Relative orbit design and control of formation around displaced solar orbits

This paper investigates the relative orbit design and control methods for formation flying around displaced solar orbits. Firstly, the relative equations of motion are developed and linearized. Then, two types of orbit design and control methods are discussed based on the linearized equations. One method uses only position feedback to control the formation, in which the relative orbit can be controlled to be an ellipse. Further, the period of relative motion and direction of relative motion plane can be designed as mission requirements. The advantage of the method is that it employs an approximate system instead of a true one to design the parameters, which overcomes the trouble of solving a transcendental equation. The other method uses the full state feedback to control the formation, in which the relative orbit can be designed arbitrarily. Two control strategies, Linear Quadratic Regulation (LQR) and Input Feedback Linearization (IFL), are discussed for the latter. Finally, simulations are given to validate the two methods.