Optimal passively-safe control of multi-agent motion with application to distributed space systems
Keywords: Aeronautics and Astronautics.

This dissertation develops a novel Dynamics, Guidance, and Control (DG&C) framework for multi-agent systems with specific application to so-called Distributed Space Systems (DSS). Spaceflight has being revolutionized by the usage of miniaturized low-size-weight-and-power (low-SWAP) satellites and commercial-off-the-shelf (COTS) technology. The trend makes access to space easier and more convenient for new and diverse stakeholders. At the same time, it enables the distribution of payload and tasks among multiple coordinated agents (i.e., DSS) enabling functionalities that are otherwise not achievable by single monolithic systems. The resulting novel DSS require autonomous and safe DG&C capabilities in a wide range of operational scenarios unmatched by previous spaceflight applications. After a review and harmonization of the mathematical foundation relevant to the DG&C of DSS, this research explores the method of variation of parameters (VoP) to conceive and develop a novel framework for optimal passively-safe control of multi-agent dynamics systems. Specifically, VoP is exploited to model the effects of non-integrable dynamics on the integration constants of an integrable portion of the governing dynamics itself. This fosters computational efficient dynamics modeling as well as inclusion of dynamics-dependent constraints with application to fault-tolerant control. Such advantages are used to address two specific challenges of the DG&C of DSS: 1) the accurate and efficient modeling of the complex relative motion dynamics in space; 2) the need of fuel and computationally efficient control algorithms capable of enforcing motion safety guarantees even in case of sudden loss of control capabilities by any agent, i.e., guarantees of passive safety. In fact, low-SWAP and COTS components reduce mission financial costs at the expense of reliability with higher risks of loss of control capabilities. This makes fault-tolerant motion safety particularly relevant, given the consequences a collision in space has in terms of debris generation and investments loss. The novel theoretical framework provides three main contributions to the state-of-the-art: 1) efficient inclusion of passive safety guarantees within a multi-agent optimal control problem solvable using direct methods, in presence of nonlinear non-integrable dynamics and realistic system uncertainties (from sensing, actuation, and unmodeled system dynamics); 2) novel closed-form linear dynamics models of the perturbed relative motion of DSS, for efficient on-board propagation, and adoption within DG&C algorithms; 3) novel closed-form solutions of passive safety for DSS, with contributions to relative orbit design in eccentric orbits and use within constrained optimal control problems. The main experimental contribution of this work is the application of the framework to the upcoming VIrtual Super Optics Reconfigurable Swarm (VISORS) mission, a first-of-a-kind nanosatellite segmented telescope due launch in 2024 with a 40 meters focal length for high-resolution imaging of the solar corona. Together with complementary challenging formation-flying test cases in eccentric orbits, the dissertation shows the advantages of the proposed approach in terms of achieved safety guarantees, control accuracy and gained fuel and computational efficiency