$\mathcal{H}_{\infty}$ and $\mu$ -Synthesis for Nanosatellites Rendezvous and Docking

Abstract

In this brief, the nanosatellite rendezvous and docking problem is tackled. It was never attempted for small spacecraft, as critical technologies, such as six-degree-of-freedom (DoF) micropropulsion systems, have only recently become available due to advances in MEMS. The typical level of noise in nanosatellites’ sensors and actuators combined with the dynamics uncertainties, low actuation capabilities, and reliability requirements makes the use of robust control appropriate. The system is described by a linearized rotation/translation, six DoFs, and coupled dynamics, including fuel sloshing. An ${\mathcal {H}_\infty }$ controller is first designed, in which robust stability and performance are assessed using structured singular values. The controller robustness is then improved using ${{\mu }}$ -synthesis. Nonlinear Monte Carlo simulations for both controllers, including realistic sensors and actuators models, are provided allowing a thorough assessment of the complete guidance, navigation and control (GNC). The sought GNC schemes are shown to be robust to the modeled uncertainties and to satisfy the docking requirements.