GALCIT Colloquium

Swarms of Silicon Wafer Integrated Femtosatellites (SWIFT) would push the frontier of the existing formation flying spacecraft concepts by one or two orders of magnitude in two major technological drivers: the enormous number (1000 or more) of spacecraft, compared with the previous 2-10 spacecraft missions and concepts; and a tiny size and "miniaturized" capability of 100-gram-class femtosats. As a result, the feasibility of SWIFT swarms is predicated on the individual and synergetic guidance and control (G&C) capabilities of the swarm that would permit synchronized swarm-keeping and reconfiguration maneuvers of thousands of femtosats. In this talk, I will emphasize how to exploit nonlinear synchronization and hierarchical decomposition to reduce the complexity of controlling a large number of satellites. First, I will present distributed, guidance and control algorithms for optimally reconfiguring swarms of spacecraft with limited communication and computation capabilities. The real-time guidance algorithm solves both the optimal assignment and collision-free trajectory generation in an integrated manner, when given the desired shape of the swarm (without pre-assigned terminal positions). The optimal assignment problem is solved using either distributed auction assignment that can vary the number of target positions or a novel probabilistic swarm guidance method that employs a time-inhomogeneous Markov chain. The optimal collision-free trajectories are generated in real time using sequential convex programming and model predictive control. The sequence of trajectories is shown to converge to a Karush-Kuhn-Tucker point of the nonconvex problem. Finally, nonlinear tracking control, combined with nonlinear phase synchronization, is utilized to track optimal reconfiguration trajectories with a property of robustness. Inspired by stable and hierarchical combinations of biological systems, contraction nonlinear stability theory provides a systematic method to reduce an arbitrarily large set of dynamics into simpler elements using hierarchical decomposition and synchronization. I will also show such incremental stability analysis can be extended to a set of Itô stochastic nonlinear systems for synchronization and nonlinear estimation in application to spacecraft swarm systems.