Control of Satellite Imaging Formations in Multi-Body Regimes
- Paper number
IAC-06-C1.8.01
- Author
Prof. Kathleen Howell, Purdue University, United States
- Coauthor
Ms. Lindsay Millard, Purdue University, United States
- Year
2006
- Abstract
Satellite imaging formations have numerous applications in the future of space exploration. These include: searches for exosolar planets, identification of black holes, and spectral characterization of distant stars. Libration point orbits may be ideal locations for such satellite imaging formations. Therefore, control of these arrays in multi-body regimes is critical. Control of satellite imaging arrays has been explored previously. Chakravorty et al. develop a model of the process of image formation in a multi-spacecraft interferometric system. They define satellite motion that covers the UV plane in minimum time. However, fuel expenditure and the dynamics governing the satellite array are not considered. Hussein et al. examine the problem of optimal formation control for imaging and fuel usage. Relative dynamics between the spacecraft are modeled as a “double integrator,” however. Previous efforts in satellite formation control have generally employed the Clohessy-Whiltshire equations, i.e., linearized two-body dynamics, to formulate control algorithms. Strategies for formation flight in multi-body systems are much less common and the increased complexity associated with the dynamical model usually extends to the controller as well. Howell et al. have identified natural solutions in the circular restricted three body problem (CR3BP) that may prove advantageous to optical satellite formation missions. These natural solutions wrap around libration point orbits in the CR3BP, creating a torus of quasi-periodic motions. Because this motion is bounded and periodic, coverage of the UV-plane is feasible over relatively short time periods, with different initial satellite configurations. These quasi-periodic motions are unstable, therefore feedback control is required to maintain a formation. A continuous control algorithm is developed, based on the characteristics of the dynamical phase space near periodic orbits in the CR3BP. Associated with these orbits are six modes: one unstable, one stable, and four center modes. By re-formulating the formation control problem in the basis of these six modes, a continuous controller is derived that removes only specific combinations of dynamical modes. This, in turn, yields bounded periodic motion for satellites within the formation with minimal control effort. Image reconstruction via these satellite formations are simulated with varying mission parameters, including: number of satellites, distance to the object of interest, observed radiation wavelength, mission duration, time between measurements, and maximum formation baseline. An image quality-based figure of merit is then applied to determine if the reconstructed image is adequately resolute. Finally, optimization techniques are applied to maximize coverage of the UV plane while minimizing fuel expenditure.
- Abstract document
- Manuscript document
IAC-06-C1.8.01.pdf (🔒 authorized access only).
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