o d 1. T h e r e p r o d u c i b i l i t y d a t a w e r e c a l c u l a t e d as f o l l o w s :
s,, =
,1
Y x i - Yx)2/(n- 1 i
;
n = 810 for m e t h o d 1, n = 270 for m e t h o d 2
Hx = 3s~.
Hy
and
Hz
a r e c a l c u l a t e d in a s i m i l a r w a y to
Hx
s= { ~ [ ( Y x ' - Yx)2 + ( Y y I 0.5
+ ( Y z i - Yz)2]/(n-
1)
;
n = 810 for m e t h o d 1, n = 270 for m e t h o d 2 H = 3s
Determining robot process capability • B. C. JIANG et al.
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Table 3. L27 (3 la) Taguchi design layout
Experiment
1
2
X * Y 3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
1 1 1 1 l 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3
1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3
1 1 1 2 2 2 3 3 3 2 2 2 3 3 3 1 1 1 3 3 3 1 1 1 2 2 2
X
Y
X * Y 4 1 1 1 2 2 2 3 3 3 3 3 3 1 1 1 2 2 2 2 2 2 3 3 3 1 1 1
5
X * Z 6
X * Z 7
Y * Z 8
Load 9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 1 2 3 2 3 1 2 3 1 2 3 1 3 1 2 3 1 2 3 1 2
1 2 3 1 2 3 1 2 3 3 1 2 3 1 2 3 1 2 2 3 1 2 3 1 2 3 1
1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2
1 2 3 2 3 1 3 1 2 2 3 1 3 1 2 1 2 3 3 1 2 1 2 3 2 3 1
Z
e
e
10
Y * Z 11
12
13
1 2 3 2 3 1 3 1 2 3 1 2 1 2 3 2 3 1 2 3 1 3 1 2 1 2 3
1 2 3 3 1 2 2 3 1 1 2 3 3 1 2 2 3 1 1 2 3 3 1 2 2 3 1
1 2 3 3 1 2 2 3 1 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1 1 2 3
1 2 3 3 1 2 2 3 1 3 1 2 2 3 1 1 2 3 2 3 1 1 2 3 3 1 2
e
Noise R1-RIO
Linear graphs: showing interactions between variables
3,f~6,/ 1
9 0
10 0
12 0
13 0
8,11 Table 4. Comparison of a robot's reproducibility for home point L = 0 kg
H Hx Hy H~
L = 0.454 kg
L = 0.227 kg
Overall
(a)*
(b)t
(c):~
(a)
(b)
(c)
(a)
(b)
(c)
(a)
(b)
(c)
2.571 1.150 1.905 1.033
2.549 1.155 2.005 0.926
1.3% 0.4% 5.3 % --10.4%
2.566 1.265 1.770 1.173
2.441 1.276 1.669 1.100
-4.9% 0.9% -- 5.7 % -6.2%
2.540 1.354 1.767 1.075
2.469 1.337 1.668 1.104
- 2.8 % - 1.3 % - 5.6 % 2.7%
2.541 1.256 1.814 1.094
2.486 1.253 1.781 1.043
- 2.2 % - 0.2 % - 1.8 % -4.7%
*(a) Method 1 : completely randomized block design (ram). : t(b) Method 2: Taguchi methods (mm). ~/(c) Percentage of difference = ((b)-(a)/(a))* 100 %.
w h e r e sx a r e t h e X - c o o r d i n a t e
standard
measurements Yx, Yy a n d Yz a r e t h e m e a n s
for
deviations of n
Yxi, Yyi
and
Yzi,
respectively s is t h e o v e r a l l s t a n d a r d d e v i a t i o n o f n m e a s u r e m e n t s Yxi, YYi a n d Yzi a r e t h e c o o r d i n a t e s f o r i n d i v i d u a l measurements Hx, Hy a n d Hz a r e t h e r e p r o d u c i b i l i t i e s f o r X - , Y- a n d Z-coordinates,
respectively, in mm
H is t h e o v e r a l l r e p r o d u c i b i l i t y i n m m n is s a m p l e size ( n = 8 1 0 f o r m e t h o d method
1, n = 2 7 0 f o r
2).
Analysis of variance (ANOVA) was applied to the H v a l u e f o r t e s t i n g t h e m a i n e f f e c t s o f l o a d , X - , Y- a n d Z coordinates and the interactions among X, Y and Z. T h e reproducibility a n a l y s i s r e s u l t s f o r h o m e p o i n t a r e i n T a b l e 4. T h e m e a n a b s o l u t e e r r o r s a n d t h e r e p e a t a -
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Robotics & Computer-Integrated Manufacturing • Volume 6, Number 1, 1989
bility values from both experiments were well within the 10.4 ~ difference. The repeatability of a certain spatial location was the spread (3s) of the repeated measurements under a certain test condition. Twenty-seven spatial points were tested. The g r o u p mean could be either the average of 30 measurements (i.e. any X-, Y- and Zcoordinate combination) or the average of 10 measurements (i.e. any load, X-, Y- and Z-coordinate combination). The latter average (i.e. g r o u p size = 10) was used for the analyses. Therefore, the repeatability data are calculated as follows:
sx,~ =
(Yxi - Yx)2/9
i = 11-20
form=2,
l o.'; i =
1-10 for m = 1,
results were similar to those from the reproducibility analysis. The repeatability values for both methods were close to the maximal of 7.9 ~o. Accuracy refers to the ability to hit what is aimed at. It is the degree of agreement between independent measurements and the target value being measured. A robot's accuracy in hitting a specific target point is c o m p u t e d comparatively in this study. In other words, the difference between the c o m m a n d e d distance and the distance measured from a starting point to a target point represents the accuracy of the r o b o t at this target point. Therefore, the accuracy data are calculated as follows:
dl = [(Yxl - n g o ) 2 d- (YYi -- H y o ) 2 q- (Yz i - H Z o ) 2 ] 0"5, i = 1 - 3 0
i=21-30form=3
d,. = 1 / l O ~ ( d i ) ; i =
Px = 1/3 ~(3sxm); m = 1 to 3
1-10 for m = 1,
i
m
i = l l - 2 0 for m = 2, i = 21-30 for m = 3
P y and Pz are calculated in a similar way to P x
A,. = ~'(d i - dm)/lO; i = 1-10 for m = 1, i = 11-20 s,={~i
[(YxI-
yx)2 + ( y Y i -
i
yy)2
for m = 2, i = 21-30 for m = 3
0.5
( Y z ~ - Yz)2]/9
; i = 1-10 for m = 1, i = 11-20 for
A= 1/3•Am;m=
1-3
tn
m = 2, i = 21-30 for m = 3 P = 1/3 ~(3sm); m = 1-3 nl
where Sxm are the X-coordinate standard deviations for g r o u p m S,,, are the overall standard deviations for g r o u p m Yxi, Yy~ and Yz~ are the X-, Y- and Z-coordinates for each individual measurement, respectively Yx, Yy and Yz are the means for Yxi, Yy~ and Yzi in a group, respectively Px, Py and Pz are the repeatabilities for X-, Y- and Zcoordinates, respectively, in m m P is the overall repeatability in m m m is group, 10 measurements per group. The repeatability analysis results are in Table 5. These
where di are the distances of each individual point Yxi, Yyi and Yzi are the X-, Y- and Z-coordinates for individual measurements, respectively H x o, H y o and Hz o are h o m e position coordinates Am is accuracy for g r o u p m in m m A is accuracy in m m m is group, 10 measurements per group. The accuracy analysis results are in Table 6. The results from both experiments are very close to the m a x i m u m of 4.9 ~o. Table 7 shows the comparison of the determining significant factors obtained by using two experimental design methods. Both methods showed a similar capability to detect statistically significant factors in this study.
Table 5. Comparison of a robot's repeatability for spatial points L = 0 kg ~" P
Px Py, Pz
L = 0.227 kg
(a)*
(b)t
(c)~:
(a)
(b)
(c)
(a)
2.560 1.655 1.687 0.646
2.584 1.670 1.719 0.595
0.9 ~o 0.9 ~o 1.9~ 7.9~o
2.546 1.501 1.663 0.694
2.498 1.610 1.579 0.692
1.7 ~o 7.3 -5.1~o -0.3~o
2.533 1.501 1.786 0.761
*(a) Method 1 : completely randomized block design (mm). "i'(b) Method 2: Taguchi methods (mm). :~(c) Percentage of difference = ((b) - (a))/(a) 100~.
L = 0.454 kg (b) 2.530 1.407 1.822 0.805
(c)
(a)
-0.1 ~ - 6.3 ~ 2.0~ 5.8~
2.516 1.522 1.712 0.700
Overall (b) 2.537 1.562 1.707 0.697
(c) 0.8~ 0.6 -0.3~ -0.4~o
Determining robot process capability • B. C. JIANG et al.
Further analysis using Taguchi methods One advantage of using Taguchi methods is that they permit S/N analysis. The S/N in Taguchi methods is a combined index that considers both variation and mean. 26 The computation of S/N values depends on the data characteristics class, i.e. if the
63
data are the smaller-the-better, the larger-the-better or the nominal-the-best. In this experiment, for example, repeatability is the smaller-the-better case, and S/N is calculated as follows:
V= (1/N)(Y~ + Y~ +... + Y~) Nab= - l O l o g V where Yi = repeatability (mm) N = number of observations
Table 6. Comparison of a robot's accuracy for spatial points
X
Accuracy (ram) (a)*
(b)t
(c):~
-255 -113 27
29.407 21.545 25.443
29.087 21.516 25.472
- 1.1 -0.1 -0.1
97 97 97
-255 -113 27
17.857 14.247 5.185
17.771 14.103 5.119
-0.5 -1.0 -1.3
187 187 187
-255 - 113 27
11.117 9.999 1.317
11.136 9.945 1.321
0.2 -0.5 0.3
-255 -113 27
37.028 39.620 35.453
37.118 39.696 35.423
0.2 0.2 -0.1
Y (mm)
Z
65 65 65
- 13 -13 - 13
65 65 65 65 65 65 175 175 175
-13 -13 -13
= S/N.
175 175 175
97 97 97
-255 -113 27
25.872 26.875 21.810
25.841 26.703 21.730
-0.1 -0.1 -0.4
175 175 175
187 187 187
-255 -113 27
13.682 13.558 6.922
13.555 13.488 6.991
-0.9 -0.5 1.0
-255 -113 27
35.523 40.193 36.535
35.374 40.382 36.465
-0.4 0.5 -0.2
285 285 285
-13 -13 -13
285 285 285
97 97 97
-255 -113 27
27.336 29.740 25.054
27.321 29.990 25.291
-0.1 0.8 0.9
285 285 285
187 187 187
-255 -113 27
15.388 16.246 6.325
15.428 16.322 6.015
0.3 0.5 -4.9
21.825
21.800
-0.1
Overall
*(a) Method 1: Completely randomized block design. t(b) Method 2: Taguchi methods. :[:(c) Percentage of difference = ((b)-(a))/(a) 100 %.
ANOVA was applied to the S/N of repeatability data obtained using method 2. The 10 repeated measurements were divided into two groups in order to generate an S/N of repeatability data for producing enough residual degrees of freedom in ANOVA. Table 8 shows the significant levels of each factor for both original repeatability data and for the S/Ns, and the associated percentage of variation explained by each factor. The following example demonstrates the advantages of using Taguchi methods: In robotic assembly work, parts can be placed in a manufacturing cell at any fixed height (i.e. a fixed Z). The weight of the parts can vary from 0.227 to 0.454 kg. The robot must be able to repetitively pick up the parts (i.e. repeatability is the only concern). Table 8. A N O V A of repeatability and S/N from L27(313) Repeatability Significant SS a-level Load X Y Z X*Y X,Z Y*Z Error
0.07 1.33 4.96 0.36 18.50 0.87 1.16 25.42
SS
0.96 0.43 0.05 0.79 0.001 0.89 0.82
S/N Significant a-level
Contribution (%)
0.96 0.56 0.10 0.77 0.04 0.82 0.30
0.27 % 3.00% 21.95 9/00 1.809/oo 64.20% 4.82 3.96
0.36 4.05 29.58 2.43 86.53 6.50 5.34 26.50
Table 7. Comparison of determining significant factors using two experimental design methods Reproducibility CRBD* TMt SS a-level:i: SS a-level Load X Y Z X,Y X,Z Y,Z
0.06 0.71 0.61 0.72 0.54 1.73 0.63
0.92 0.39 0.44 0.38 0.83 0.33 0.79
0.11 0.64 1.14 0.83 0.18 0.59 1.71
0.87 0.45 0.25 0.36 0.98 0.82 0.38
* CRBD--completely randomized block design. t T M - - T a g u c h i methods. :~ a-level--significant a-level.
Repeatability CRBD SS a-level SS 0.31 1.98 12.57 1.06 34.16 2.09 2.04
0.78 0.22 0.0001 0.44 0.001 0.51 0.53
0.07 1.33 4.96 0.36 18.50 0.87 1.16
Accuracy TM
CRBD
TM
a-level
SS
a-level
SS
a-level
0.96 0.43 0.05 0.79 0.001 0.89 0.82
0.78 3682.00 14175.77 1049.21 592.16 314.88 264.11
0.80 0.001 0.001 0.001 0.001 0.001 0.001
5.58 1245.59 4732.17 349.37 207.60 88.85 105.94
0.31 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
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Robotics & Computer-Integrated Manufacturing • Volume 6, N u m b e r 1, 1989
Two methods can optimize the specified task condition. One method is to choose the maximum S/rN from the factor combinations tested as shown in Table 9. Consequently, the best location for the 0.227-kg load is at (65,175), and the best location for the 0.454-kg load is at (175,65). If we list the best several combinations, a certain area or volume can be identified as the optimum working area. The second method was further examined in this area or volume to determine the best factor combination. Another experiment was conducted by using an L9(34) orthogonal array. This design accommodates four factors with three levels each. However, no interactions between variables can be analyzed. Since a fixed Z could be used, the best Z level (Z = 27 ram) was chosen. Three Z levels were selected to test the sensitivity of this height. Three X levels and Y levels were selected based on the best working area identified from the previous experiment. The experimental layout is shown in Table 10. A similar ANOVA applied to the repeatability and S/N showed that the load significantly affected the repeatability of raw data and S/N while the Y-axis significantly affected the raw data only (Table 11). A
Table 11. A N O V A of repeatability and S/N from L9(34) Taguchi design Repeatability Significant SS ~-level Load X Y Z Error
1.02 0.33 0.62 0.07
0.01 0.16 0.05 0.63
SS 27.38 7.90 12.66 * 1.80
S/N Significant ~t-level
Contribution (%)
0.06 0.19 7.05 --
55.04 15.88 25.45 --
* Pooled into error term.
SIN 3.00, 2.00 1.00-
0.362 X/
0.206
yj
-i,856
0.00 -I.00-2.00 -3.00
x
-2.559 I
I
Levels
Fig. 2. Repeatability S/N for three X and Y levels. Table 9. Repeatability sflq for L27(313)
S/N X
Y
Load = 0.227 kg
Load = 0.454 kg
65 65 65
65 175 285
- 5.98 -5.65 -8.53
-6.50 -9.71 --11.40
175 175 175
65 175 285
-6.75 -6.83 -10.66
-5.49 -5.99 -10.60
285 285 285
65 175 285
-13.02 -6.11 -6.73
-9.77 -5.68 -7.68
Table 10. L9(34) Taguchi design layout
Experiment
Load
X
Y
Z
1
1
1
1
1
2 3 4 5 6 7 8 9
1 1 2 2 2 3 3 3
2 3 1 2 3 1 2 3
2 3 2 3 1 3 1 2
2 3 3 1 2 2 3 1
Load levels: 0, 0.227, 0.454 kg. X levels: 65, 120 and 175 ram. Y levels: - 13, 42 and 97 ram. Z levels: 2, 27 and 52 mm.
Noise R1-R10
Duncan multiple range test was also conducted on three Z levels and showed no significant difference among the three levels. Figure 2 shows that X and Y interactively affected the S/N of repeatability, although this interaction could not be statistically analyzed. A list of X Y combinations, S/Ns, and repeatability data is given in Table 12. The best repeatability zone consisted of the three points along the diagonal axis of the test area (i.e. X1 Y1, )(2 Y2 and X 3 ]"3)- The next best zone and the worst zone were the upper left and lower right regions, respectively (see Fig. 3). Therefore, the recommendation is to place the assembly parts at the points along the diagonal line shown in Fig. 3 and at a height of 27 _ 25 mm. DISCUSSION Specifications provided by most robot manufacturers give repeatability data as a range (e.g. _+0.1 ram). These repeatability data are equivalent to the + 3s value in this study. This information is useful when a task's spatial direction is not critical (e.g. pick up a cylindrical part in an assembly task). From the results of this study, the spreads of X-, Y- and Z-coordinates provide valuable information when the direction of robot motion is of concern for a
Determining robot process capability • B. C. J1ANG et al. Table 12. X and Y levels and corresponding repeatability and
S/N X
Y
Repeatability (mm)
S/N
65 65 65
-13 42 97
0.784 1.112 0.946
1.66 - 1.00 0.42
120 120 120
-13 42 97
1.690 0.805 1.115
--4.68 1.84 -0.94
175 175 175
- 13 42 97
1.704 1.262 0.812
-4.66 -2.05 1.14
iiiiiiiiiiiii!;'~ .
i!:'
2-
I
3
Fig. 3. Three zones of different repeatability groups.
task (e.g. the relative position of a robot to the object that it will pick up in a robotic cell). For example, repeatability in the Z-direction was always better than in the X- and Y-directions for this robot. The robot's relative position in the X Y plane more critically affects its repeatability. Therefore, process capability testing can yield directional information. From the results of this study, both randomized complete block design and Taguchi design methods yielded very similar results in determining a robot's process capability (within 10.4%). However, Taguchi methods can be used to optimize the operation of a robot as described in the previous example. If this robot's process capability does not meet a certain task requirement, a new robot must be selected and a new test run to determine its process capability. A potential use of Taguchi methods is for examining the effectiveness of changing robot design parameters (called "tolerance design" in Taguchi methods), especially if the cost is known. This application will help a robot manufacturer quickly determine/improve its robot design parameters to yield better process capability. FUTURE STUDY A major concern of the robot user is how to determine the best operating characteristics for obtaining optimum process capability. This information is required when placing a robot in the workplace, particularly in an unmanned manufacturing
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cell. Therefore, not only the determination of a robot's process capability but also the optimization of its operational parameters is important. The Taguchi methods used in this study provided significant benefits in determining/optimizing a robot's process capability. The amount of data required was significantly reduced and the optimization could be achieved. More factors can be considered when Taguchi methods are used (e.g. load, speed, spatial location, point-to-point and continuous-path motions) so that an effective testing procedure can be developed for determining a robot's process capability. The capability of the measuring system is a major concern in determining a robot's process capability. The 3-D accuracy of the WATSMART system is about 1 mm. A simple test was conducted to determine the repeatability of the W A T S M A R T system. The following points were measured within a cubic calibration frame that is 0.6 m on each side: eight points inside corners, four points on two side planes and two points in the center of the frame. The results of 10 repeated measurements showed that the repeatability (3s) of the system is 0.780 mm, and three axes' repeatabilities are 0.329 mm (3sx), 0.612 mm (3sv) and 0.357mm (3s=), respectively. The repeatability at the center of the calibration frame was about two times better than at the corner points. Many robots have better accuracy and repeatability than the WATSMART system. To improve the measuring system's accuracy and repeatability is critical. CONCLUSION The comparison of the two methods for use in determining/optimizing a robot's process capability showed the following: Taguchi methods required only one-third the data that the randomized complete block design method required, yet yielded similar results in quantifying a robot's process capability (within the 10.4% difference). A testing procedure developed using Taguchi methods can examine more factors than a procedure developed using the randomized complete block design method. REFERENCES 1. Ayres, R. U., Miller, S. M." Robotics: Applications and Social Implications. Cambridge, MA, Ballinger, 1983. 2. Borrel, P., Dombre, E., Guerdon, J.P., Liegois, A.: Workspace and control strategy determination for an underwater manipulator. In: Proc. IEEE Conf. Dec&. Control 80-83, Dec. 1987. 3. Brown, L. B.: A random-path laser interferometer system. Presented at the Int. Congr. Appl. Lasers ElectroOpt., San Francisco, CA, 11-14 Nov. 1985. 4. Chabrol, J.: Industrial robot standardization at ISO. Robotics 3: 229-233, 1987.
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5. Critchlow, A.J.: Application to Robotics. New York, MacMillan, 1985. 6. Gendron, W. A., Sommer, H. J. III: Pulsed sonic coordinate digitization using point-effect microphones. Robotics Res. Adv. Appl. 167, 1982. 7. Hackwood, G. B., Trimmer, W. S.: High precision robot system for inspection and testing of electronic devices. In: Proc. Int. Conf. Robotics, 13-15 Mar. 1984. 8. Harris, E. W.: Error recovering for robotic component insertion. IBM Tech. Disclosure Bull. 26(11): 5328-5329, 1984. 9. Hecker, E. P., Zellmann, M. T.: Point-of-use find posts. I B M Tech. Disclosure Bull. 26(11): 5894-5895, 1984. 10. Hunter, J. S.: Statistical design applied to product design. J. QuaL Technol. 17(4): 210-221, 1985. 11. Industrial Technology Institute, Robot Evaluation Center. Ann Arbor, MI, 1986. 12. International Organization for Standardization (ISO), Working draft on manipulating industrial robots--performance criteria and related testing methods. ISO/TC 184/SC 2/WG 2 N 8, 1987. 13. Jiang, B. C., Black, J. T.: Improving and measuring robot process capability. CIM Rev. 3(4): 44-49, 1987. 14. Jiang, B. C., Black, J. T.: Robot process capability study. Presented at the 1987 Manu. Syst. Res. Conf., Ann Arbor, MI, 6-9 Oct. 1987. 15. Jiang, B. C., Black, J. T., Duraisamy, R.: A review of recent developments in robot metrology. J. Mfo. Systems 7(4): 339-357, 1988. 16. Kackar, R. N.: Off-line quality control, parameter design and the Taguchi method. Qual. Technol. 17(4): 176-188, 1985. 17. Lembke, J. R., Jones, L. L.: Measurement of robot accuracy using the Latin square three-dimensional ball plate. Final Report, Bendix, Kansas City, KS: BDB-6132992, 1983. 18. Makino, H., Furuya, N.: Performance tests for CP motion with the SCARA robot. In: Proc. 15th Int. Syrup. Ind. Robots, p. 1011-1020, 1985. 19. Makino, H., Taniguchi, N.: Standard performance test methods for planar positioning assembly robots. Ann. CIRP 34: 33-36, 1985. 20. Martin, J. F.: An acoustic ranging system for robot position control and tracking. Soc. Manu. Eng. Tech. Pap. MS84-1039, 1984. 21. Nof, S. Y., Lechtman, H.: Robot time and motion system providesGmeans of evaluating alternate robot
work methods. Ind. En9. 38-48, Apr. 1982. 22. Paul, R. P.: Robot Manipulator. Cambridge, MA, MIT Press, 1981. 23. Robotic Industries Association. Draft American national standard for industrial robots--performance evaluation. Ann Arbor, MI, 1987. 24. Robotics and Automation Applications Consulting Center. Robot assessment program. Dearborn, MI, Ford Motor Company, 1984. 25. Smith, D. N., Heytler, P.: Industrial Robots: Forecasts and Trends, Delphi Study, Dearborn, MI, 2nd edition. Soc. Manu. Eng., 1985. 26. Taguchi, G.: Specification value and quality control. Int. QC Forum II(6): 8-27, 1984. 27. Taguchi, G., Wu, Y. I.: Introduction to Off-Line Quality Control. Central Japan Quality Association, 1979. 28. Takeyasu, K. T., Goto, T., Inoyama, T.: Precision insertion control robot and its application. J. Eng. Ind. 1313-1318, 1976. 29. Tsai, R. Y., Huang, T. S.: Estimating three-dimensional motion parameters of a rigid planar path. IEEE Trans. Acous. Speech Signal Process. ASSP-29(6): 1147-1152, 1981. 30. Vira, N., Lau, K.: Design and testing of an extensible ball bar for measuring the positioning accuracy and repeatability of industrial robots. In: 14th North Am. Manu. Res. Conf. Proc., 28-30 May 1986. pp. 583-590. 31. Warnecke, H. J., Brodbeck, B., Schiele, G.: Results of the examination of industrial robots on a test stand. Institute for Production Automation, Stuttgart, West Germany, Personal communication, 1986. 32. Warnecke, H. J., Schiele, G.: Performance characteristics and performance testing of industrial robots--state of the art. In: Proc. Robotics Europe 1st Conf., 27-28 June 1984. pp. 5-17. 33. Warnecke, H. J., Schraft, R. D., Wanner, M. C.: Application of the experimental modal-analysis in the performance testing procedure of industrial robots. In: Proc. Robotics Europe 1st Cot~, 27-28 June 1984. pp. 45-54. 34. Warnecke, H. W., Schraft, R. D., Wanner, M. C.: Performance testing. In: Handbook o f Industrial Robotics, Nof, S. Y. (Ed.) New York, John Wiley, pp. 158-166, 1985. 35. Whitney, D. E., Lozinski, C. A., Rourke, J. M.: Industrial robot forward calibration method and results. Dyn. Sys. Meas. Control 108: 1-8, 1986.
0736 5845/89 $3.00 + 0.00 ~:, 1989 Maxwell Pergamon Macmillan plc
Printed in Great Britain
•
Paper D E T E R M I N I N G R O B O T PROCESS CAPABILITY U S I N G TAGUCHI METHODS B E R N A R D C. J I A N G , J T. B L A C K , JAMES N . H O O L a n d C. M . W u Industrial Engineering Department, Auburn University, AL 36849, U.S.A. The robot process capability problem is outlined and terms are defined. Recent efforts to measure robot capability are reviewed. Two methods were used to analyze robot process capability data: the randomized complete block design method and Taguchi statistical experimental design methods. The purpose of the study was to compare the results obtained by these two methods and determine which method was better for analyzing the data to be used in determining]optimizing a robot's process capability. Three-dimensional (3-D) coordinate data were obtained using a WATSMART vision system to determine a robot's process capability. Three levels of four independent variables--load, X-, Y- and Z- coordinates--were chosen for the study. Both analysis methods yielded similar results in determining a robot's process capability (within 10.4 %). The Taguchi methods required significantly fewer data than the randomized complete block design used. Taguchi methods also optimized a robot's process capability.
In a process capability study of a machine tool, the parts made on the machine are measured to determine the machine tool's process accuracy and precision and the effect of varying input parameters on the process capability. For example, in lathe turning, precision decreases (variability increases) as the diameter of the workpiece increases. However, in robot material handling or material assembly, no product or output can be examined (measured) directly to determine the process capability. Therefore, a different method must be developed to determine the process capability of a robot. To do that, a means must be provided to independently measure the robot end effector's spatial location, three-dimensionally, at any specific time. A review of the measurement techniques and the testing methods, conditions and specifications is given in Ref. 15. A sound experimental design is necessary because of the many variables which influence a robot's process capability interactively. 14 The randomized complete full factorial design method is used to obtain the most complete information. However, this method requires the collection of a large amount of data and extensive data analysis, yet does not optimize the process capability for the factors considered. Although other types of experimental designs (e.g. Latin square design) require significantly fewer data, they usually lose certain information and still have the same shortcoming as the randomized complete design. A major concern of the robot user is how to determine the best operating characteristics for
INTRODUCTION Robot use is increasing in industries worldwide. Robot installations in the United States increased from a few hundred in 1970 to 4200 in 1984.1'2s The electronics and precision equipment industry is expected to double its market share from 8 % in 1985 to 16% in 1995. 25 Process capability data are vital in designing and implementing robots for manufacturing and assembly applications. Most manufacturers provide specifications for their robots. However, most of the current specifications are for a static condition or a range of extreme conditions of performance, e.g. the capacity of weight handled (0-20 kg), the velocity of movement (1-20 cm/sec) and the positioning tolerance ( + 0.5 mm). However, when a robot performs a task (during a process), neither the manufacturer nor the users know its process capability characteristics. The manufacturer lacks an acceptable methodology and measuring technique to determine a robot's process capability, and companies using robots often do not have the personnel to determine a robot's process capability. Furthermore, quality control objectives cannot be accomplished if the robot process capability is unknown. Acknowledegment--This project was supported by National Science Foundation Grant No. DMC-8519778 and the Advanced Manufacturing Technology Center at Auburn University. Special thanks to Ms. A. H. Honnell and Ms. P. S. Flick of the A M T C Information Resources Laboratory for the preparation of this manuscript.
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Robotics & Computer-IntegratedManufacturing • Volume 6, Number 1, 1989
optimizing process capability. This information is required when placing a robot in the workplace, particularly in an unmanned manufacturing cell. Therefore, not only the determination of a robot's process capability but also the optimization of its operational parameters is important. Using statistical Taguchi experimental design methods to determine and optimize a robot's process capability 14 is also possible. To evaluate the applicability of Taguchi methods for determining a robot's process capability, a comparative study was conducted of two types of experimental design methods--the randomized complete block design method and Taguchi methods.
OBJECTIVES The objective of this study was to compare the results obtained by two methods of experimental design and analysis. Method 1 used the randomized complete block design method and method 2 used Taguchi statistical experimental design methods. When supplied with sufficient information for process capability determination, method 2 not only required significantly fewer data, but also provided a means to optimize the experiment parameters in the study.
D E F I N I T I O N OF T E R M S The concept of process capability for a manufacturing process has been known for a long time. However, robot process capability is new. Although the terms "accuracy", "repeatability", "reproducibility" and "stability" seem intuitively clear, disagreement exists about their proper meanings. For the purpose of communication, the following definitions will apply. Although the given generic definitions apply to both point-to-point and continuous-path motions of a robot, only the point-to-point case is studied in this paper. • Robot process capability: Refers to the ability of a robot to perform consistently a job with a certain degree of accuracy, repeatability, reproducibility and stability. It is a function of task variables such as move speed, spatial position and load. • Accuracy: Refers to the ability to hit what is aimed at. It is the degree of agreement between independent ineasurements and the target value being measured. • Repeatability: Refers to the process variability. It is the degree of mutual agreement between independent measurements under specified conditions. This term is also called "precision". • Reproducibility: Refers to the deviation from or difference between the means of measurements
taken from repeated tests that hit the same target but developed from different starting points. • Stability: Refers to the difference in the average o f at least two sets of measurements obtained with the same target from the same starting point at different times. This term is also called "drift". BACKGROUND Process capability has been referred to as the positional accuracy, repeatability, reproducibility and stability when a robot performs a task. Most research has been with the control device 7-9'28 or path determination 2'7 to enhance the robot's capability to locate a point in space and to repetitively perform a job. The traditional methods-time-measurement (MTM) technique has been used to determine the required time for a certain job. 2' This technique is called robot time and motion (RTM). The factors considered in the RTM technique were a robot's mechanical design and work patterns. Some other process characteristics considered include arm movement velocity and reach distance. However, the study did not examine the interaction of these process characteristics and the consequent process capability. Some work has been done on the robot calibration method. 22'35 Whitney e t aL 35 discussed a calibration procedure for serial link manipulators. The procedure used a model whose parameters represented link lengths, joint encoder offsets, the relative orientations of consecutive axes, and the observed effects of joint compliance, backlash, and gear transmission errors. They used a least squares numerical search algorithm with theodolite measurements of tool positions and the robot's joint encoder readings to estimate all of the model's parameters. The study proved that a robot's positioning errors could be reduced significantly. However, the difference between a calibration study and a process capability study is that the latter is done to determine operational (during usage) characteristics, while the former is done to develop a method to adjust positioning errors (which seldom consider the process parameters). Furthermore, the measurement system for determining a robot's process capability must be independent of the robot. The calibration system can be part of the robot, which can cause intrinsic errors. However, robot calibration is a valuable technique for robot manufacturers to use in verifying the design of a robot. Warnecke e t al. 34 reported several methods for measuring a robot's spatial location, such as using contact sensors (e.g. a touch-trigger probe, a 3-D measuring head) and noncontact sensors (e.g. a theodolite, an optoelectronic system and a laser system). In
Determining robot process capability • B. C. JIANGet al. most cases, inductive sensors were superior to ultrasound, laser and photogrammetry because of data processing, distance, resolution, linearity and price. Test results were reported based on the studies done at the Institute for Production Automation (IPA), F . R . G . 3x-33 In general, data specified were positioning accuracy, path accuracy, and overshooting. One way to measure robot process capability is to use appropriate contact-sensing devices (touch-trigger probes) with feedback capability. 34 For example, Lembke and Jones 17 designed a Latin square threedimensional ball plate (LSBP) to characterize a robot's accuracy and repeatability. To design the LSBP, they used the Latin square design concept and used 16 different height poles, with 4 on each row and 4 on each column. The touch-trigger probe generated a signal upon contact from any direction. The probe was interfaced to the robot through an input channel. A program was written to move the probe slowly into the vicinity of a ball and to stop upon contact with it. Each ball was approached from the top and four sides to permit estimation of the bali's center location. Vira and Lau 3° at the National Bureau of Standards used a 1-D extensible ball bar to measure the positioning accuracy and repeatability of industrial robots. The extensible ball bar had a 5-cm travel radius and was monitored by a built-in electronic transducer which had 2.5-/~m resolution. At each end of the bar was a precision steel sphere. One sphere was magnetically attached to a socket which was firmly located within the robot's work zone. The center of the sphere becomes the origin of the measurement system. The other sphere was mounted on a universal joint which was attached to the robot end effector. A probe installed in the ball bar measured the radial displacement between the two spheres. Tests conducted to quantify errors of a commercially available robot were: point-to-point teach mode, wrist rotation, circular movement, and drift (for the robot's thermal stability). They stated that although an extensible ball bar is a reliable and economical instrument, application of it is limited to only 1-D measurement. Another way to measure a robot's spatial location is to use appropriate noncontact-sensing devices with position sensing capability. These systems can be acoustic -6"2° video-, 7'24'29 and laser-based. 3 As an example, the Robotics and Automation Applications Consulting Center (RAACC) 24 developed a procedure to test a robot's accuracy and precision before the robot was put into a workplace. Tests included the verification of manufacturer's specification: accuracy of repeatable placement, accuracy of playback to commanded position, stabilization and others. The positioning measurement was determined with non-
57
contact eddy current measurement system equipment (Kaman Sciences Corporation model KD-4358 with model 15U1 sensors) arranged in three planes. Two levels (max. and 50 %) of payload, arm reach and speed were reported and analyzed (e.g. statistical characteristics) for robot process capability information. In 1986, RAACC reported a modified robot-testing procedure which included point-to-point, path control, continuous path and cycling tests. The setup was also changed to use the Selspine Robot Check System (Selcom Selective Electronic, Inc.). This vision system included two cameras, a micro-PDP 11/23 computer, LEDs and control unit, calibration fixture and plotter. This optoelectronic motion-analysis system used active light sources to determine actual positions of moving objects in space. These positions can be presented in Cartesian coordinates and can be calculated into speed and acceleration. The Industrial Technology Institute 11 reported a similar testing procedure. The Robotic Industries Association (RIA) formed a committee in 1985 to develop standards for the methods used in the testing procedure for evaluating industrial robotic systems. In a revised RIA draft for robot performance testing standards, 23 a standard test plane and standard test path were proposed. The standard test plane is "one which is orthogonal to the (1, 1 , - 1) vector or the base coordinate system'. 23 This plane is at a 45 ° angle to the horizontal plane. The standard path is a zigzag path passing through the center of the standard test plane. The length of each zigzag segment is either 200, 500, or 1000 ram, depending on the type of robot being tested. The robot is commanded to go from the first segment to the last segment and then to swing back from the end point to the starting point. Eight performance factors are determined by a series of tests: accuracy, repeatability, overshoot, settling time, segment cycle time, deviation from standard test path, warm-up drift, and static compliance. Test payload should be 50 % or more of the manufacturer's rated payload and must be in one of the 12 categories ranging from 0 to 140 kg as listed in the standards. The International Organization for Standardization (ISO) is another organization involved in the standard development effort. The subcommittee on performance testing is composed of delegates from the Federal Republic of Germany, France, Japan, Sweden, the United Kingdom, and the United States. 4 Their draft standards, as of August 1987,12 defined a test cube as the largest volume that can be covered in the working envelope. Four optional testing planes (i.e. the center X Y , YZ, and X Z planes, and the plane that is at a 45 ° angle to the center X Y plane) are defined.
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Robotics & Computer-Integrated Manufacturing • Volume 6, Number 1, 1989
Four corner points plus the center point make the five testing points. The payload and speed used in a test should generally be at 100 ~o of the rated payload and 100 ~ of the rated speed, respectively. A 50 ~ payload and a 50~o or 10~o speed may be used as alternative testing conditions. In Japan, Makino and his colleagues 18'~9 proposed "standard performance test methods for planar positioning assembly robots". The proposed tests for a planar positioning robot consist of six point-to-point tasks (swinging 300 ram, time vs. distance characteristics, base-running, pick-and-place, palletizing and peg insertion), and three continuous-path tasks (linear interpolation, circular interpolation and spline interpolation. Both standard working area and maximum working area were considered. The proposal followed Japan Industries Standards and specified the points of measurement at the four corners of the standard working area. Thirty measurements were taken at each point, and the spread of the distribution __+3s (where s is the standard deviation) was given. In summary, many factors can affect robot process capability, such as gravity, acceleration, backlash error, temperature, bearing plan and windup play. 5 These factors are categorized into task, human and environmental attributes (see Table 1). To isolate one factor from another is not easy; however, the overall improvement of robot process capability is feasible. Jiang and Black 13 reported on four techniques for measuring and improving robot process capability: changing the robot design; using work holders; positioning with contact sensing devices; and positioning with noncontact sensing devices.
EXPERIMENT To compare the results from two methods for determining/optimizing a robot's process capability, the following experimental conditions were chosen: three load levels (0, 0.227 and0.454 kg), X-coordinate (left/right, 65, 175 and 285 mm), Y-coordinate (in/out, - 1 3 , 97 and 207 mm), and Z-coordinate (up/down, - 2 5 3 , - 1 1 3 and 27 mm).
Method 1. Using the randomized complete block design A randomized complete block design was used, with each load level treated as a block to facilitate data collection. Twenty-seven spatial locations and 10 replications were randomized within each block. The design layout is shown in Table 2. The 27 points covered, approximately two-thirds of the maximum of the X- and Y-reaches in the first quadrant, and onehalf of the maximum Z-reach (Fig. 1). The robot was commanded to move from the home position (0, 0, 0~ to each of the 27 spatial locations in random order.
Table 1. Factors associated with a robot's process capability Attributes Robot Design
Control
Specification
Task
Human
Environmental
Factors Type: servo point-to-point, non-servo pointto-point, servo continuous-path Work envelope: cylindrical, spherical,jointed arm, rectangular Arm: number of joints, degree of freedom, weight, shape, length, material, tolerance End effector: material, size, shape, mobility, compliance, strength, sensor Type: air logic, stepping drum Memory type and capacity: standard (single program, multiple program), optional (expansion of standard different controller) Software: main program, subprogram, degree of intelligence Power supply: electric, hydraulic, pneumatic Movement range, velocityrange, repeatability, cycle time, reliability, number of years used, frequency of use, mobility, commonality, training and maintenance requirements Object: load, shape, size, material, load distribution, location, distance, direction Accuracy requirements Repeatability requirements Force requirements Frequency of task performance requirements Task type: process materials (painting, welding, grinding), material handling, assembly (pick up and place, insertion), loose registration, inspection (finding burrs) Operator skill, programmer skill, operator variations Psychological factors: mood, motivation, coordination Temperature, air velocity, humidity, stability, dust, floor loading, peripheral equipment, safety, electrical noise
For each movement, 3-D coordinate data were collected for the starting point (i.e. home position) and the ending point (i.e. a certain spatial point) by using a 3-D vision system called WATSMART.
Method 2.
Using the Taguchi statistical experimental
design Taguchi methods 1°'16'27 are quick and efficient methods for optimizing the design and performance of processes and products. They concentrate on finetuning products and processes by selecting the best combination of relevant controllable factors so that process or product performance is least sensitive to factors (noise) that are difficult, expensive or impossible to control. Taguchi methods have been used very effectively in Japan for many years. They have only recently been introduced in the United States where they are used primarily in the automotive industry.
59
Determining robot process capability • B. C. JIANG et al. Table 2. Completely randomized block design layout X
Load
R
1
1 2
2
1 2
3
1 2
1
Y
1
Z
123
2
2
3
12 3
12 3
1
2
123
123
3 3 1 2 3
1 123
2
3
1 2 3
12 3
io
io
io Load levels: 0, 0.227 and 0.454 kg. X levels: 65, 175 and 285 mm. Y levels: - 13, 97 and 207 mm. Z levels: - 2 5 3 , - 1 1 3 and 27 mm. R levels: Replications (10).
Taguchi methods allow us to: • Examine m a n y variables in a simple design (orthogonal array). Significantly fewer tests are required than with m a n y other experimental designs. • Determine quickly the optimal or near-optimal operating conditions by employing a signal-tonoise ratio (S/N) that simultaneously measures process accuracy and repeatability. This condition can be further examined by changing the tolerance of each parameter (called tolerance design). • Combine on- and off-line quality engineering efforts into an overall system. An L27(313) orthogonal array was used for this study. The design layout and the variable assignments are shown in Table 3. Notice that method 2 had only one-third the data that method 1 had. To make the comparison, the subset data from method 1 were used for the method 2 analysis.
Equipment The noncontact 3-D coordinate measuring system (WATSMART) used to collect data in this experiment consisted of two high-resolution infrared cameras (positioning sensors), an IBM PC/AT, and data collection and analysis software. An active infrared lightemitting diode (IRED) was attached to the robot arm as a marker. The X- and Y-coordinates of the marker were detected by both cameras. Then a direct linear transformation (DLT) technique was used to convert data to 3-D coordinates. This equipment was chosen because it can measure the characteristics of robot
motion, i.e. it can continuously measure a robot's point-to-point and continuous-path motions to obtain a robot's kinematic data, and perhaps to control a robot in real time. A R H I N O robotic arm, a five-motor-controlled educational robot, was used in this experiment. The robot controller was interfaced with an IBM PC. The robot could be commanded to move by either controlling each joint m o t o r or by entering spatial point coordinates. The latter method was used in this experiment.
Results The objective of this study was to compare two methods of obtaining/analyzing data for use in determining/optimizing a robot's process capability. Reproducibility and repeatability data can be expressed as the spread (3s) of the measurements. In the spatial sense, this 3s value represents the radius of a sphere that covers the measured data points. These overall indicators can be broken into the spread of each of the X-, Y- and Z-coordinate components (i.e. 3sx, 3Sy and 3Sz). The three axes components provide valuable directional information while the overall reproducibility/repeatability is a simple integrated indicator. Only the home point could be analyzed for reproducibility because this was the only location tested. In method 1, a total of 810 measurement data were used under three load levels and 27 spatial locations with 10 replications under each condition. In method 2, a
60
Robotics & Computer-Integrated Manufacturing • Volume 6, Number 1, 1989 Y (mm)
Z (mm)
= ,
~
a
-- y tmrrO
Selected Points
(X) in the Study
Calibration Frame
RHINO Robo!
Camera # 2
Camera #1
illlllll
Prinler
IBM PC/AT
WATSMART Conlroller
Holler
Fig. 1. Experimental layout.
subset of 270 m e a s u r e m e n t d a t a was used u n d e r t h e s a m e c o n d i t i o n s as in m e t h o d 1. T h e r e p r o d u c i b i l i t y d a t a w e r e c a l c u l a t e d as f o l l o w s :
s,, =
,1
Y x i - Yx)2/(n- 1 i
;
n = 810 for m e t h o d 1, n = 270 for m e t h o d 2
Hx = 3s~.
Hy
and
Hz
a r e c a l c u l a t e d in a s i m i l a r w a y to
Hx
s= { ~ [ ( Y x ' - Yx)2 + ( Y y I 0.5
+ ( Y z i - Yz)2]/(n-
1)
;
n = 810 for m e t h o d 1, n = 270 for m e t h o d 2 H = 3s
Determining robot process capability • B. C. JIANG et al.
61
Table 3. L27 (3 la) Taguchi design layout
Experiment
1
2
X * Y 3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
1 1 1 1 l 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3
1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3
1 1 1 2 2 2 3 3 3 2 2 2 3 3 3 1 1 1 3 3 3 1 1 1 2 2 2
X
Y
X * Y 4 1 1 1 2 2 2 3 3 3 3 3 3 1 1 1 2 2 2 2 2 2 3 3 3 1 1 1
5
X * Z 6
X * Z 7
Y * Z 8
Load 9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 1 2 3 2 3 1 2 3 1 2 3 1 3 1 2 3 1 2 3 1 2
1 2 3 1 2 3 1 2 3 3 1 2 3 1 2 3 1 2 2 3 1 2 3 1 2 3 1
1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2
1 2 3 2 3 1 3 1 2 2 3 1 3 1 2 1 2 3 3 1 2 1 2 3 2 3 1
Z
e
e
10
Y * Z 11
12
13
1 2 3 2 3 1 3 1 2 3 1 2 1 2 3 2 3 1 2 3 1 3 1 2 1 2 3
1 2 3 3 1 2 2 3 1 1 2 3 3 1 2 2 3 1 1 2 3 3 1 2 2 3 1
1 2 3 3 1 2 2 3 1 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1 1 2 3
1 2 3 3 1 2 2 3 1 3 1 2 2 3 1 1 2 3 2 3 1 1 2 3 3 1 2
e
Noise R1-RIO
Linear graphs: showing interactions between variables
3,f~6,/ 1
9 0
10 0
12 0
13 0
8,11 Table 4. Comparison of a robot's reproducibility for home point L = 0 kg
H Hx Hy H~
L = 0.454 kg
L = 0.227 kg
Overall
(a)*
(b)t
(c):~
(a)
(b)
(c)
(a)
(b)
(c)
(a)
(b)
(c)
2.571 1.150 1.905 1.033
2.549 1.155 2.005 0.926
1.3% 0.4% 5.3 % --10.4%
2.566 1.265 1.770 1.173
2.441 1.276 1.669 1.100
-4.9% 0.9% -- 5.7 % -6.2%
2.540 1.354 1.767 1.075
2.469 1.337 1.668 1.104
- 2.8 % - 1.3 % - 5.6 % 2.7%
2.541 1.256 1.814 1.094
2.486 1.253 1.781 1.043
- 2.2 % - 0.2 % - 1.8 % -4.7%
*(a) Method 1 : completely randomized block design (ram). : t(b) Method 2: Taguchi methods (mm). ~/(c) Percentage of difference = ((b)-(a)/(a))* 100 %.
w h e r e sx a r e t h e X - c o o r d i n a t e
standard
measurements Yx, Yy a n d Yz a r e t h e m e a n s
for
deviations of n
Yxi, Yyi
and
Yzi,
respectively s is t h e o v e r a l l s t a n d a r d d e v i a t i o n o f n m e a s u r e m e n t s Yxi, YYi a n d Yzi a r e t h e c o o r d i n a t e s f o r i n d i v i d u a l measurements Hx, Hy a n d Hz a r e t h e r e p r o d u c i b i l i t i e s f o r X - , Y- a n d Z-coordinates,
respectively, in mm
H is t h e o v e r a l l r e p r o d u c i b i l i t y i n m m n is s a m p l e size ( n = 8 1 0 f o r m e t h o d method
1, n = 2 7 0 f o r
2).
Analysis of variance (ANOVA) was applied to the H v a l u e f o r t e s t i n g t h e m a i n e f f e c t s o f l o a d , X - , Y- a n d Z coordinates and the interactions among X, Y and Z. T h e reproducibility a n a l y s i s r e s u l t s f o r h o m e p o i n t a r e i n T a b l e 4. T h e m e a n a b s o l u t e e r r o r s a n d t h e r e p e a t a -
62
Robotics & Computer-Integrated Manufacturing • Volume 6, Number 1, 1989
bility values from both experiments were well within the 10.4 ~ difference. The repeatability of a certain spatial location was the spread (3s) of the repeated measurements under a certain test condition. Twenty-seven spatial points were tested. The g r o u p mean could be either the average of 30 measurements (i.e. any X-, Y- and Zcoordinate combination) or the average of 10 measurements (i.e. any load, X-, Y- and Z-coordinate combination). The latter average (i.e. g r o u p size = 10) was used for the analyses. Therefore, the repeatability data are calculated as follows:
sx,~ =
(Yxi - Yx)2/9
i = 11-20
form=2,
l o.'; i =
1-10 for m = 1,
results were similar to those from the reproducibility analysis. The repeatability values for both methods were close to the maximal of 7.9 ~o. Accuracy refers to the ability to hit what is aimed at. It is the degree of agreement between independent measurements and the target value being measured. A robot's accuracy in hitting a specific target point is c o m p u t e d comparatively in this study. In other words, the difference between the c o m m a n d e d distance and the distance measured from a starting point to a target point represents the accuracy of the r o b o t at this target point. Therefore, the accuracy data are calculated as follows:
dl = [(Yxl - n g o ) 2 d- (YYi -- H y o ) 2 q- (Yz i - H Z o ) 2 ] 0"5, i = 1 - 3 0
i=21-30form=3
d,. = 1 / l O ~ ( d i ) ; i =
Px = 1/3 ~(3sxm); m = 1 to 3
1-10 for m = 1,
i
m
i = l l - 2 0 for m = 2, i = 21-30 for m = 3
P y and Pz are calculated in a similar way to P x
A,. = ~'(d i - dm)/lO; i = 1-10 for m = 1, i = 11-20 s,={~i
[(YxI-
yx)2 + ( y Y i -
i
yy)2
for m = 2, i = 21-30 for m = 3
0.5
( Y z ~ - Yz)2]/9
; i = 1-10 for m = 1, i = 11-20 for
A= 1/3•Am;m=
1-3
tn
m = 2, i = 21-30 for m = 3 P = 1/3 ~(3sm); m = 1-3 nl
where Sxm are the X-coordinate standard deviations for g r o u p m S,,, are the overall standard deviations for g r o u p m Yxi, Yy~ and Yz~ are the X-, Y- and Z-coordinates for each individual measurement, respectively Yx, Yy and Yz are the means for Yxi, Yy~ and Yzi in a group, respectively Px, Py and Pz are the repeatabilities for X-, Y- and Zcoordinates, respectively, in m m P is the overall repeatability in m m m is group, 10 measurements per group. The repeatability analysis results are in Table 5. These
where di are the distances of each individual point Yxi, Yyi and Yzi are the X-, Y- and Z-coordinates for individual measurements, respectively H x o, H y o and Hz o are h o m e position coordinates Am is accuracy for g r o u p m in m m A is accuracy in m m m is group, 10 measurements per group. The accuracy analysis results are in Table 6. The results from both experiments are very close to the m a x i m u m of 4.9 ~o. Table 7 shows the comparison of the determining significant factors obtained by using two experimental design methods. Both methods showed a similar capability to detect statistically significant factors in this study.
Table 5. Comparison of a robot's repeatability for spatial points L = 0 kg ~" P
Px Py, Pz
L = 0.227 kg
(a)*
(b)t
(c)~:
(a)
(b)
(c)
(a)
2.560 1.655 1.687 0.646
2.584 1.670 1.719 0.595
0.9 ~o 0.9 ~o 1.9~ 7.9~o
2.546 1.501 1.663 0.694
2.498 1.610 1.579 0.692
1.7 ~o 7.3 -5.1~o -0.3~o
2.533 1.501 1.786 0.761
*(a) Method 1 : completely randomized block design (mm). "i'(b) Method 2: Taguchi methods (mm). :~(c) Percentage of difference = ((b) - (a))/(a) 100~.
L = 0.454 kg (b) 2.530 1.407 1.822 0.805
(c)
(a)
-0.1 ~ - 6.3 ~ 2.0~ 5.8~
2.516 1.522 1.712 0.700
Overall (b) 2.537 1.562 1.707 0.697
(c) 0.8~ 0.6 -0.3~ -0.4~o
Determining robot process capability • B. C. JIANG et al.
Further analysis using Taguchi methods One advantage of using Taguchi methods is that they permit S/N analysis. The S/N in Taguchi methods is a combined index that considers both variation and mean. 26 The computation of S/N values depends on the data characteristics class, i.e. if the
63
data are the smaller-the-better, the larger-the-better or the nominal-the-best. In this experiment, for example, repeatability is the smaller-the-better case, and S/N is calculated as follows:
V= (1/N)(Y~ + Y~ +... + Y~) Nab= - l O l o g V where Yi = repeatability (mm) N = number of observations
Table 6. Comparison of a robot's accuracy for spatial points
X
Accuracy (ram) (a)*
(b)t
(c):~
-255 -113 27
29.407 21.545 25.443
29.087 21.516 25.472
- 1.1 -0.1 -0.1
97 97 97
-255 -113 27
17.857 14.247 5.185
17.771 14.103 5.119
-0.5 -1.0 -1.3
187 187 187
-255 - 113 27
11.117 9.999 1.317
11.136 9.945 1.321
0.2 -0.5 0.3
-255 -113 27
37.028 39.620 35.453
37.118 39.696 35.423
0.2 0.2 -0.1
Y (mm)
Z
65 65 65
- 13 -13 - 13
65 65 65 65 65 65 175 175 175
-13 -13 -13
= S/N.
175 175 175
97 97 97
-255 -113 27
25.872 26.875 21.810
25.841 26.703 21.730
-0.1 -0.1 -0.4
175 175 175
187 187 187
-255 -113 27
13.682 13.558 6.922
13.555 13.488 6.991
-0.9 -0.5 1.0
-255 -113 27
35.523 40.193 36.535
35.374 40.382 36.465
-0.4 0.5 -0.2
285 285 285
-13 -13 -13
285 285 285
97 97 97
-255 -113 27
27.336 29.740 25.054
27.321 29.990 25.291
-0.1 0.8 0.9
285 285 285
187 187 187
-255 -113 27
15.388 16.246 6.325
15.428 16.322 6.015
0.3 0.5 -4.9
21.825
21.800
-0.1
Overall
*(a) Method 1: Completely randomized block design. t(b) Method 2: Taguchi methods. :[:(c) Percentage of difference = ((b)-(a))/(a) 100 %.
ANOVA was applied to the S/N of repeatability data obtained using method 2. The 10 repeated measurements were divided into two groups in order to generate an S/N of repeatability data for producing enough residual degrees of freedom in ANOVA. Table 8 shows the significant levels of each factor for both original repeatability data and for the S/Ns, and the associated percentage of variation explained by each factor. The following example demonstrates the advantages of using Taguchi methods: In robotic assembly work, parts can be placed in a manufacturing cell at any fixed height (i.e. a fixed Z). The weight of the parts can vary from 0.227 to 0.454 kg. The robot must be able to repetitively pick up the parts (i.e. repeatability is the only concern). Table 8. A N O V A of repeatability and S/N from L27(313) Repeatability Significant SS a-level Load X Y Z X*Y X,Z Y*Z Error
0.07 1.33 4.96 0.36 18.50 0.87 1.16 25.42
SS
0.96 0.43 0.05 0.79 0.001 0.89 0.82
S/N Significant a-level
Contribution (%)
0.96 0.56 0.10 0.77 0.04 0.82 0.30
0.27 % 3.00% 21.95 9/00 1.809/oo 64.20% 4.82 3.96
0.36 4.05 29.58 2.43 86.53 6.50 5.34 26.50
Table 7. Comparison of determining significant factors using two experimental design methods Reproducibility CRBD* TMt SS a-level:i: SS a-level Load X Y Z X,Y X,Z Y,Z
0.06 0.71 0.61 0.72 0.54 1.73 0.63
0.92 0.39 0.44 0.38 0.83 0.33 0.79
0.11 0.64 1.14 0.83 0.18 0.59 1.71
0.87 0.45 0.25 0.36 0.98 0.82 0.38
* CRBD--completely randomized block design. t T M - - T a g u c h i methods. :~ a-level--significant a-level.
Repeatability CRBD SS a-level SS 0.31 1.98 12.57 1.06 34.16 2.09 2.04
0.78 0.22 0.0001 0.44 0.001 0.51 0.53
0.07 1.33 4.96 0.36 18.50 0.87 1.16
Accuracy TM
CRBD
TM
a-level
SS
a-level
SS
a-level
0.96 0.43 0.05 0.79 0.001 0.89 0.82
0.78 3682.00 14175.77 1049.21 592.16 314.88 264.11
0.80 0.001 0.001 0.001 0.001 0.001 0.001
5.58 1245.59 4732.17 349.37 207.60 88.85 105.94
0.31 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
64
Robotics & Computer-Integrated Manufacturing • Volume 6, N u m b e r 1, 1989
Two methods can optimize the specified task condition. One method is to choose the maximum S/rN from the factor combinations tested as shown in Table 9. Consequently, the best location for the 0.227-kg load is at (65,175), and the best location for the 0.454-kg load is at (175,65). If we list the best several combinations, a certain area or volume can be identified as the optimum working area. The second method was further examined in this area or volume to determine the best factor combination. Another experiment was conducted by using an L9(34) orthogonal array. This design accommodates four factors with three levels each. However, no interactions between variables can be analyzed. Since a fixed Z could be used, the best Z level (Z = 27 ram) was chosen. Three Z levels were selected to test the sensitivity of this height. Three X levels and Y levels were selected based on the best working area identified from the previous experiment. The experimental layout is shown in Table 10. A similar ANOVA applied to the repeatability and S/N showed that the load significantly affected the repeatability of raw data and S/N while the Y-axis significantly affected the raw data only (Table 11). A
Table 11. A N O V A of repeatability and S/N from L9(34) Taguchi design Repeatability Significant SS ~-level Load X Y Z Error
1.02 0.33 0.62 0.07
0.01 0.16 0.05 0.63
SS 27.38 7.90 12.66 * 1.80
S/N Significant ~t-level
Contribution (%)
0.06 0.19 7.05 --
55.04 15.88 25.45 --
* Pooled into error term.
SIN 3.00, 2.00 1.00-
0.362 X/
0.206
yj
-i,856
0.00 -I.00-2.00 -3.00
x
-2.559 I
I
Levels
Fig. 2. Repeatability S/N for three X and Y levels. Table 9. Repeatability sflq for L27(313)
S/N X
Y
Load = 0.227 kg
Load = 0.454 kg
65 65 65
65 175 285
- 5.98 -5.65 -8.53
-6.50 -9.71 --11.40
175 175 175
65 175 285
-6.75 -6.83 -10.66
-5.49 -5.99 -10.60
285 285 285
65 175 285
-13.02 -6.11 -6.73
-9.77 -5.68 -7.68
Table 10. L9(34) Taguchi design layout
Experiment
Load
X
Y
Z
1
1
1
1
1
2 3 4 5 6 7 8 9
1 1 2 2 2 3 3 3
2 3 1 2 3 1 2 3
2 3 2 3 1 3 1 2
2 3 3 1 2 2 3 1
Load levels: 0, 0.227, 0.454 kg. X levels: 65, 120 and 175 ram. Y levels: - 13, 42 and 97 ram. Z levels: 2, 27 and 52 mm.
Noise R1-R10
Duncan multiple range test was also conducted on three Z levels and showed no significant difference among the three levels. Figure 2 shows that X and Y interactively affected the S/N of repeatability, although this interaction could not be statistically analyzed. A list of X Y combinations, S/Ns, and repeatability data is given in Table 12. The best repeatability zone consisted of the three points along the diagonal axis of the test area (i.e. X1 Y1, )(2 Y2 and X 3 ]"3)- The next best zone and the worst zone were the upper left and lower right regions, respectively (see Fig. 3). Therefore, the recommendation is to place the assembly parts at the points along the diagonal line shown in Fig. 3 and at a height of 27 _ 25 mm. DISCUSSION Specifications provided by most robot manufacturers give repeatability data as a range (e.g. _+0.1 ram). These repeatability data are equivalent to the + 3s value in this study. This information is useful when a task's spatial direction is not critical (e.g. pick up a cylindrical part in an assembly task). From the results of this study, the spreads of X-, Y- and Z-coordinates provide valuable information when the direction of robot motion is of concern for a
Determining robot process capability • B. C. J1ANG et al. Table 12. X and Y levels and corresponding repeatability and
S/N X
Y
Repeatability (mm)
S/N
65 65 65
-13 42 97
0.784 1.112 0.946
1.66 - 1.00 0.42
120 120 120
-13 42 97
1.690 0.805 1.115
--4.68 1.84 -0.94
175 175 175
- 13 42 97
1.704 1.262 0.812
-4.66 -2.05 1.14
iiiiiiiiiiiii!;'~ .
i!:'
2-
I
3
Fig. 3. Three zones of different repeatability groups.
task (e.g. the relative position of a robot to the object that it will pick up in a robotic cell). For example, repeatability in the Z-direction was always better than in the X- and Y-directions for this robot. The robot's relative position in the X Y plane more critically affects its repeatability. Therefore, process capability testing can yield directional information. From the results of this study, both randomized complete block design and Taguchi design methods yielded very similar results in determining a robot's process capability (within 10.4%). However, Taguchi methods can be used to optimize the operation of a robot as described in the previous example. If this robot's process capability does not meet a certain task requirement, a new robot must be selected and a new test run to determine its process capability. A potential use of Taguchi methods is for examining the effectiveness of changing robot design parameters (called "tolerance design" in Taguchi methods), especially if the cost is known. This application will help a robot manufacturer quickly determine/improve its robot design parameters to yield better process capability. FUTURE STUDY A major concern of the robot user is how to determine the best operating characteristics for obtaining optimum process capability. This information is required when placing a robot in the workplace, particularly in an unmanned manufacturing
65
cell. Therefore, not only the determination of a robot's process capability but also the optimization of its operational parameters is important. The Taguchi methods used in this study provided significant benefits in determining/optimizing a robot's process capability. The amount of data required was significantly reduced and the optimization could be achieved. More factors can be considered when Taguchi methods are used (e.g. load, speed, spatial location, point-to-point and continuous-path motions) so that an effective testing procedure can be developed for determining a robot's process capability. The capability of the measuring system is a major concern in determining a robot's process capability. The 3-D accuracy of the WATSMART system is about 1 mm. A simple test was conducted to determine the repeatability of the W A T S M A R T system. The following points were measured within a cubic calibration frame that is 0.6 m on each side: eight points inside corners, four points on two side planes and two points in the center of the frame. The results of 10 repeated measurements showed that the repeatability (3s) of the system is 0.780 mm, and three axes' repeatabilities are 0.329 mm (3sx), 0.612 mm (3sv) and 0.357mm (3s=), respectively. The repeatability at the center of the calibration frame was about two times better than at the corner points. Many robots have better accuracy and repeatability than the WATSMART system. To improve the measuring system's accuracy and repeatability is critical. CONCLUSION The comparison of the two methods for use in determining/optimizing a robot's process capability showed the following: Taguchi methods required only one-third the data that the randomized complete block design method required, yet yielded similar results in quantifying a robot's process capability (within the 10.4% difference). A testing procedure developed using Taguchi methods can examine more factors than a procedure developed using the randomized complete block design method. REFERENCES 1. Ayres, R. U., Miller, S. M." Robotics: Applications and Social Implications. Cambridge, MA, Ballinger, 1983. 2. Borrel, P., Dombre, E., Guerdon, J.P., Liegois, A.: Workspace and control strategy determination for an underwater manipulator. In: Proc. IEEE Conf. Dec&. Control 80-83, Dec. 1987. 3. Brown, L. B.: A random-path laser interferometer system. Presented at the Int. Congr. Appl. Lasers ElectroOpt., San Francisco, CA, 11-14 Nov. 1985. 4. Chabrol, J.: Industrial robot standardization at ISO. Robotics 3: 229-233, 1987.
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5. Critchlow, A.J.: Application to Robotics. New York, MacMillan, 1985. 6. Gendron, W. A., Sommer, H. J. III: Pulsed sonic coordinate digitization using point-effect microphones. Robotics Res. Adv. Appl. 167, 1982. 7. Hackwood, G. B., Trimmer, W. S.: High precision robot system for inspection and testing of electronic devices. In: Proc. Int. Conf. Robotics, 13-15 Mar. 1984. 8. Harris, E. W.: Error recovering for robotic component insertion. IBM Tech. Disclosure Bull. 26(11): 5328-5329, 1984. 9. Hecker, E. P., Zellmann, M. T.: Point-of-use find posts. I B M Tech. Disclosure Bull. 26(11): 5894-5895, 1984. 10. Hunter, J. S.: Statistical design applied to product design. J. QuaL Technol. 17(4): 210-221, 1985. 11. Industrial Technology Institute, Robot Evaluation Center. Ann Arbor, MI, 1986. 12. International Organization for Standardization (ISO), Working draft on manipulating industrial robots--performance criteria and related testing methods. ISO/TC 184/SC 2/WG 2 N 8, 1987. 13. Jiang, B. C., Black, J. T.: Improving and measuring robot process capability. CIM Rev. 3(4): 44-49, 1987. 14. Jiang, B. C., Black, J. T.: Robot process capability study. Presented at the 1987 Manu. Syst. Res. Conf., Ann Arbor, MI, 6-9 Oct. 1987. 15. Jiang, B. C., Black, J. T., Duraisamy, R.: A review of recent developments in robot metrology. J. Mfo. Systems 7(4): 339-357, 1988. 16. Kackar, R. N.: Off-line quality control, parameter design and the Taguchi method. Qual. Technol. 17(4): 176-188, 1985. 17. Lembke, J. R., Jones, L. L.: Measurement of robot accuracy using the Latin square three-dimensional ball plate. Final Report, Bendix, Kansas City, KS: BDB-6132992, 1983. 18. Makino, H., Furuya, N.: Performance tests for CP motion with the SCARA robot. In: Proc. 15th Int. Syrup. Ind. Robots, p. 1011-1020, 1985. 19. Makino, H., Taniguchi, N.: Standard performance test methods for planar positioning assembly robots. Ann. CIRP 34: 33-36, 1985. 20. Martin, J. F.: An acoustic ranging system for robot position control and tracking. Soc. Manu. Eng. Tech. Pap. MS84-1039, 1984. 21. Nof, S. Y., Lechtman, H.: Robot time and motion system providesGmeans of evaluating alternate robot
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