Modeling, Dynamics and Control of a Variable Topology Tethered Space System

Radar remote sensing is a powerful tool to characterize the subsurface structures here on Earth and at other planetary bodies. For scientific investigation of the surface and subsurface properties, the radar observations must be unambiguously localized at horizontal and vertical scales that resolve the characteristic features under investigation. Determining the source of the radar echoes either requires assumptions about the structure under investigation or the direction of the radar observation. The Mars sounders have illustrated that surface echoes contribute to a higher-than-expected level of contamination, which limits the radar's detection capabilities in the subsurface. The only effective way to limit the contamination is to focus the antenna's footprint by increasing the size of the aperture. Ice and subsurface radar sounder typically operate at low frequencies in the HF or VHF bands. To achieve an antenna footprint at kilometer scales from low Earth orbit (LEO), the length of the antenna aperture is of the order of kilometers. To effectively create this large antenna aperture and synthesize the desired footprint, the elements of the array must maintain a relative position to one another, and the position must be known accurately. The relative spacing between the elements determines the shape and level of the synthesized antenna's side-lobes (where the antenna pattern is ideally suppressed). The maximum extent of the array determines the resolution of the synthesized antenna's footprint. The number of elements decides the antenna gain, which ultimately increases the sensitivity of the radar. In this paper we study the dynamics of a tethered space system able to support the aforementioned antenna array. We consider an EndFire array made up of ten antenna elements, aligned along the local vertical thanks to gravity gradient stabilization. The modeling process is explored by steps. We expand a simple tether model by employing a discretized mass approach. The antenna elements are referred to as 'climbers' and are constrained to the tether. Exact nonlinear dynamics are propagated with respect to the orbital frame of reference, according to the equations presented by Quadrelli in his works. Tethered formations have flown more often than free-flying spacecraft swarms and have proven to be much more stable and reliable. The presence of a mechanical link between the antenna elements leads to inexpensive formation reconfiguration maneuvers. Flexibility and reconfigurability are key for reusable space systems, so we propose a relative-position control system for multiple climbers and explore the topic of variable length tethers. The topics of attitude stabilization and optimal orbital correction maneuvers are also considered. We conclude with some considerations regarding scalability and simulation times.