Attitude synchronization of multiple spacecraft with cone avoidance constraints

In this paper, we consider a team of spacecraft which requires changing its orientation to a common attitude using a decentralized control scheme under a connected communication topology, while satisfying cone avoidance constraints due to blind celestial objects, plume impingement and so on. For this purpose, we first combine consensus theory and optimization theory to develop a quaternion-based attitude consensus protocol. Based on the communication graph at each time step, each spacecraft generates a guidance command or reference attitude trajectory by synthesizing a series of Laplacian-like matrix P(t), using semidefinite programming (SDP) which involves linear matrix inequalities (LMIs). It is analytically shown that this series of matrices P(t) is capable of collectively driving the initial attitudes to a common consensus attitude. For satisfying cone avoidance constraints, exclusion zones are then identified and expressed as LMIs. This identification of the exclusion zones gives rise to selecting safe waypoints from the reference attitude trajectory and then to passing through the selected waypoints while avoiding the exclusion zones via proper control inputs. This solution procedure is demonstrated via numerical simulations of coordinated attitude rendezvous and attitude formation acquisition of multiple spacecraft with cone avoidance manoeuvres.