TPF-I SWG Report - Exoplanet Exploration Program - NASA

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A PPENDIX C 2. Identical FACS flight software load on all S/C a. Each S/C FACS S/W is capable of taking on the formation leader/follower role. Formation and Attitude Control System (FACS) Algorithms Formation Estimator The formation estimator optimally combines measurements from multiple sensors and produces estimates of different accuracy and bandwidth using an extended Kalman filter – to produce inter-s/c range and bearing estimates. In the case of the <strong>TPF</strong>-I mission, each of the spacecraft will have a variety of sensors for different phases of the mission. The formation-estimator algorithm will optimally combine the available sensor signals to provide the best inertial attitude estimate of each spacecraft and also the s/c-to-s/c relative position estimate. A high-level architecture and representative simulation is shown in Fig. C-2. Formation estimation consists of estimating both local spacecraft attitude and the relative position of all the other spacecraft in the formation. The latter we refer to as translation estimation. Attitude Estimation The attitude estimator determines the attitude of a spacecraft body frame with respect to an inertial frame, given star tracker and gyroscope measurements. Each spacecraft estimates its own attitude, and only local information is required. Estimation in general consists of a propagation step based on the physics-based dynamic model and an update step in which sensor measurements are combined with the propagated estimate. The spacecraft attitude depends on applied torques (e.g., from thruster and reaction wheels), which are governed by Euler’s equations. Although Euler’s equations are an accurate representation of the spacecraft dynamics, the input torques due to thruster firings are difficult to model. Hence, Euler’s equations do not provide an accurate means of propagating the attitude states of the spacecraft. Instead a kinematic model is used (i.e., relating angular velocity to attitude) where the angular velocity is measured by the gyroscopes. The sensor measurement for the update step comes from the star tracker(s). Another important aspect of the attitude estimation problem is that gyroscopes have biases. The bias of each gyroscope must be added to the attitude estimation problem to obtain accurate estimates. Combining a gyroscope model with the kinematic attitude equation, one can obtain an equation for the errors in the attitude and bias estimates. Based on the above model, an optimal Kalman estimator has been designed. Translation Estimation On each spacecraft the translation estimator estimates the position of every other spacecraft in the formation with respect to itself. One complication in relative translation estimation is that it is coupled one way to attitude estimation. Relative sensors provide measurements between sensor frames on respective spacecraft. However, since a center-of-mass to center-of-mass (CM) relative position vector is desired for control, the estimator must transfer from the two sensor frames (one on each spacecraft involved in the measurement) to an inertial frame. This transfer requires the attitudes of both spacecraft. 176
F ORMATION F LYING A L G O R I T H M D E V E L O P M E N T Figure C-1. Formation & Attitude Control System Architecture. The measurement update for the translation estimator is much more complex than for the attitude estimator because there are three levels of inter-spacecraft sensing (acquisition, medium, and fine) and these measurements are in terms of range and bearings; whereas, the state is in terms of Cartesian relative position. Each sensor measurement must also be transformed. The relative translation estimator has two components: 1) a Kalman filter; and 2) an acceleration data processing (ADP) algorithm, which produces bias-corrected CM acceleration estimates. 1. Including all the necessary transformations and incorporating communicated data, an optimal Kalman estimator has been designed for the translation degrees of freedom. As each more precise level of sensing is acquired, the error in the estimate decreases. With the precision sensors locked, the resulting error that has been simulated is on the order of a few tens of millimeters, which meets the requirements for <strong>TPF</strong>-I. 177
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JPL Publication 07-1 Terrestrial Pl
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Abstract Over the past two years, t
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Acknowledgements Twenty-two represe
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Table of Contents 1 Introduction...
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4.8.3 Post-Nulling Calibration.....
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6.4.5 Double Fourier Interferometry
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I NTRODUCTION 1 Introduction Over 2
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I NTRODUCTION et al. 2004), and res
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I NTRODUCTION Standard Interferomet
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I NTRODUCTION 1.4 References Angel,
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C HAPTER 2 0.7 to 1.5 AU scaled by
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C HAPTER 2 Table 2-2. Illustrative
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C HAPTER 2 Classical interferometry
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C HAPTER 2 trivial in the absence o
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C HAPTER 2 Figure 2-3. Simulated mi
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C HAPTER 2 would be in atmospheres
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C HAPTER 2 Figure 2-6. The mid-infr
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C HAPTER 2 Lines of constant stella
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C HAPTER 2 presence of zodiacal clo
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C HAPTER 2 S EZ 2π ∫ θ max ∫
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C HAPTER 2 Figure 2-11. Observation
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C HAPTER 2 Figure 2-12. Models of t
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C HAPTER 2 Beichman, C. A., Fridlun
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C HAPTER 2 2.7.4 Suitable Targets E
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C HAPTER 2 Reach, W. T., Franz, B.
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C HAPTER 3 3.1.1 Darwin/TPF-I Prope
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C HAPTER 3 clouds or an OB associat
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C HAPTER 3 Figure 3-3. Three possib
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C HAPTER 3 the circumstellar disk,
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C HAPTER 3 Figure 3-6. (Left panel)
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C HAPTER 3 Continuum interferometry
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C HAPTER 3 Figure 3-9: Simulated im
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C HAPTER 3 3.3 Conclusions Darwin/T
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C HAPTER 3 Nguyen, H. T., Kallivaya
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D ESIGN AND A R C H I T E C T U R E
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C HAPTER 5 Heavy launch vehicle. Th
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C HAPTER 5 5.3.2 Combiner Spacecraf
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C HAPTER 5 5.3.5 Beam Transfer betw
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C HAPTER 5 Figure 5-8. Control sche
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C HAPTER 5 Figure 5-9. First sectio
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C HAPTER 5 Figure 5-9 shows the fir
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C HAPTER 5 5.4.4 Shear Metrology Sh
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C HAPTER 5 Figure 5-15. TPF-I Fligh
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C HAPTER 5 secondary mirror along t
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C HAPTER 5 a) c) b) d) IWA = 43 mas
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C HAPTER 5 planets found. Figure 5-
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C HAPTER 5 30 25 5 M earth 3 M eart
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C HAPTER 5 5.8.4 Angular Resolution
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Page 145 and 146: T E C H N O L O G Y R OADMAP FOR TP
Page 173 and 174: F UTURE D EVELOPMENTS 7 Preparatory
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Page 177 and 178: F UTURE D EVELOPMENTS Table 7-1. Pr
Page 179 and 180: D ISCUSSION AND C ONCLUSION 8 Discu
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Page 183 and 184: T E C H N O L O G Y A DVISORY C O M
Page 185 and 186: F L I G H T S YSTEM C ONFIGURATION
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Page 194 and 195: A PPENDIX C Once the formation has
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Page 198 and 199: A PPENDIX C Figure C-4. FAST Flight
Page 200 and 201: A PPENDIX C The “true” time of
Page 202 and 203: A PPENDIX C References Cohen, S., a
Page 204 and 205: A PPENDIX D DC DCB DM DM DOCS DOD D
Page 206 and 207: A PPENDIX D NaCl NAR NASA NASTRAN N
Page 208 and 209: A PPENDIX E Appendix E TPF-I Review
Page 210 and 211: A PPENDIX F Alice Quillen, Universi
Page 212: A PPENDIX F Figure 3-1 - Original f
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TPF-I SWG Report - Exoplanet Exploration Program - NASA

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