Speaker
Mr
AYKUT kutlu
(Middle East Technical University)
Description
Aykut Kutlu and Ozan Tekinalp
Middle East Technical University
Ankara, Turkey
EXTENDED ABSTRACT
A simulation and analysis tool for satellite formation is presented. The tool models the relative motion of a chief-deputy satellite formation, offers ways of selecting proper initial conditions for the formation, and helps examine the results obtained from linear and nonlinear models.
Simulation tool is developed in MATLAB environment providing visualization of the formation. User interface of the tool is created by MATLAB GUI, giving a user friendly environment (Figure 1). In this frame, this tool computes the relative dynamics of the deputy satellite with respect to the chief satellite, calculates the required initial conditions for the deputy satellite for keeping the satellites in the desired formation, and offers the required orbital corrections. Nonlinear relative dynamic model and commonly used linear models are also included in this tool, providing an environment to compare the results of the linear and nonlinear formation design approaches.
Figure 1: Main window of the simulation tool
The tool has three main parts: Pre-processing, Processing and Post-processing. In pre-processing part, user must define the chief’s orbital parameters, initial conditions and the inputs required for the simulation. The main window for the deputy has two parts to compute its motion using Keplerian relative motion and using orbital parameters. These two main computations run two separate simulations.
After setting up the initial parameters, the processing part is run in MATLAB SIMULINK environment, to compute the relative motion of the deputy generating the outputs needed for the analysis of the formation. The block diagrams parts of the code are given in Figures 2 and 3.
Figure 2: Block diagram of model that use the Keplerian equations of motion
Figure 3: Block diagram of model with orbital elements.
An orbit propagator based on the Keplarian two-body equations of motion are used to simulate the orbital motion of the spacecraft. 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. The Kepler’s equation states that:
(1)
where, M is the mean anomaly, E is the eccentric anomaly, is the angular velocity of the orbital mean motion, is the epoch time, and is the mean anomaly at epoch. The differential equations of motion used to obtain relative dynamics of the deputy satellite with respect to chief satellite are given in Equation-2.
(2a)
(2b)
(2c)
In the above equation, are the components of the disturbance vector, and are the control forces, and and are the relative position of the follower satellite with respect to the leader satellite expressed in leader perifocal frame.
Figure 4: Position Vectors and LVLH Axes Frame
The orbital-period commensurability, energy matching condition and initial orbital conditions are the main terms that should be taken into consideration in for developing an optimal formation keeping scheme. The required initial conditions and the required orbital corrections in order to maintain the formation are computed by using this energy matching concept (Alfriend et. al., 2010).
The relative position of the deputy is also expressed using orbital elements. This method, originally suggested by G.W. Hill, and it has been widely employed in the analysis of relative satellite motion. One of the main advantages of the orbital elements approach is to obtain a non-differential relative position equation and incorporate the orbital perturbations. The deputy’s relative position defined using orbital elements is given in Equation-3 and various parameters are shown in Figure 5.
(3)
Figure 5: Orbital Elements
The post-processing part is common for both models. It provides to visualize all the parameters computed by the processing part. Some of the results that may be displayed are the relative distance between two satellites, the projection view of the relative motion, the orbital parameters (semimajor axis, inclination, etc.), thrust implementation and its value. Here, the orbital motion in a 2D Earth map and in a 3D Earth model are also used to visualize the motion (Figure 6) Furthermore, it is possible to visualize the motion by running 3D Animation. Here, the 3D motion is given with respect to ECI and ECEF frames, both in space view or satellite view (Figure 7).
Figure 6: 2D Mapping
Figure 7: 3D Animation
In the final manuscript, the details of the simulation tool will be provided. Final manuscript will focus especially on the selection of the initial conditions defined in terms of orbital elements of the chief and deputy satellites. The linear procedures used for determining the initial conditions for relative motion consider near circular orbit and they are valid for orbits with small eccentricities and even for close formations (i.e., the distance between satellites is about 1 km). However, for formations with relative distances greater than 10 km, it is not possible to obtain a stable formation by using the initial conditions computed using linearized schemes. In this case, nonlinear effects should be added to the initial conditions predictions.
In the final manuscript, we will present the orbit analysis tool in detail. Also to be presented is a new method that incorporates the nonlinear effects in the selection of initial conditions in terms of orbital parameters. The approach taken will be described in detail, and the success of the approach will be demonstrated through simulations.
References
Alfriend, K.T., Vadali, S.R., Gurfil, P., Jonatan, P.H., Breger, L.S. (2010), Spacecraft Formation Flying, Dynamics, Control and Navigation, Elsevier, Bulrington, MA, USA, 2010.
Chris Sabol, Rich Burns, and Craig A. McLaughlin. (2001), Satellite Formation Flying Design and Evolution, Journal Of Spacecraft And Rockets, Vol. 38, No. 2, March–April 2001
H.Cui, J.Li, Y.Gao. (2006), An Orbital Design Method for Satellite Formation Flying, Journal of Mechanical Science and Technology, Vol.20, No.2,pp177-184,2006.
D. Dumitriu, S. Marques, P. U. Lima, J. C. Bastante, J. Araújo, L. F. Peñín, A. Caramagno, B. Udrea, Optimal Guidance And Decentralised State Estimation Applied To A Formation Flying Demonstration Mission In GTO.
J.S. Llorente, A. Agenjo , C. Carrascosa , C. de Negueruela, A. Mestreau-Garreau, A. Cropp, A. Santovincenzo. (2013), PROBA-3: Precise formation flying demonstration mission, Elsevier, 2013
| Applicant type | First author |
|---|
Primary author
Mr
AYKUT kutlu
(Middle East Technical University)
Co-author
Prof.
Ozan Tekinalp
(Middle East Technical University, Chair of the Department of Aerospace Engineer)
