Linear and nonlinear control strategies for formation and station keeping of spacecrafts within the context of the three body problem

The problem of spacecraft formation control and reconfiguration for halo orbit around the second libration point (L2) of the Sun–Earth Three Body (TB) system is investigated. Station keeping, reconfiguration and precision formation control of spacecrafts on halo orbits are performed via the use of the nonlinear Integral Sliding Mode (ISM) method as well as the optimal closed loop Linear Quadratic Regulator (LQR) approach. In this regard the nonlinear relative dynamics of deputy–chief spacecrafts are derived within the concept of the three body problem. The behavior of the two controllers are compared for different tasks of the formation mission in order to determine the more preferred strategy that fulfills the desired response behavior. In addition the controllers are evaluated for robustness in terms of their compensation against the major source of environmental disturbance, namely the Moonʹs gravity perturbation.