Optimal collision avoidance maneuver control for formation flying satellites using linear programming

The safety of the close formation flying satellites in the cross-track plane is studied. Based on the description of the geometry of formation configuration in the cross-track plane, the target formation configuration is expressed by the parameters of the safe ellipse which remains out of the avoidance region, and is optimized by Newton method. The problem to control the satellites to reach the safe ellipse is solved in the framework of linear programming algorithms. A numeric simulation is given to validate the effectiveness of the proposed method.