Dynamic Behavior Analysis and Stability Control of Tethered Satellite Formation Deployment

In recent years, Tethered Space Systems (TSSs) have received significant attention in aerospace research as a result of their significant advantages: dexterousness, long life cycles and fuel-less engines. However, configurational conversion processes of tethered satellite formation systems in a complex space environment are essentially unstable. Due to their structural peculiarities and the special environment in outer space, TSS vibrations are easily produced. These types of vibrations are extremely harmful to spacecraft. Hence, the nonlinear dynamic behavior of systems based on a simplified rigid-rod tether model is analyzed in this paper. Two stability control laws for tether release rate and tether tension are proposed in order to control tether length variation. In addition, periodic stability of time-varying control systems after deployment is analyzed by using Floquet theory, and small parameter domains of systems in asymptotically stable states are obtained. Numerical simulations show that proposed tether tension controls can suppress in-plane and out-of-plane librations of rigid tethered satellites, while spacecraft and tether stability control goals can be achieved. Most importantly, this paper provides tether release rate and tether tension control laws for suppressing wide-ranging TSS vibrations that are valuable for improving TSS attitude control accuracy and performance, specifically for TSSs that are operating in low-eccentricity orbits.

Precise Relative Orbit Determination for Chinese TH-2 Satellite Formation Using Onboard GPS and BDS2 Observations

TH-2 is China’s first short-range satellite formation system used to realize interferometric synthetic aperture radar (InSAR) technology. In order to achieve the mission goal of InSAR processing, the relative orbit must be determined with high accuracy. In this study, the precise relative orbit determination (PROD) for TH-2 based on global positioning system (GPS), second-generation BeiDou navagation satellite system (BDS2), and GPS + BDS2 observations was performed. First, the performance of onboard GPS and BDS2 measurements were assessed by analyzing the available data, code multipath errors and noise levels of carrier phase observations. The differences between the National University of Defense Technology (NDT) and the Xi’an Research Institute of Surveying and Mapping (CHS) baseline solutions exhibited an RMS of 1.48 mm outside maneuver periods. The GPS-based orbit was used as a reference orbit to evaluate the BDS2-based orbit and the GPS + BDS2-based orbit. It is the first time BDS2 has been applied to the PROD of low Earth orbit (LEO) satellite formation. The results showed that the root mean square (RMS) of difference between the PROD results using GPS and BDS2 measurements in 3D components was 2.89 mm in the Asia-Pacific region. We assigned different weights to geostationary Earth orbit (GEO) satellites to illustrate the impact of GEO satellites on PROD, and the accuracy of PROD was improved to 7.08 mm with the GEO weighting strategy. Finally, relative orbits were derived from the combined GPS and BDS2 data. When BDS2 was added on the basis of GPS, the average number of visible navigation satellites from TH-2A and TH-2B improved from 7.5 to 9.5. The RMS of the difference between the GPS + BDS2-based orbit and the GPS-based orbit was about 1.2 mm in 3D. The overlap comparison results showed that the combined orbit consistencies were below 1 mm in the radial (R), along-track (T), and cross-track (N) directions. Furthermore, when BDS2 co-worked with GPS, the average of the ambiguity dilution of precision (ADOP) reduced from 0.160 cycle to 0.153 cycle, which was about a 4.4% reduction. The experimental results indicate that millimeter-level PROD results for TH-2 satellite formation can be obtained by using onboard GPS and BDS2 observations, and multi-GNSS can further improve the accuracy and reliability of PROD.