Dynamics and Control of Helical Arrays in Low Earth Orbit

Spacecraft formation flying is an anticipated critical technology, needed to enhance astrophysical and science missions in near-Earth and interplanetary environments. Enabling a set of distributed spacecraft to corporate together, collectively fulfilling a mission objective, has proven to have several benefits over the conventional large single entity spacecraft. Mission cost and risk are reduced, while the retrieval of scientific data is significantly increased. Augmented adaptability and flexibility will play a crucial role in future space missions which require radar apertures that are excessively large and not practical to built. 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 Small-Sats, either deployable or free-flying, can deliver a comparable or greater mission capability than large monolithic spacecraft, but with significantly enhanced flexibility (adaptability, scalability, evolvability, and maintainability) and robustness (reliability, survivability, and fault-tolerance). This research is aligned with the NASA Technology Roadmap for Robotics and Autonomous Systems (TA4), in particular TA4.5 System-Level Autonomy (Activity Planning; Autonomous Guidance and Control; and Multi-Agent Coordination) and TA4.6 Autonomous Rendezvous and Docking. This paper outlines the design of a small-satellite helical formation, serving as a Synthetic Aperture Radar (SAR) in low Earth orbit. The macro topic treated in this paper is the analysis of the feasibility and problems related to the operation of autonomous satellite formations serving as a Synthetic Aperture Radar (SAR) in low Earth orbit. An earlier preliminary version of this work was presented recently [1]. The main objective is to control with great precision the relative 6DoF dynamics of the followers with respect to a leader satellite in order to allow a correct taking of the data required by the mission. The differential accelerations to which the formation satellites are subjected make it necessary to implement control techniques for their re-positioning. To ensure a long mission duration, the number of such correction maneuvers should be minimized. In an autonomous formation perspective, such corrections are computed by the spacecrafts themselves, which therefore need to be equipped with sufficient computational resources. In this paper the problems just presented are described in detail and some techniques to mitigate their effects are reported. In order to have results more similar to reality, a high precision dynamic propagation model has been created and validated with the NASA General Mission Analysis Tool (GMAT). This model includes harmonics of the gravitational potential up to order 21, drag, solar pressure and third-body perturbation (Moon and Sun) [2]. After defining the external environment in which the satellites operate, the problem of maintaining the desired configuration of the system is addressed through two different analyzes: uncontrolled dynamics stability analysis and active formation control. The study of uncontrolled formation stability aims to derive the initial conditions of the formation satellites that most closely minimize the relative drift between followers and leader. This allows to reduce the number of maneuvers required to maintain the formation given a fixed interval of time. Despite the careful choice of initial conditions, this drift, although minimal, will tend to alter the initial configuration until the formation is no longer operational. For these reasons, an active control solution, aiming to minimize the amount of fuel used to perform the correction maneuver, has been implemented. The optimal controller is presented in different variants, in particular two strategies, centralized and decentralized, have been implemented in the context of Sequential Convex Programming (SCP). Both types of control were analyzed considering possible un-modeled external factors. Some test cases are reported so that discussion and conclusions can be made regarding the limitations and issues associated with the methodologies implemented.