St-Hubert, Quebec, Canada J3Y 8Y9

ABSTRACT

 In this paper, a vision system is introduced and used to measure the flatness of an inflatable structure membrane. The principle of the vision system, calibration and measurement steps are introduced first. Then it is used to measure a 200mm×300mm Kapton membrane. The results show that very good accuracy (on the order of 0.1mm) can be achieved. The measurement speed is also very fast, it takes less than 0.1s to get 300points in 3D coordinates.

We are currently working on an in-house R&D project in the development of a large surface area to mass ratio inflatable space structure with possible applications as a Synthetic Aperture Radar (SAR) antenna. It is expected that the membrane will be subjected to flatness problem during its lifetime in orbit due to the thermal variation in space. A pure passive control method may not be sufficient to maintain the membrane flatness. Hence an active control system is currently being studied to adjust the boundary tensions according to the thermal variation.

Fig. 1 Sketch of Inflatable Structure

  A practical difficulty to realize an active control system is how to measure the membrane flatness in space. We have developed an estimation scheme using neural network, which maps boundary stretching tensions Membrane and space environment (mainly the temperature) to membrane flatness. After neural network training completes, the membrane flatness can be estimated by inputting the measured stretching tensions and space environment to the neural network model. To train the neural network coefficients, stil we need to measure the membrane using non-contacting measurement system. In this paper, a vision system is introduced and used to measure the membrane flatness. System principle, calibration, measurement steps are introduced. The results show that very fast speed (it takes less than 0.1s to get 300 points in 3D coordinates) can be obtained with very good accuracy (on the order of 0.1mm).

The vision system Automation Manager is a high-resolution high-speed measurement system developed by Soft Automation Inc. It consists of a Del P4 2.4GHz computer, a light projector and a 1300×1000 pixels CMOS camera. Normally, one camera can only capture a 2D image at a time, and cannot give 3D coordinates of points on an object surface by a single image. That is why Photogrammetry technique needs multiple pictures to extract 3D coordinates of points on a physical object. These pictures can be taken either by multiple cameras placed at different locations, or by moving one camera through different locations. Photogrammetry technique also needs to perform referencing to identify which marked point in each image is the same physical point on the object. Manual intervention is usually required to ensure correct referencing, and this may take much time. So the photogrammetry technique is unacceptable for our tests since fast measurement is required. In order to obtain fast measurements, the Automation Manager vision system uses only one image to determine 3D coordinates of points, but with the aid of calibrated light planes projected by a projector. The concept is illustrated in Figure 2.

Fig2. Principal of Vision System

The projector projects a light plane at around 45 degree angle onto the object surface, which produces an intersection curve or a straight line if the surface is flat. For any point on the intersection, it is seen by the camera through a straight line radiating from the camera focal point to the selected point. Therefore its location can be determined as the intersection point of the light plane and the radiating line. Its coordinates can be easily calculated if the light plane equation and the radiating line equation are known. Project more light planes to cover the whole area of interest, and choose more points on each intersection curve, we can easily determined the object surface flatness by calculating the 3D coordinates of these selected points.

Camera Calibration

[x,y,z,1][M] = [u,v,t]

Light Planes Calibration

 Light planes calibration determines the equations of light planes projected by the projector. The calibration procedure uses the same rig as the camera calibration that set a plate at 2 different heights (the heights are known). But this time there is no target on the plate. At each height the projector is turned on and multiple lines are projected on the plate. To calibrate a light plane, take multiple points on the two lines projected on the plate by this light plane (at 2 heights). Because camera calibration has completed, the U and V coordinates for these points and corresponding radiating line equations can be easily determined. Substitute the known z coordinates of these points into the corresponding radiating line equations, x and y coordinates are then obtained.

 With these obtained 3D coordinates, a light plane equation can be determined by solving an eigenvalue problem:

[W][P]= 0

Measurement Procedure

 For a specific observed point, its U and V coordinates can be easily identified first.

Then the equation of the corresponding radiating line can be expressed as the intersection of 2 planes:

[x, y ,z] [L]= K

Measurement Accuracy

 In practical flatness measurement, the projector shines dark strips (instead of lines) on the membrane. The two edges of each strip corresponds to two light planes. The vision system uses a standard edge finding method, which can typically find edges to 0.1 pixels.

After applying calibrations, the system accuracy is on the order of 0.1 mm for a field of view of 500mm×500mm. To improve measurement accuracy, lens distortion compensation can be applied. A laser projector is also helpful to achieve better accuracy, since sharper line edges can be obtained.

Membrane Flatness Calculation

 With the obtained 3D coordinates of the points distributed on the membrane, the membrane flatness is defined as the standard deviation of these points. The calculation of the standard deviation involves the same procedure as light plane calibration. Substitute all the obtained 3D coordinates into Eq.(8) and Eq.(9) (not shown), the standard deviation is then the square root of the smallest eigenvalue of W divided by the total number of points. The corresponding eigenvector determines the least square best-fit plane, given as Eq.(10) (not shown).

MEMBRANE FLATNESS MEASUREMENT

 The membrane to be measured is a 200mm×300mm rectangular Kapton Membrane stressed by 3 tensions along each edge. To actively control the membrane flatness, shape memory alloy actuators and strain gages are installed with the links. The whole setup and the link design are shown in Figure 3 and Figure 4. A very thin coating is put on one side of the membrane such that the intersection curves projected on it can be seen clearly.

Fig 3 Picture of the membrane structure

 To calibrate the camera, two flat aluminum plates are used. One is used as the base plate and the other as the reference plate. A pattern of 117 dots is printed on a paper, which is then glued on the reference plate. The reference plate is then placed above the base plate supporting by four posts. To have different heights of the reference plate, totally eight posts are produced, four of them are 20mm high and the other four are 40mm high. Three positioning brackets are mounted on the base plate to ensure no in-plane displacement occurs when the reference plate is put at the two different heights. Figure 5 shows the two plates and how they are placed.

Fig 4 Arrangment of actuator and sensors

Mount the camera about 1.5m above the two plates (Here only one camera is used. The second camera shown in the picture is only for future use to cover larger area). A 3D Cartesian coordinate system is established, shown in Figure 6. Using the camera calibration program, the camera calibration matrix is determined. It should be noticed that the coordinate is not a physical object established on the reference plate, instead it is only a set of reference information memorized by the measurement software. For performing measurement, the reference plate and base plate will be removed and the structure to be measured will be placed here.

(a) Base Plate, Positioning Brackets and Post

(b) Base Plate, Reference Plate and Dot Targets

Fig 5 Base Plate and Reference Plate for camera calibration

Fig 6 3d Cartesian coordinate system and camera calibration

For light plane calibration, we use the same base plate, reference plate, positioning brackets and posts, but the paper glued on the reference plate with printed targets is replaced by a blank paper. To have multiple light planes, a gobo, shown in Figure 7, is designed, manufactured and installed on the projector. Mount the projector at around 45 degree angle and adjust its focus, multiple dark strips are projected on the reference plate (Figure 8). Each strip has two edges, which correspond to two light planes. From right to left, twenty-two light planes are selected (these light planes cover the area of the membrane to be measured) and numbered from one to twenty-two. Using light plane calibration program, and changing the height of the reference plate, twenty-two light planes are calibrated. The obtained light plane parameters are listed in Table 1.

Fig 7 The gobo used for projecting planes

Fig 8 Light Planes Calibration

The light plane intercepts on x, y and z axes are shown in Figure 9. After calibration, al the identified parameters, including the camera calibration matrix and light plane equations, have been automatically input to the measurement program. Locations of the camera and the projector are now not allowed to move, otherwise calibrations have to be performed again.

It is clear from Figure 9 (a) that from right to left, the light plane intercepts on axes x and z are becoming closer to the origin (note that their values are negative and the distances to the origin are becoming smaller). However, the intercepts on axis y shown in Figure 9 (b) seem untidy. That does not imply large error has been generated in the light plane calibration procedure. Instead the seemingly disordered phenomenon results from the shape of the strips shined on the membrane. Figure 10 shows the diagram of light plane intercepts on axis y, in which two adjacent strips are projected on the x-y plane (z=0). The two straight edges of a strip are not parallel, and   the intercepts of edge i, i+1, i+2 and i+3 do not line up in the same order on axis y. This phenomenon dose not affect the measurement accuracy. It is only an issue of point distribution on the membrane.

(a) On axes x and z	(b) On axis Y

Fig 9 Light Plane Intercepts on axes

Fig 10 Diagram of Light Plane Intercepts on y axis

Furthermore, the practical strip "distortion" is not serious as shown in Figure 10. The practical absolute values of the intercepts on axis y are on the order of 10000 mm, which is around 1000 times the width of a dark strip.

   After camera and light planes are calibrated, the membrane flatness measurement is ready. Remove the two plates for light planes calibration and place the membrane structure on the table. Adjust its location such that the calibrated 22 light planes (11 dark strips) can be clearly seen on the membrane. Load measurement program into workspace, and select 15 points at each intersection curve. Run the program, it gives al the values of these 330 points coordinates. The program can also give the maximal z coordinate, the minimal z coordinate, the best fit plane of the these points and the largest amplitude of the membrane wrinkle. Figure 11 shows the membrane picture and the 330 points selected.  The point with the largest out-of-plane displacement 1.1mm is marked. Change the tension pulling the membrane to improve its flatness and perform measurement again, the largest out-of-plane displacement is now reduced to 0.18mm. It takes only 0.1s to complete one measurement of 330 points coordinates.

(b) Measurement 1	(b) Measurement 1

Figure 11 Picture of membrane with selected points extreme point marked

CONCLUDING REMARKS

 An in-house R&D project in the development of inflatable space structures is ongoing with possible applications to a Synthetic Aperture Radar (SAR) antenna. To implement an active control to improve the membrane flatness, a vision system is needed to train a neural network model, which is used to estimate membrane flatness. The required vision system needs to be able to give membrane flatness values with high speed, since numerous data are needed to train a neural network. In this paper, Automation Manager vision system is introduced and used to measure a 200mm×30mm Kapton membrane.

ACKNOWLEDGEMENT

 The authors would like to thank Mr. Frank Meyer, Creative Lifestyles Inc., for his help in preparing this paper.

REFERENCES

1. Jenkins, C.H.M. (Editor), "Gosamer Spacecraft: Membrane and Inflatable Structures Technology for Space Applications", Progress in Astronautics and Aeronautics, Vol.191, 2001.

2. Cadogan, D., Grahne M., "Inflatable Space Structures: A New Paradigm for Space Structure Design", Proceedings of the 49th International Astronautical Congress, Sept.28-Oct 2, 1998, Melbourne, Australia, IAF-98-I.1.02.

3. Lin J. K. H., and Cadogan D.P., "An Inflatable Microstrip Reflectarray Concept for Ka-Band Applications", Proceedings of the 41st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference & Exhibit, April 3-6, 2000, Atlanta, AIAA2000-1831.

4. Karooka D.K., Jensen D.W., 2001, "Advanced Space Structure Concepts And Their Development", Proceedings of the 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference and Exhibit, April 16-19, 2001, Seattle, AIAA-2001-1257.