Path planning for multiple spacecraft using consensus with LMI avoidance constraints

This paper presents a consensus-based path planning algorithm for a team of communicating spacecraft. The central idea is the development of a new efficient method of incorporating collision avoidance into the consensus algorithm. This is done by applying the concept of quadratically constrained attitude control (Q-CAC), where attitude constraints are represented as a set of linear matrix inequalities (LMI), and solved by semidefinite programming. Lyapunov-based stability analysis is also presented, together with simulation results for a team of spacecraft engaging in arbitrary formation reconfigurations, to demonstrate the effectiveness of the approach.