Optimal Control of a Spinning Double-Pyramid Earth-Pointing Tether Formation
- Paper number
IAC-06-C1.3.06
- Author
Dr. Paul Williams, Australia
- Year
2006
- Abstract
The dynamics and control of a tethered satellite formation for Earth-pointing observation missions is considered. Formation flying of spacecraft provides many advantages in terms of scientific and observational data that is difficult to obtain using other methods. There are several options available for flying spacecraft in formation. The most common approach is to simply utilize free-flying spacecraft. In this case, highly accurate propagation and control laws are necessary to maintain separation constraints over the life of the mission. This makes the use of fuel for stationkeeping and other maneuvers a necessity. Another approach that has been considered utilizes tethers to interconnect the spacecraft so that the drift that normally occurs for free-flying satellites is moderated by the tension forces in the tethers. Previous studies have looked at a variety of tether formation configurations for different applications, including spinning triangular configurations in the orbital plane, deep-space configurations with central hub, and Earth-pointing configurations. For most applications in Earth orbit, a tether formation must be spinning in order to maintain tension in the tethers. It is possible to obtain periodic spinning solutions for a formation whose initial conditions are close to the orbit normal for a triangular configuration. However, these solutions contain significant deviations of the satellites on a “relative sphere.” To maintain a plane of satellites spinning normal to the orbit plane, it is necessary to utilize “anchors”. Such a configuration resembles a double-pyramid. In this paper, control of a double-pyramid tethered formation is studied. The equations of motion are derived in a floating orbital coordinate system for the general case of an elliptic reference orbit. The motion of the satellites are derived assuming inelastic tethers that can vary in length in a controlled manner. Cartesian coordinates provide a simple means of expressing the equations of motion, together with a set of constraint equations for the tether tensions. Periodic optimal control theory is applied to the system to determine sets of controlled periodic trajectories by varying the lengths of all interconnecting tethers (nine in total).
- Abstract document
- Manuscript document
IAC-06-C1.3.06.pdf (🔒 authorized access only).
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