Robust Passively Safe Spacecraft Swarming via Closed-form and Optimization-based Control Approaches

Miniaturized space-borne multi-agent systems, a.k.a spacecraft swarms, promise to overcome the limitations of monolithic satellites, across the board, from capabilities to mission costs. Nevertheless, the use of low-size-weight-and-power as well as commercial-off-the-shelf hardware make them more prone to contingencies which may cause loss of control capabilities. Therefore, spacecraft swarms shall be collision-free in the presence of contingencies that prevent trajectory re-planning and control on the short term. Passive safety consists in guaranteeing safe separation robust to control losses, while in presence of system uncertainties. This paper explores both closed-form and direct optimization-based approaches to swarm passive safety, highlighting advantages, limitations and comparing them on a representative test case drawn from the upcoming VIrtual Super Optics Reconfigurable Swarm (VISORS) mission. The underlying shared mathematical foundation is the modeling of the swarm dynamics through a state parameterization in integration constants. Such state choice provides unique geometrical intuition at closed-form level, and makes passive safety tractable at direct optimization level. In particular, it permits to exploit variation of parameters to reduce the number of constraints required to enforce passive safety, and to compensate for nonintegrable dynamics and uncertainty effects. Besides the key trades, this paper shows how the presented approaches can enable tight and reconfigurable satellite swarming in the presence of contingencies.