TPF-I SWG Report - Exoplanet Exploration Program - NASA

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 TPF-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.
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