Discrete control method for the formation flying around Lagrange point

The formation flying around Lagrange points will benefit deep space exploration greatly due to the special location of the Lagrange points. The paper investigated the discrete control method for the formation flying around the Lagrange point. First, a simple iterative algorithm, which could calculate the control quantity, was given. Based on this algorithm, two control strategies were introduced. Then, several performance indexes related to formation error and energy consumption were defined. By simulating the circular formation flying examples, two strategies are compared and analyzed. The simulation results show that strategy two superior to strategy one either in energy consumption or in error control. For strategy two, the energy consumption increases with formation radius when the impulse time span is fixed. When the formation radius is fixed, the formation error decrease with the impulse time span exponentially. But the energy consumption changes slightly with the impulse time span.