Quasi-linear optimization for multiple-spacecraft clustering

Several missions have utilised halo orbits around the L1 and L2 Lagrange points of the Earth-Sun system. Due to the instability of these orbits, station-keeping techniques are required to prevent escape after orbit insertion. This paper considers using solar sail propulsion to provide station-keeping at quasi-periodic orbits around L1 and L2. Stable manifolds will be identified which provide near-Earth insertion to a quasiperiodic trajectory around the libration point. The possible control techniques investigated include solar sail area variation and solar sail pitch and yaw angle variation. Hill's equations are used to model the dynamics of the problem and optimal control laws are developed to minimise the control requirements. The constant thrust available using solar sails can be used to generate artificial libration points sunwards of L1 or Earthwards of L2. A possible mission to position a science payload sunward of L1 will be investigated. After insertion to a halo orbit at L1, gradual solar sail deployment can be performed to spiral sunwards along the Sun-Earth axis. Insertion DV requirements and area variation control requirements will be examined. This mission could provide advance warning of Earthbound CME (Coronal Mass Ejections) responsible for magnetic storms.