1. SPACECRAFT FORMATION FLYING
A SIMULATION TOOL TO DESIGN SATELLITE FORMATIONS
Aykut Kutlu1 and Prof.Dr. Ozan Tekinalp2
Middle East Technical University
Ankara, Turkey
[1PhD Student, Aerospace Engineering Department,
[2]Professor, Aerospace Engineering Dept.,
ICATT-2016

2. SPACECRAFT FORMATION FLYING
Contents
Introduction, Definitions
Simulation Tool Details
Graphical User Interface: Main and Sub Windows
Modeling Relative Motion Using the Keplerian Formulation
Modeling Relative Motion Using Orbital Elements
Modeling Desired Formation Flight: ICs Computation Methods
Projected Circular Orbit based ICs computation [1]
Geometrical Relative Orbit Modeling based ICs Computation[2]
Optimization based ICs Computation
Analyses and Results

3. SPACECRAFT FORMATION FLYING
Introduction, Definitions
Definition done by NASA’s Goddard Space Flight Center (GSFC) :
“an end-to-end system including two or more space vehicles and a
cooperative infrastructure for science measurement, data acquisition, processing, analysis and distribution”.
Approaches defined for FF
Orbit Tracking
Each satellite is controlled to a particular predetermined desired orbit.
Leader/Follower
Leader spacecraft is controlled to a reference orbit and the other follower spacecraft in the formation control their relative stated to that leader.
Virtual Structure
Virtual structure and virtual center approaches fit a set of desired states to a formation in a way that minimizes the overall state error of the formation.
 Swarming
Simple heuristic control laws for arranging arbitrarily large numbers of vehicles into regular arrangements based on local information.

4. Simulation Tool

5. Modeling Relative Motion
Keplerian Formulation
Equations of Relative Motion in the unperturbed case:

6. Modeling Relative Motion
Chief’s orbit propagation
The chief’s position is computed using an orbit propagator including the variation of the mean classical orbital elements. The perturbations due to non-spherical earth (J2), due to moon and sun are included on the computations.
As known, Kepler’s equation states that:
J2 perturbations:

7. Modeling Relative Motion
Keplerian Formulation, Simulation Block Diagram

8. Simulation Tool

9. Simulation Tool

10. Simulation Tool

11. Modeling Relative Motion
Orbital Elements Formulation

12. Formation Design via OEs
Orbital Elements Formulation Block Diagram
Initial distance
&
phase angle
Initial
Orbital
Elements

13. Comparaison of the modeling methods
Kepler Formulation VS Orbital Elements Formulation
These two different modeling methods give different solution for the relative motion analyses. For example for initial relative conditions given as

14. Comparaison of these two modeling methods
Kepler Formulation VS Orbital Elements Formulation
it is seen that the obtained motion dynamics is critically different, especially for y axis relative motion. For a very specific the initial condition values, it is possible to obtain the similar dynamic for both the modeling method, for:

15. Modeling Desired Formation Flight
Initial Conditions Computation:
Along Track and Cross Track ICs for Projected Circular Orbit (PCO-ICs) [1]
An approximate solution to determine the initial conditions for near circular orbit
Formation Design with desired distance and angular position: the along track and the cross track initial conditions

16. Modeling Desired Formation Flight
Initial Conditions Computation:
Geometrical Relative Orbit Modeling (GROM) [2]
Spherical geometrical representation of the relative motion
A set of equation to determine the orbital parameters of the deputy satellite for desired relative orbit size (along track (Ay) and cross track (Az) distance) and the relative phase angle ψ [2]:
Figure 8. Geometrical Relative Orbit Modeling [2]

17. Modeling Desired Formation Flight
Initial Conditions Computation:
Optimal ICs, performs optimization to determine the Initial Conditions (OPTICs)
Question: Is it possible to find ICs set that ensure formation flight scheme for any arbitrary desired formation scheme, by using an OPTIMIZATION method ?
A minimization function based on the Energy Matching Approach, that theoretically guaranties the formation flight, is written:
The initial relative positions are described by a desired azimuth, desired elevation angle and desired distance. The initial position in Cartesian coordinate system according to the desired azimuth and elevation

18. Analyses and Results 3 Diferent Cases are taken into consideration
Orbital elements values of the Chief satellite

19. Orbital Elements based Modeling
Analyses and Results
PCO-ICs’ Results
PCO-ICs, Case-1 Results
Results using
Nonlinear Modeling
Results using
Orbital Elements based Modeling

20. Orbital Elements based Modeling
Analyses and Results
PCO-ICs’ Results
PCO-ICs, Case-2 Results
Results using
Nonlinear Modeling
Results using
Orbital Elements based Modeling

21. Orbital Elements based Modeling
Analyses and Results
PCO-ICs’ Results
PCO-ICs, Case-3 Results
Results using
Nonlinear Modeling
Results using
Orbital Elements based Modeling

22. Orbital Elements based Modeling
Analyses and Results
GROM’s Results
Case-1 Results
Results using
Nonlinear Modeling
Results using
Orbital Elements based Modeling

23. Orbital Elements based Modeling
Analyses and Results
GROM’s Results
Case-2 Results
Results using
Nonlinear Modeling
Results using
Orbital Elements based Modeling

24. Orbital Elements based Modeling
Analyses and Results
GROM’s Results
Case-3 Results
Results using
Nonlinear Modeling
Results using
Orbital Elements based Modeling

25. Analyses and Results OPT-ICs’ Results Case-1 Results Case-2 Results
Results using
Nonlinear Modeling
Results using
Nonlinear Modeling

26. Analyses and Results OPT-ICs’ Results Case-3 Results Results using
Nonlinear Modeling

27. Analyses and Results Long-time (10 days) simulations results
Case-1 Results
The relative distances computed at the end of the 10th day are approximately 4 km for Case-1.

28. Analyses and Results Long-time (10 days) simulations results
Case-2 Results
The relative distances computed at the end of the 10th day are approximately 10 km for Case-2.

29. Analyses and Results Long-time (10 days) simulations results
Case-3 Results
The relative distances computed at the end of the 10th day are approximately 7 km for Case-3.
These results can be considered as a efficiency measure of the OPT-ICs.

30. Analyses and Results OPT-ICs’ Results
For a desired elevation and azimuth:
x_dot_0 = e+01 m/sec
y_dot_0 = e+02 m/sec
z_dot_0 = e+00 m/sec
x_0 = e+05 m
y_0 = e+05 m
z_0 = e+05 m

31. Simulation Tool – Post Processing

32. Simulation Tool – Post Processing

33. Conclusion
In this study, the common methods used for satellite formation flight are presented.
The main goals were to present the developed simulation tool and to present the results obtained according to the approaches and models used
According to the results, it seen that that the optimization based method, OPTICs ensures the desired formation flight for any arbitrary flight scheme (relative distance and initial phase angle) and provides more stable, long-term flight compared to the other two methods.
OPTICs provides reliable ICs for an initial relative position having both elevation and azimuth angles. It means that is it possible to define desired initial relative position in three dimensions, in XYZ axis frame. OPTICs provides ICs that ensure the formation flight for any desired initial position.

34. References
[1] Alfriend K.T., Vadali S.R., Gurfil P., Jonatan P.H., Breger L.S. , Spacecraft Formation Flying, Dynamics, Control and Navigation, Elsevier, Bulrington, MA, USA, 2010.
[2] S.Sub Lee, Dynamics and Control of Satellite Relative Motion: Designs and Applications, PhD. Dissertation, Blacksburg, Virginia March 20, 2009
[3] Chris Sabol, Rich Burns, and Craig A. McLaughlin., “Satellite Formation Flying Design and Evolution”, Journal Of Spacecraft And Rockets, Vol. 38, No. 2, March–April 2001
[4] H.Cui, J.Li, Y.Gao. (2006), “An Orbital Design Method for Satellite Formation Flying", Journal of Mechanical Science and Technolojy, Vol.20, No.2,pp ,2006.
[5] Mark B. Milam, Nicolas Petit, and Richard M. Murray., “Constrained Trajectory Generation For Micro-Satellite Formation Flying”, AIAA , California Institute of Technology.

35. THANK YOU ?