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s95-20, 1 Computer-Aided Engineering and Mechatronics in the Design of Apparel Equipment
FACULTY ADVISORS: Timothy G. Clapp (Textile Engr.) and Jeffrey W. Eischen (Mechanical Engr.) - North Carolina State University, Frank W. Paul (Mechanical Engr.) and Christopher D. Rahn( Mechanical Engr.)-Clemson University. GRADUATE STUDENTS: W. Clifton(MS 1996)- Mechanical Engineering NCSU, Steve 0. Mast(MS), Sandeep Shenoy(MS), Nick Costescu(PhD)- Mechanical Engineering Clemson. TEAM LEADER: J. W. Eischen ANNUAL REPORT: March 1995-August 1996.
ABSTRACT This research project combines computer-aided-engineering methods with practical control strategies to develop precise fabric handling capabilities. The primary goal is to develop mechatronic design concepts for assembly processes such as: folding, joining, placing, and locating that take into account variability in fabric material properties such as weight and stiffness. Three-dimensional modeling of fabric drape and manipulation using the finite element method has been simplified for the design of fabric handling control systems. Iterative algorithms for fabric folding with precise position control were developed and experimentally implemented. A robot system folds the fabric, measures the resulting position using a vision system, and corrects the folding trajectory. The system adapts to changing fabric parameters, friction, and folding speed. Position errors of less than 1.2 mm are achieved within 6 folds for limp fabrics. Stiff fabrics require more complex control algorithms and additional folds to obtain similar position errors.
I. PROJECT GOALS AND RELEVANCE TO NTC GOALS The key question and challenge for this research project is: Can computer-aidedengineering techniques commonly used in the automotive and aerospace industries be applied to the design and development of fabric handling equipment? And, can the machinery be designed to accommodate multiple part configurations (shape, thickness, etc.) and material properties (weight, stiffness, etc.)? The major objective of this research project is then to combine computer-aidedengineering methods with practical control strategies to develop precise fabric handling capabilities. The primary goal is to develop mechatronic design concepts for assembly processes such as: folding, joining, placing, and locating that take into account variability in fabric material properties such as weight and stiffness. Advanced three-dimensional modeling of fabric drape and manipulation using the finite element method will be simplified for the design of fabric handling control systems. Controls that stabilize the fabric
National Textile Center Annual Report: November 1996
223
s95-20, 2 motion and allow accurate handling with minimum wrinkling will be investigated. Proof of concept demonstrations have been constructed to show techniques for systematically adjusting for material property variation. Other potential applications for this technology in future years would include 3D fabric processes such as shape pressing and sewing. Computer-aided-engineering is prevalent in many high technology industries in the US, including automotive and aerospace. Computer simulation of manufacturing processes during the equipment design phase is an accepted procedure. This same approach must be implemented in the design of fabric handling equipment. Machinery must be engineered in advance to accommodate multiple part configurations and material properties. Competitive advantage from Demand Activated Manufacturing will require this level of knowledge.
II. TECHNICAL APPROACH AND PROGRESS TO DATE Flexible automation allows apparel manufacturers to respond quickly to rapidly changing market conditions while minimizing skilled labor. Successful automation in the apparel industry has primarily been limited to fixed automation using special purpose, mass production machines. Flexible automation using general purpose machines is difficult because the limp nature of the fabric complicates actuation and sensing, thus adding cost and complexity. A wide variety of materials need to be handled with diverse bending stiffnesses, weights, and frictional characteristics. Additionally, these characteristics vary from part to part and with temperature and humidity. Dependable flexible automation requires feedback to adapt to these variations. A number of researchers focused on automating entire apparel manufacturing lines. The Charles Stark Draper Laboratory and Textile/Clothing Technology Corporation [l] applied large scale automation to the men’s clothing industry. MIT1 [2] implemented similar apparel automation systems. Taylor and Taylor [3] developed an automated line for the assembly of men’s underwear. Other researchers concentrated on fabric handling. Gunner [4] investigated the laying of fabric strips on moving conveyor belts. Brown et. al. [5] used Konopasek’s [6] equations to derive trajectories for fabric standing. Eischen and Kim [7] used a nonlinear technique to solve for fabric standing up, laying down, and folding trajectories. This year, under NTC funding, we have developed iterative position control for folding, a fundamental fabric handling operation. A fast, memorized folding trajectory is implemented using an industrial robot. A vision system measures the fabric position error after each fold. If the error is too large, the trajectory is modified on-line and the fabric is refolded. This process repeats until small errors are achieved. EXPERIMENTAL
IMPLEMENTATION
This section details the progress to date in the experimental implementation of a mechatronic apparel handling operation. The chosen operation is described, the experi-
224
National Textile Center Annual Report: November 1996
s95-20, 3 mental apparatus is discussed, and the automation algorithm is detailed. Figure 1 shows the two dimensional fabric fold automated in this research. The fabric starts flat on the table and the left (manipulated) end moves until it lies on top of the right (free) end. In an actual apparel manufacturing process, the fabric would typically next undergo a sewing or joining operation. This requires precise alignment of the two ends of the fabric to each another and to the work table. The objective, therefore, is to prevent the motion of the free end of the fabric during the fold. We assume that the robot picks up fabric samples from a stack using a special purpose gripper that allows fabric rotation such as a Dinned clunicker ISl.
.
.
. .
.
Manipulated End
Work Table
l
Free End
Figure l- Two Dimensional Fabric Folding Figure 2 shows a schematic of the equipment used in the experiment. An 80 cm by 8 cm fabric strip attaches to a robot end effector. A vision system measures the free end motion using a camera located directly above the free end. The end effector consists of a horizontal bar parallel to the work surface. The fabric end loops around the bar to form a pin connection with the robot. The pin connection eliminates in plane moments on the manipulated end of the fabric. The fabric rests on a painted Formica work table. Five fabrics representing a wide range of properties are used: 1. Acetate Satin, 2. Combed Cotton Velveteen, 4. Mere. Cotton Twill, and 5. 65/35 Poplin. Physical properties for these fabrics (and others) were reported in [9]. The software for the system runs on two Sun workstations and consists of three parts. The vision control software gathers the image data from the camera, processes it, and calculates the error associated with fabric motion. The robot software controls the end effector trajectory. The main control software coordinates these two programs, provides the user interface, and implements the iterative control algorithm. The main control software starts by sending the initial trajectory to the robot control software. The trajectory can be based on the finite element computer simulation or chosen
National Textile Center Annual Report: November 1996
. End
225
CCD Camera
Work Table Servo Amplifiers
Sun Workstation (Robot Control)
Sun Workstation (Image Processing and Control Feedback)
Figure 2- Schematic of the Experimental Setup arbitrarily. As the robot moves through the trajectory, snapshots are taken at specified waypoints and free end position is calculated. Upon completion of the fold, the main control software calculates the fold error. If the error exceeds a threshold, then the trajectory is adjusted, the robot picks up the fabric and lays it on the work table, and the process repeats. The error calculation requires digitization of the snapshot by the computer. Software thresholds the snapshot into binary data, and finds the fabric edges. The free end motion is measured relative to the starting fabric position. The system has a resolution of f0.6mm Figure 3 shows typical fabric configurations at the end of folding. Figure 3(a) shows the zero error configuration. If the free edge of the fabric pushes right during folding, then the final configuration corresponds to Figure 3(b). F i g ure 3(c) shows the configuration if the fabric pulls left during folding. Figure 3(d) corresponds to undesirable fabric looping. CONTROL ALGORITHM
226
National Ttzxtile Center Annual Report: November 1996
s95-20, 5 End Effector
Folded
Folded r\ Fabric
(a) Good Fold (E=O)
(b) Push (E
End Effector
Folded -Fabric
(c) Pull 0)
Folded
V-4 E
(d) Overlap (E
End Effector
7-4 E
End Effector
k-4 E
Figure 3- Four Representative Final Configurations Discretization of the folding trajectory into a series of equally spaced way points connected by line segments allows representation of the trajectory by a single vector Yl
P=
Y2 ..
Yn points-1 Yn point8 Three points specify the simplest trajectory: one variable internal point y2 in the center of the trajectory and two fixed end points yr and ys. More complicated trajectories have additional internal points. The error (E) associated with a given fold depends upon p. The algorithm attempts to find a p which makes E = 0, or find a root of E(p). A number of numerical root finding algorithms can be used for this purpose. These routines require multiple function evaluations, with each evaluation corresponding to a different fold trajectory. Thus, the system must be able to fold the fabric, measure the error, replace the fabric in its initial position, and repeat the process until a root is found. It is assumed that the fabric folding characteristics do not change from one fold to the next. Finally, the number of way points and hence size of p starts at npoints = 3 and increases if no root is found after k,,, iterations. The robot picks up the first piece of fabric (part) and lays it on the work table. The robot executes the fold for p = po . The computer reads the error from the vision sensor. If the error is less than a threshold value, E , then folding is complete and a new part is loaded. If the error exceeds the threshold, then a root finding algorithm searches for p which provides E(p) = 0 . If the root finder does not converge in k,,, iterations, then npoints increases, and p is initialized to the midpoints of the line segments of the previous
National Textile Center Annual Report: November 1996
227
S95-20, 6 trajectory. Two root finding methods are used by the control algorithm. They require neither excessive function evaluations nor function derivatives. For three point paths, a simple gradient descent method [lo] works best. For paths with multiple interior points, Powell’s method [ll] is used. RESULTS Figure 4 shows the E(p) = E(y2) with npoints = 3 for several fabrics. For each fabric, pushing occurs for small yz and pulling for large yz. The error curve for fabric 1 (Figure 4(a)) dips slightly near yz = 60 cm because the fabric forms a loop. Fabric 1 has a broad range of possible center heights with no error (20cm < yz < 50cm) . Fabrics 2-4 (Figures 4(b)-4(d)) have a narrow but nonzero range of center heights with zero error. Thus, the root finding scheme appears reasonable for these test fabrics using only three points. The algorithm starts with a three point path and p initialized to
(2) Figure 5 displays the results of the control algorithm applied to fabrics 1 through 4 using only three point trajectories and the gradient descent root finder. The center height initializes at 40 cm, half the fabric length. The average end effector velocity,
Vavg =
Trajectory Length Time
(3)
is 17.3 cm/set. Fabric 1 requires no iterations because the initial error is zero. The other three plots show the initial and final trajectories, initial and final errors, and the number of folds (Ic ) required to achieve E < E . In all cases, an acceptable solution is reached after a small number of iterations. Figure 5 also shows the initial and final E and yz values. The algorithm accurately finds the root. A three point path does not converge to an acceptable error for fabric 5. Experiments showed that E(p) # 0 with npoints = 3 for any value of y2 . The control algorithm then adds an internal point. With two internal points, the error reduces to 1.2 mm after eleven folds. A final test demonstrated the versatility of the control algorithm. The best three point trajectory for Fabric 4 at Vavs = 17.3 cm/s is tested for Vavs ranging from 7.6 to 29.3 cm/set. Small errors occur for Vavs < 25 cm/set and unacceptable large errors occur for Vavg > 27 cm/s . Activation of the control algorithm drastically improves the errors for Vavg > 25 cm/s . The controller adjusts the path at Vavs =26, 28,and 29 cm/set to achieve less than half the uncontrolled error. COMPUTER
SIMULATION
A computer simulation tool has been developed that allows modeling of various fabric manipulation processes that occur during manufacturing. Fabric parts are modeled as very
228
National Textile Center Annual Report: November 1996
(bl Fabric 1
150 t
0
20
60
80
-100’
0
20
40 ~2 (cm)
60
80
40 ~2 0-d
60
80
(cl
200 150
40 ~2 (cm)
-
Fabric 3
-50 + 0
20
40 ~2 (cm)
60
80
-100
0
+
+
+++
20
Figure 4- Fabric Motion Error for Three Point Trajectories: ‘+’ Data Points; ‘0’ Algorithm Starting Point; ‘*’ Algorithm Ending Point flexible elastic beams that can accommodate stretching and bending in a single plane. The governing equilibrium equations are solved using the finite element method. The nonlinear moment curvature response is measured directly with the Kawabata Test System, or with a simpler drape test. Realistic manipulation processes involve interaction of fabric parts with other objects such as: work surfaces, robot manipulators, other fabrics. Therefore, the ability to model contact has been implemented. A key aspect of this research was development of a capability to determine optimum ways to manipulate fabric parts while minimizing sliding of the fabric or forces generated in the fabric. This feature allows intelligent selection of initial manipulation paths for the control system just described. Details of the finite element approach are given in [12] and [13]. CONCLUSIONS Repeatable fabric handling operations can be controlled using an iterative approach.
National Textile Center Annual Report: November 1996
229
(a)
60 50-
Fabric 1
S95-20. 8 k=l
40-
E. On W-4or 0
20
40
B 7 80
60
0
20
x 0-d (cl
60
40 x(cm)
60
80
NJ)
60 5040 -
20
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10
10-
f-l
n
4U’
a-- . . . _ 0
20
40 x0-N
- - _ .
60
>( . . .
80
alt W-400
ICI
20
40 x(m)
-----.-._._
60
Figure 5- Initial ( o ) and Final ( x ) Trajectories for Four Fabrics Using Three Points For four of the five fabrics tested in this research, simple three point trajectories provide errors of less than 1.2 mm in less than 6 folds. A fifth fabric, with a very high stiffness to weight ratio, required a four point trajectory and 11 folds to achieve an error of less than 1.2 mm. The control system adapts the folding trajectory in response to changes in speed and fabric properties. This control concept can be applied to many fabric handling operations requiring accurate position control.
III. STUDENT PROGRESS Woodrow Clifton is the first student to graduate with an advanced degree after completing research sponsored by the NTC. He earned his MS in Mechanical Engineering at NC State in June 1996 under the direction of Dr. J. W. Eischen. He is now employed
230
National Textile Center Annual Revort: November 1996
-s 80
s95-20, 9 by the BASF Fiber Products Division at the Clemson Plant in Central, SC. This plant produces nylon fibers for the carpet industry. He wrote a paper that will be presented at the Pan American Congress of Applied Mechanics Conference. Steve Mast is finishing his Master’s thesis under the guidance of Drs. Paul and Rahn. He wrote a paper that has been submitted to the International Journal of Clothing Science and Technology based on his work in iterative fabric folding control. He is currently employed by Secor in North Carolina. Sandeep Joshi is developing advanced sensors and control algorithms for fabric positioning on a surface with friction. He has completed his first year in the MS program and has designed and constructed a test stand. He is now implementing adaptive fabric. position controllers. Nick Costescu is a Ph.D. candidate electrical engineering student who is working part time on this project. He provides advice and guidance on electronics design, computer interfacing, and software development for the experiments.
IV.
INDUSTRY
COLLABORATION
A video tape has been prepared to illustrate the capabilities of our Puma robot and the associated sensors. This tape will be used in upcoming meetings with industry to facilitate understanding our research approach. Jud Early at TC2 is supportive of the goals and objectives of this research project and has agreed to meet with us and provide input regarding the direction of our experimental work. Leonard Brewington at Milliken has also been supportive of our work and believes it may have an application in airbag manufacturing. During the Fall of 1996 we plan to visit several Milliken airbag plants. It is our intention to tailor our experimental investigation towards fabric handling problems that are relevant to industry problems.
V. PUBLICATIONS [l.] “Iterative Techniques for Fabric Position Control During Folding,” submitted to International Journal of Clothing Science and Technology, June 1996. [2.] “Finite-Element Modeling and Control of Flexible Fabric Parts,” IEEE Computer Graphics and Applications, Special Issue on Computer Graphics in Textiles and Apparel, Volume 16, Number 5, pgs. 71-80, (Invited Paper) [3.] “Optimum Manipulation Strategies for Limp Fabric Materials,” with W. Clifton, to appear in the Proceedings of the Fifth Pan American Congress of Applied Mechanics Conference, San Juan, Puerto Rico, Jan. 1997. [4.] “Optimum Fabric Trajectories for Edge Position and Control,” Clifton, W., MS Thesis, North Carolina State University, 1996.
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231
s95-20, 10
VI. REFERENCES [ 1.1 Charles Stark Draper Lab, Inc., Report on the Fourth-Year Research and Development Program for the Tailored Clothing Technology Corporation, June 28, 1985. [2.] Jones, S.H., MITI: Progress Report, Apparel Ind., Feb. 1985, pp. 46-49. [3.] Taylor P.M. and G.E. Taylor, “Progress Toward Automated Garment Manufacture”, Sensory Robotics For the Handling of Limp Materials, ed. Paul M. Taylor, 1990. [4.] Gunner, M.B., P.M. Taylor, and A. J. Wilkinson, “Placing Fabric onto Moving Surfaces”, International Journal of Clothing Science and Technology, Vol. 2 No. 3/4, 1990, pp. 56-64. [5.] Brown, P.R. III, D.R. Buchanan, and T.G. Clapp, “Large-deflection Bending of Woven Fabric for Automated Material-Handling”, Textile Research Journal, Vol. 81 No. 1, 1990, pp. 1-14. [6.] Konopasek, M. and J.W.S. Hearle, “Computational Theory for Bending Curves. Part I: The Initial Value Problem for the Three-Dimensional Elastic Bending Curve”, Fibre Science and Technology, Vol. 5, 1972, pp.= l-28. [7.] Eischen J.W. and Y.G. Kim, “Optimization of Fabric Manipulation during Pick/Place Operations”, International Journal of Clothing Science and Technology, Vol. 5 No. 3/4, 1993, pp. 68-76. [8.] Clupicker Manual, Jet Sew, Barnevelde, New York. [9.] National Textile Center 1995 Annual Report, pp. 275-281. [IO.] Astrom, K.J. and B. Wittenmark, Adaptive Control, Addison Wesley, Reading MA, 1989. [ll.] Powell. M.J.D, “An Efficient Method for Finding the Minimum of a Function of Several Variables Without Calculating Derivatives”, Computer Journal, Vol. 7, 1965, pp. 155-162. [ 12.1 “Finite-El ement Modeling and Control of Flexible Fabric Parts,” IEEE Computer Graphics and Applications, Special Issue on Computer Graphics in Textiles and Apparel, Volume 16, Number 5, pp. 71-80. [13.] “Optimum Fabric Trajectories for Edge Position and Control,” Clifton, W., MS Thesis, North Carolina State University, 1996.
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National Textile Center Annual Report: November 1996
FACULTY ADVISORS: Timothy G. Clapp (Textile Engr.) and Jeffrey W. Eischen (Mechanical Engr.) - North Carolina State University, Frank W. Paul (Mechanical Engr.) and Christopher D. Rahn( Mechanical Engr.)-Clemson University. GRADUATE STUDENTS: W. Clifton(MS 1996)- Mechanical Engineering NCSU, Steve 0. Mast(MS), Sandeep Shenoy(MS), Nick Costescu(PhD)- Mechanical Engineering Clemson. TEAM LEADER: J. W. Eischen ANNUAL REPORT: March 1995-August 1996.
ABSTRACT This research project combines computer-aided-engineering methods with practical control strategies to develop precise fabric handling capabilities. The primary goal is to develop mechatronic design concepts for assembly processes such as: folding, joining, placing, and locating that take into account variability in fabric material properties such as weight and stiffness. Three-dimensional modeling of fabric drape and manipulation using the finite element method has been simplified for the design of fabric handling control systems. Iterative algorithms for fabric folding with precise position control were developed and experimentally implemented. A robot system folds the fabric, measures the resulting position using a vision system, and corrects the folding trajectory. The system adapts to changing fabric parameters, friction, and folding speed. Position errors of less than 1.2 mm are achieved within 6 folds for limp fabrics. Stiff fabrics require more complex control algorithms and additional folds to obtain similar position errors.
I. PROJECT GOALS AND RELEVANCE TO NTC GOALS The key question and challenge for this research project is: Can computer-aidedengineering techniques commonly used in the automotive and aerospace industries be applied to the design and development of fabric handling equipment? And, can the machinery be designed to accommodate multiple part configurations (shape, thickness, etc.) and material properties (weight, stiffness, etc.)? The major objective of this research project is then to combine computer-aidedengineering methods with practical control strategies to develop precise fabric handling capabilities. The primary goal is to develop mechatronic design concepts for assembly processes such as: folding, joining, placing, and locating that take into account variability in fabric material properties such as weight and stiffness. Advanced three-dimensional modeling of fabric drape and manipulation using the finite element method will be simplified for the design of fabric handling control systems. Controls that stabilize the fabric
National Textile Center Annual Report: November 1996
223
s95-20, 2 motion and allow accurate handling with minimum wrinkling will be investigated. Proof of concept demonstrations have been constructed to show techniques for systematically adjusting for material property variation. Other potential applications for this technology in future years would include 3D fabric processes such as shape pressing and sewing. Computer-aided-engineering is prevalent in many high technology industries in the US, including automotive and aerospace. Computer simulation of manufacturing processes during the equipment design phase is an accepted procedure. This same approach must be implemented in the design of fabric handling equipment. Machinery must be engineered in advance to accommodate multiple part configurations and material properties. Competitive advantage from Demand Activated Manufacturing will require this level of knowledge.
II. TECHNICAL APPROACH AND PROGRESS TO DATE Flexible automation allows apparel manufacturers to respond quickly to rapidly changing market conditions while minimizing skilled labor. Successful automation in the apparel industry has primarily been limited to fixed automation using special purpose, mass production machines. Flexible automation using general purpose machines is difficult because the limp nature of the fabric complicates actuation and sensing, thus adding cost and complexity. A wide variety of materials need to be handled with diverse bending stiffnesses, weights, and frictional characteristics. Additionally, these characteristics vary from part to part and with temperature and humidity. Dependable flexible automation requires feedback to adapt to these variations. A number of researchers focused on automating entire apparel manufacturing lines. The Charles Stark Draper Laboratory and Textile/Clothing Technology Corporation [l] applied large scale automation to the men’s clothing industry. MIT1 [2] implemented similar apparel automation systems. Taylor and Taylor [3] developed an automated line for the assembly of men’s underwear. Other researchers concentrated on fabric handling. Gunner [4] investigated the laying of fabric strips on moving conveyor belts. Brown et. al. [5] used Konopasek’s [6] equations to derive trajectories for fabric standing. Eischen and Kim [7] used a nonlinear technique to solve for fabric standing up, laying down, and folding trajectories. This year, under NTC funding, we have developed iterative position control for folding, a fundamental fabric handling operation. A fast, memorized folding trajectory is implemented using an industrial robot. A vision system measures the fabric position error after each fold. If the error is too large, the trajectory is modified on-line and the fabric is refolded. This process repeats until small errors are achieved. EXPERIMENTAL
IMPLEMENTATION
This section details the progress to date in the experimental implementation of a mechatronic apparel handling operation. The chosen operation is described, the experi-
224
National Textile Center Annual Report: November 1996
s95-20, 3 mental apparatus is discussed, and the automation algorithm is detailed. Figure 1 shows the two dimensional fabric fold automated in this research. The fabric starts flat on the table and the left (manipulated) end moves until it lies on top of the right (free) end. In an actual apparel manufacturing process, the fabric would typically next undergo a sewing or joining operation. This requires precise alignment of the two ends of the fabric to each another and to the work table. The objective, therefore, is to prevent the motion of the free end of the fabric during the fold. We assume that the robot picks up fabric samples from a stack using a special purpose gripper that allows fabric rotation such as a Dinned clunicker ISl.
.
.
. .
.
Manipulated End
Work Table
l
Free End
Figure l- Two Dimensional Fabric Folding Figure 2 shows a schematic of the equipment used in the experiment. An 80 cm by 8 cm fabric strip attaches to a robot end effector. A vision system measures the free end motion using a camera located directly above the free end. The end effector consists of a horizontal bar parallel to the work surface. The fabric end loops around the bar to form a pin connection with the robot. The pin connection eliminates in plane moments on the manipulated end of the fabric. The fabric rests on a painted Formica work table. Five fabrics representing a wide range of properties are used: 1. Acetate Satin, 2. Combed Cotton Velveteen, 4. Mere. Cotton Twill, and 5. 65/35 Poplin. Physical properties for these fabrics (and others) were reported in [9]. The software for the system runs on two Sun workstations and consists of three parts. The vision control software gathers the image data from the camera, processes it, and calculates the error associated with fabric motion. The robot software controls the end effector trajectory. The main control software coordinates these two programs, provides the user interface, and implements the iterative control algorithm. The main control software starts by sending the initial trajectory to the robot control software. The trajectory can be based on the finite element computer simulation or chosen
National Textile Center Annual Report: November 1996
. End
225
CCD Camera
Work Table Servo Amplifiers
Sun Workstation (Robot Control)
Sun Workstation (Image Processing and Control Feedback)
Figure 2- Schematic of the Experimental Setup arbitrarily. As the robot moves through the trajectory, snapshots are taken at specified waypoints and free end position is calculated. Upon completion of the fold, the main control software calculates the fold error. If the error exceeds a threshold, then the trajectory is adjusted, the robot picks up the fabric and lays it on the work table, and the process repeats. The error calculation requires digitization of the snapshot by the computer. Software thresholds the snapshot into binary data, and finds the fabric edges. The free end motion is measured relative to the starting fabric position. The system has a resolution of f0.6mm Figure 3 shows typical fabric configurations at the end of folding. Figure 3(a) shows the zero error configuration. If the free edge of the fabric pushes right during folding, then the final configuration corresponds to Figure 3(b). F i g ure 3(c) shows the configuration if the fabric pulls left during folding. Figure 3(d) corresponds to undesirable fabric looping. CONTROL ALGORITHM
226
National Ttzxtile Center Annual Report: November 1996
s95-20, 5 End Effector
Folded
Folded r\ Fabric
(a) Good Fold (E=O)
(b) Push (E
End Effector
Folded -Fabric
(c) Pull 0)
Folded
V-4 E
(d) Overlap (E
End Effector
7-4 E
End Effector
k-4 E
Figure 3- Four Representative Final Configurations Discretization of the folding trajectory into a series of equally spaced way points connected by line segments allows representation of the trajectory by a single vector Yl
P=
Y2 ..
Yn points-1 Yn point8 Three points specify the simplest trajectory: one variable internal point y2 in the center of the trajectory and two fixed end points yr and ys. More complicated trajectories have additional internal points. The error (E) associated with a given fold depends upon p. The algorithm attempts to find a p which makes E = 0, or find a root of E(p). A number of numerical root finding algorithms can be used for this purpose. These routines require multiple function evaluations, with each evaluation corresponding to a different fold trajectory. Thus, the system must be able to fold the fabric, measure the error, replace the fabric in its initial position, and repeat the process until a root is found. It is assumed that the fabric folding characteristics do not change from one fold to the next. Finally, the number of way points and hence size of p starts at npoints = 3 and increases if no root is found after k,,, iterations. The robot picks up the first piece of fabric (part) and lays it on the work table. The robot executes the fold for p = po . The computer reads the error from the vision sensor. If the error is less than a threshold value, E , then folding is complete and a new part is loaded. If the error exceeds the threshold, then a root finding algorithm searches for p which provides E(p) = 0 . If the root finder does not converge in k,,, iterations, then npoints increases, and p is initialized to the midpoints of the line segments of the previous
National Textile Center Annual Report: November 1996
227
S95-20, 6 trajectory. Two root finding methods are used by the control algorithm. They require neither excessive function evaluations nor function derivatives. For three point paths, a simple gradient descent method [lo] works best. For paths with multiple interior points, Powell’s method [ll] is used. RESULTS Figure 4 shows the E(p) = E(y2) with npoints = 3 for several fabrics. For each fabric, pushing occurs for small yz and pulling for large yz. The error curve for fabric 1 (Figure 4(a)) dips slightly near yz = 60 cm because the fabric forms a loop. Fabric 1 has a broad range of possible center heights with no error (20cm < yz < 50cm) . Fabrics 2-4 (Figures 4(b)-4(d)) have a narrow but nonzero range of center heights with zero error. Thus, the root finding scheme appears reasonable for these test fabrics using only three points. The algorithm starts with a three point path and p initialized to
(2) Figure 5 displays the results of the control algorithm applied to fabrics 1 through 4 using only three point trajectories and the gradient descent root finder. The center height initializes at 40 cm, half the fabric length. The average end effector velocity,
Vavg =
Trajectory Length Time
(3)
is 17.3 cm/set. Fabric 1 requires no iterations because the initial error is zero. The other three plots show the initial and final trajectories, initial and final errors, and the number of folds (Ic ) required to achieve E < E . In all cases, an acceptable solution is reached after a small number of iterations. Figure 5 also shows the initial and final E and yz values. The algorithm accurately finds the root. A three point path does not converge to an acceptable error for fabric 5. Experiments showed that E(p) # 0 with npoints = 3 for any value of y2 . The control algorithm then adds an internal point. With two internal points, the error reduces to 1.2 mm after eleven folds. A final test demonstrated the versatility of the control algorithm. The best three point trajectory for Fabric 4 at Vavs = 17.3 cm/s is tested for Vavs ranging from 7.6 to 29.3 cm/set. Small errors occur for Vavs < 25 cm/set and unacceptable large errors occur for Vavg > 27 cm/s . Activation of the control algorithm drastically improves the errors for Vavg > 25 cm/s . The controller adjusts the path at Vavs =26, 28,and 29 cm/set to achieve less than half the uncontrolled error. COMPUTER
SIMULATION
A computer simulation tool has been developed that allows modeling of various fabric manipulation processes that occur during manufacturing. Fabric parts are modeled as very
228
National Textile Center Annual Report: November 1996
(bl Fabric 1
150 t
0
20
60
80
-100’
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40 ~2 (cm)
60
80
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+++
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Figure 4- Fabric Motion Error for Three Point Trajectories: ‘+’ Data Points; ‘0’ Algorithm Starting Point; ‘*’ Algorithm Ending Point flexible elastic beams that can accommodate stretching and bending in a single plane. The governing equilibrium equations are solved using the finite element method. The nonlinear moment curvature response is measured directly with the Kawabata Test System, or with a simpler drape test. Realistic manipulation processes involve interaction of fabric parts with other objects such as: work surfaces, robot manipulators, other fabrics. Therefore, the ability to model contact has been implemented. A key aspect of this research was development of a capability to determine optimum ways to manipulate fabric parts while minimizing sliding of the fabric or forces generated in the fabric. This feature allows intelligent selection of initial manipulation paths for the control system just described. Details of the finite element approach are given in [12] and [13]. CONCLUSIONS Repeatable fabric handling operations can be controlled using an iterative approach.
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Figure 5- Initial ( o ) and Final ( x ) Trajectories for Four Fabrics Using Three Points For four of the five fabrics tested in this research, simple three point trajectories provide errors of less than 1.2 mm in less than 6 folds. A fifth fabric, with a very high stiffness to weight ratio, required a four point trajectory and 11 folds to achieve an error of less than 1.2 mm. The control system adapts the folding trajectory in response to changes in speed and fabric properties. This control concept can be applied to many fabric handling operations requiring accurate position control.
III. STUDENT PROGRESS Woodrow Clifton is the first student to graduate with an advanced degree after completing research sponsored by the NTC. He earned his MS in Mechanical Engineering at NC State in June 1996 under the direction of Dr. J. W. Eischen. He is now employed
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s95-20, 9 by the BASF Fiber Products Division at the Clemson Plant in Central, SC. This plant produces nylon fibers for the carpet industry. He wrote a paper that will be presented at the Pan American Congress of Applied Mechanics Conference. Steve Mast is finishing his Master’s thesis under the guidance of Drs. Paul and Rahn. He wrote a paper that has been submitted to the International Journal of Clothing Science and Technology based on his work in iterative fabric folding control. He is currently employed by Secor in North Carolina. Sandeep Joshi is developing advanced sensors and control algorithms for fabric positioning on a surface with friction. He has completed his first year in the MS program and has designed and constructed a test stand. He is now implementing adaptive fabric. position controllers. Nick Costescu is a Ph.D. candidate electrical engineering student who is working part time on this project. He provides advice and guidance on electronics design, computer interfacing, and software development for the experiments.
IV.
INDUSTRY
COLLABORATION
A video tape has been prepared to illustrate the capabilities of our Puma robot and the associated sensors. This tape will be used in upcoming meetings with industry to facilitate understanding our research approach. Jud Early at TC2 is supportive of the goals and objectives of this research project and has agreed to meet with us and provide input regarding the direction of our experimental work. Leonard Brewington at Milliken has also been supportive of our work and believes it may have an application in airbag manufacturing. During the Fall of 1996 we plan to visit several Milliken airbag plants. It is our intention to tailor our experimental investigation towards fabric handling problems that are relevant to industry problems.
V. PUBLICATIONS [l.] “Iterative Techniques for Fabric Position Control During Folding,” submitted to International Journal of Clothing Science and Technology, June 1996. [2.] “Finite-Element Modeling and Control of Flexible Fabric Parts,” IEEE Computer Graphics and Applications, Special Issue on Computer Graphics in Textiles and Apparel, Volume 16, Number 5, pgs. 71-80, (Invited Paper) [3.] “Optimum Manipulation Strategies for Limp Fabric Materials,” with W. Clifton, to appear in the Proceedings of the Fifth Pan American Congress of Applied Mechanics Conference, San Juan, Puerto Rico, Jan. 1997. [4.] “Optimum Fabric Trajectories for Edge Position and Control,” Clifton, W., MS Thesis, North Carolina State University, 1996.
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VI. REFERENCES [ 1.1 Charles Stark Draper Lab, Inc., Report on the Fourth-Year Research and Development Program for the Tailored Clothing Technology Corporation, June 28, 1985. [2.] Jones, S.H., MITI: Progress Report, Apparel Ind., Feb. 1985, pp. 46-49. [3.] Taylor P.M. and G.E. Taylor, “Progress Toward Automated Garment Manufacture”, Sensory Robotics For the Handling of Limp Materials, ed. Paul M. Taylor, 1990. [4.] Gunner, M.B., P.M. Taylor, and A. J. Wilkinson, “Placing Fabric onto Moving Surfaces”, International Journal of Clothing Science and Technology, Vol. 2 No. 3/4, 1990, pp. 56-64. [5.] Brown, P.R. III, D.R. Buchanan, and T.G. Clapp, “Large-deflection Bending of Woven Fabric for Automated Material-Handling”, Textile Research Journal, Vol. 81 No. 1, 1990, pp. 1-14. [6.] Konopasek, M. and J.W.S. Hearle, “Computational Theory for Bending Curves. Part I: The Initial Value Problem for the Three-Dimensional Elastic Bending Curve”, Fibre Science and Technology, Vol. 5, 1972, pp.= l-28. [7.] Eischen J.W. and Y.G. Kim, “Optimization of Fabric Manipulation during Pick/Place Operations”, International Journal of Clothing Science and Technology, Vol. 5 No. 3/4, 1993, pp. 68-76. [8.] Clupicker Manual, Jet Sew, Barnevelde, New York. [9.] National Textile Center 1995 Annual Report, pp. 275-281. [IO.] Astrom, K.J. and B. Wittenmark, Adaptive Control, Addison Wesley, Reading MA, 1989. [ll.] Powell. M.J.D, “An Efficient Method for Finding the Minimum of a Function of Several Variables Without Calculating Derivatives”, Computer Journal, Vol. 7, 1965, pp. 155-162. [ 12.1 “Finite-El ement Modeling and Control of Flexible Fabric Parts,” IEEE Computer Graphics and Applications, Special Issue on Computer Graphics in Textiles and Apparel, Volume 16, Number 5, pp. 71-80. [13.] “Optimum Fabric Trajectories for Edge Position and Control,” Clifton, W., MS Thesis, North Carolina State University, 1996.
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