Dynamics and Optimal Control for Free-Flight and Tethered Arrays in Low Earth Orbit

Spacecraft formation flying is an anticipated critical technology, needed to enhance near-Earth and interplanetary astrophysics and science missions. Enabling a set of distributed spacecraft to corporate together, collectively fulfilling an objective, has proven to have several benefits over a conventional large single spacecraft. Mission cost and risk are reduced, while the retrieval of scientific data is increased. The key strategic goal of our work is to develop active and passive radar remote sensing applications based on distributed array architectures. Distributed formations of low-cost SmallSats, either deployable or free-flying, can deliver a comparable or greater mission capability than large monolithic spacecraft, but with significantly enhanced flexibility and robustness. This research is aligned with NASA's Technology Roadmap for Robotics and Autonomous Systems. This paper outlines the design of a formation, serving as a synthetic aperture radar (SAR) in low Earth orbit. The Earth's oblateness (J2-effect), atmospheric drag, and solar radiation pressure significantly affect the pattern, necessitating periodic orbit corrections to maintain stability. To fly optimal paths and keep communications with the Deep Space Network minimal, autonomous Guidance, Navigation and Control algorithms are required. Additionally, SAR requires high precision pointing, inter-satellite position and orientation knowledge, time and phase synchronization of the elements of the array, and a profiled deployment strategy, which raises the need for sophisticated attitude dynamics and control systems. The high relative position and attitude knowledge, as well as the relative time and phase synchronization, are critical technologies under development, and not available yet. Two system configurations are considered in this paper: one in which the spacecraft are free-flyers, synthesizing a helix structure, and another one in which the spacecraft are connected by tethers, forming an end-fire-array aligned along the orbit radial. Compared to spacecraft in formation, tethered spacecraft have flown many more times. Generally, tethers allow a high reliability and low control cost alternative to distributed formations in close proximity, currently requiring active human-in-the-loop control. For both applications, unified exact nonlinear dynamics is required, formulated based on six orbital elements, in which the dynamics is propagated separately for each spacecraft. This implies that the conventional chief and deputy notion, as in the Clohessy-Wiltshire equations, is not necessary. Once the absolute motion state is available from the simulation, the relative motion can be estimated for sensing. Attitude is parameterized with quaternions. Convex optimization is used for minimizing control cost, employing a centralized approach. For free-flyers collision avoidance is required to guarantee safety. The adapted coupled mechanism is more precise, but induces significantly more complexity in the dynamics, the control, and the estimation. Simulations show that both arrays are proper considerations for flight applications. The tethered end-fire-array requires less fuel than the helix on account of the natural stability provided by the gravity gradient, and also provides the required rigidity needed in the pointing stability. The assessed orbital behaviour may used to constrain the SAR performance.