Resumen de Dynamics and control of tethered satellite formations in low-Earth orbits
Manrico Fedi Casas
This thesis is focused on the study of dynamics and control of a multi-tethered satellite formation, where a multi-tethered formation is made up with several satellites (agents) connected by means of cables (tethers). The goal of the first part of the study is to evaluate the effect of tether mass on multi-tethered clusters. Due to the complexity of the formations analyzed, the stability of the formation is assessed through a numerical simulation. The behavior is evaluated in the ideal case of circular orbits, but also in non-ideal cases such as that of elliptical reference orbit or perturbed motion. For circular reference orbits, the dynamics of tethered satellite formation is studied, showing that tether mass affects formation dynamics for closed configurations featuring external tethers. This leads to significant instability effects affecting the position of deputies with respect to the parent body neglected by a more elementary modeling approach. When combined effect of orbit eccentricity and tether mass on tethered formations is analyzed, the most noticeable effect due to eccentricity is the increase in the variation of the local spin rate of the cluster between perigee and apogee passes of the reference elliptical orbit. This effect has consequences over the elongation of tethers, shape of tether oscillations and angular separation between adjacent tethers especially for open formations. When taking into account the J2 effect on massive tethered satellite formations, in the Earth¿facing scenario, the trajectory of the parent body presents oscillations of increasing amplitude in the direction perpendicular to the orbital plane. The second part of the study is focused on deriving a control law for position and attitude control of an Earth-facing double pyramid multi-tethered cluster. The control problem is decomposed in two levels: A first level to perform position and attitude coarse control of the formation as a whole, and a second level to achieve accurate position and control of each agent of the cluster. For the purpose of attitude control, and taking advantage again of the similarities between a tethered cluster and a rigid body, the virtual structure approach is chosen as the most suitable option. The formulation shown in this thesis augments the general virtual structure equations valid for a static formation by adding the kinematics of a spinning formation, since the original formulation is valid only to achieve a static final state. The controller is designed to modify the spin rate and the moment of inertia of the formation through a reeling mechanism, and therefore to be able to control the Likins-Pringle tilting angle of the cluster. For the derivation of the accurate positioning control law, the study initially discusses different alternatives based on the state of the art of the robotics control literature. After evaluating other alternatives, two control laws are chosen for this application: One based on a PID controller and one based on the sliding mode control technique. For the sliding mode based control, a proof of semi-global exponential stability is provided. Results of a representative simulation assess the viability of the control approach proposed leading to a submillimetric positioning accuracy.
