- Email: [email protected]
Celestial Star Determination Using Artificial Neural Networks
8a-06 1
Copyright © 1996 IFAC 13th Triennial World Congress, San Francisco, USA
CELESTIAL STAR DETERMINATION USING ARTIFICIAL NEURAL NETWORKS Thomas Lindblad, Clark S Lindsey Royal Institute of Technology, Department of Physics, Frescativagen 24, S-I04 05 Stockholm, Sweden [email protected]
and
Age Eide Ostfold College, Os Alle 11, N-1757 Halden, Norway
Abstract: In the present paper we suggest the use of artificial neural networks in hardware for the use with star trackers on satellites. In particular micro-satellites should benefit from this low weight solution. Other features of the approach is the redundancy of neural networks, their ability to generalize, noise resistance and speed. Keywords: Attitude control, aerospace, satellite control, neural networks
1. INTRODUCTION Star trackers are devices for satellites and space probes designed to determine with high precision the attitude of the vehicle with little or no any a-priori knowledge. An image of some stars is used and serves as the basis to find the full attitude knowledge instantaneously. This information may just be used for reference (coordinate mark) in connection with other instruments or serve as a part of an attitude stabilising system. Controlling the attitude implies that there is a "desired situation", and some force or forces are present to the system to change the attitude. Both reactions to the "disturbing forces" and a reference for the desired situation must be supplied to the control system. The objective of the star tracker is to provide the reference. The star tracker is composed of optics, a charge-coupled device (CCO) detector, read-out electronics and some digital processors with pertinent auxiliary devices.
A typical star tracker may have a field of view (FoV) of 20 x 20 degrees, a 512x512 CCO and a sensitivity range of magnitude M - +0.1 to + 4.5. These characteristics yields a > 50% probability of up to ten stars in the FoV. The star catalogue on the onboard computer typically involves some 2000 stars making it possible to determine the attitude to within 10 - 50 arc sec every 0.2 second. For spinning vehicles one may have to give up accuracy in the case of large angular velocities. Sensitivity, accuracy and the number of stars seen during a single revolution are essential inputs in order to optimize the system. The processor mentioned above is generally a conventional von Neumann device. However, the fact that the recorded star intensity varies, the revolution speed may vary, etc calls for a certain slack in operation. This may imply that an artificial neural network ANN may be used. For micro-satellites, such an ANN solution should also
7470
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2. ATTITUDE AND CONTROL While some experiments on-board a space craft may require a stable pointing platform other experiment have short integration time and require only the celestial angles at the time of the measurement. Some experiments may require only the pointing angles, while others may also require the rotation angle. Small and micro satellites may not even be equipped with a control systems, but still the experiments on board may require that the attitude be known. This means that to a certain extent the problem of attitude determination and attitude control is decoupled. The attitude determination will, however, depend strongly on the stabilization of the satellite. Small satellites are generally spin stabilized, which will impose certain requirements on the star tracker as well as on the position on board the satellite.
3.
b
a
provide a system which is lighter than conventional ones (typically in the range of 2.5 - 3 kg).
..
c
•
• d
M
Radius/rom uguide starU Fig. 1. Preprocessing for star pattern recognition. A recorded CCD-image is shown in a. The brightest star (the guide star) is found in b and a pattern field of view (pattern FOY) is defined having half the FOY of the the sensor. The star within the pattern-FOY are found in c and their intensity (magnitude M) as a function of the radius from the guide star is plotted in d.
CELESTIAL ATTITUDE DETERMINATION Generally the spacecraft uses its sun (or horizon) sensor to slew until the sensor has locked onto the sun (horizon). If a three-axis orientation is required, the vehicle is rotated around the axis to the sun to fmd an appropriate star pattern in a direction perpendicular to the solar equator. This is a fairly slow process that uses the thrusters and actuators extensively. A "star pattern recognition system" typically consists of the following components: Optics assembly CCD Preprocessor system Computer system The CCD records a (sometimes defocused) portion of the sky. Electronic systems determine both the centroids of each star in the FOV and their intensities. Following preprocessing, which possibly includes noise removal as well, a so called 'pattern field of view' is defined around the brightest star. This star will be referred to as the guide star (marked with a large "+" in fig. 1) The pattern FOV is a circular one and has half the radius of the sensors FOV. The preprocessor will measure the linear distance be-
tween each star and the guide star and store this value together with the relative intensity of the star. We have now obtained an image that is invariant to translation and rotational perturbations. It should be stressed that we recognise a "fingerprint" of a particular guide star and surrounding weaker stars. In order to determine the direction of the optical axis of the star camera we have to add the angle between the center of the CCD image and the guide star. In practice this is obtained from the pixel position of the guide star relative to the center of the image. In the case of a star tracker for a spin stabilized satellite, there would be a preprocessor to include this rotation. A commercial stellar attitude sensor, like e.g. the CT633 of Ball Corp., generally has an autonomous mode of operation (star search, acquisition, track, and identification; attitude update) and a standard data interface. The CT-663 has a 20x20 deg. FOV, 512x512 pixel CCD detector, and a sensitivity that with >90% (59%) probability results in at least six (eleven) stars in the FOV - The star catalogue contains 2000 stars.
7471
7472
7473
Copyright © 1996 IFAC 13th Triennial World Congress, San Francisco, USA
CELESTIAL STAR DETERMINATION USING ARTIFICIAL NEURAL NETWORKS Thomas Lindblad, Clark S Lindsey Royal Institute of Technology, Department of Physics, Frescativagen 24, S-I04 05 Stockholm, Sweden [email protected]
and
Age Eide Ostfold College, Os Alle 11, N-1757 Halden, Norway
Abstract: In the present paper we suggest the use of artificial neural networks in hardware for the use with star trackers on satellites. In particular micro-satellites should benefit from this low weight solution. Other features of the approach is the redundancy of neural networks, their ability to generalize, noise resistance and speed. Keywords: Attitude control, aerospace, satellite control, neural networks
1. INTRODUCTION Star trackers are devices for satellites and space probes designed to determine with high precision the attitude of the vehicle with little or no any a-priori knowledge. An image of some stars is used and serves as the basis to find the full attitude knowledge instantaneously. This information may just be used for reference (coordinate mark) in connection with other instruments or serve as a part of an attitude stabilising system. Controlling the attitude implies that there is a "desired situation", and some force or forces are present to the system to change the attitude. Both reactions to the "disturbing forces" and a reference for the desired situation must be supplied to the control system. The objective of the star tracker is to provide the reference. The star tracker is composed of optics, a charge-coupled device (CCO) detector, read-out electronics and some digital processors with pertinent auxiliary devices.
A typical star tracker may have a field of view (FoV) of 20 x 20 degrees, a 512x512 CCO and a sensitivity range of magnitude M - +0.1 to + 4.5. These characteristics yields a > 50% probability of up to ten stars in the FoV. The star catalogue on the onboard computer typically involves some 2000 stars making it possible to determine the attitude to within 10 - 50 arc sec every 0.2 second. For spinning vehicles one may have to give up accuracy in the case of large angular velocities. Sensitivity, accuracy and the number of stars seen during a single revolution are essential inputs in order to optimize the system. The processor mentioned above is generally a conventional von Neumann device. However, the fact that the recorded star intensity varies, the revolution speed may vary, etc calls for a certain slack in operation. This may imply that an artificial neural network ANN may be used. For micro-satellites, such an ANN solution should also
7470
tI
.:fi
2. ATTITUDE AND CONTROL While some experiments on-board a space craft may require a stable pointing platform other experiment have short integration time and require only the celestial angles at the time of the measurement. Some experiments may require only the pointing angles, while others may also require the rotation angle. Small and micro satellites may not even be equipped with a control systems, but still the experiments on board may require that the attitude be known. This means that to a certain extent the problem of attitude determination and attitude control is decoupled. The attitude determination will, however, depend strongly on the stabilization of the satellite. Small satellites are generally spin stabilized, which will impose certain requirements on the star tracker as well as on the position on board the satellite.
3.
b
a
provide a system which is lighter than conventional ones (typically in the range of 2.5 - 3 kg).
..
c
•
• d
M
Radius/rom uguide starU Fig. 1. Preprocessing for star pattern recognition. A recorded CCD-image is shown in a. The brightest star (the guide star) is found in b and a pattern field of view (pattern FOY) is defined having half the FOY of the the sensor. The star within the pattern-FOY are found in c and their intensity (magnitude M) as a function of the radius from the guide star is plotted in d.
CELESTIAL ATTITUDE DETERMINATION Generally the spacecraft uses its sun (or horizon) sensor to slew until the sensor has locked onto the sun (horizon). If a three-axis orientation is required, the vehicle is rotated around the axis to the sun to fmd an appropriate star pattern in a direction perpendicular to the solar equator. This is a fairly slow process that uses the thrusters and actuators extensively. A "star pattern recognition system" typically consists of the following components: Optics assembly CCD Preprocessor system Computer system The CCD records a (sometimes defocused) portion of the sky. Electronic systems determine both the centroids of each star in the FOV and their intensities. Following preprocessing, which possibly includes noise removal as well, a so called 'pattern field of view' is defined around the brightest star. This star will be referred to as the guide star (marked with a large "+" in fig. 1) The pattern FOV is a circular one and has half the radius of the sensors FOV. The preprocessor will measure the linear distance be-
tween each star and the guide star and store this value together with the relative intensity of the star. We have now obtained an image that is invariant to translation and rotational perturbations. It should be stressed that we recognise a "fingerprint" of a particular guide star and surrounding weaker stars. In order to determine the direction of the optical axis of the star camera we have to add the angle between the center of the CCD image and the guide star. In practice this is obtained from the pixel position of the guide star relative to the center of the image. In the case of a star tracker for a spin stabilized satellite, there would be a preprocessor to include this rotation. A commercial stellar attitude sensor, like e.g. the CT633 of Ball Corp., generally has an autonomous mode of operation (star search, acquisition, track, and identification; attitude update) and a standard data interface. The CT-663 has a 20x20 deg. FOV, 512x512 pixel CCD detector, and a sensitivity that with >90% (59%) probability results in at least six (eleven) stars in the FOV - The star catalogue contains 2000 stars.
7471
7472
7473