PD-fuzzy formation control for spacecraft formation flying in elliptical orbits

A PD-fuzzy associated control method is presented for formation control of spacecraft formation flying in elliptical orbits, on the basis of two-body relative dynamics. Since the two-body relative system for elliptical orbits is time-variable and strongly coupling, the fuzzy formation control of formation flying is mainly studied. In the fuzzy control system, the relative position and velocity errors are selected as fuzzy linguistic variables, and the coupling effect is considered during the establishment of the fuzzy rules. Moreover, the addition and the weighted average principle are adopted in order to counteract the effect among the opposite rules. Then the coupling effects can be furthest reduced. In addition, the proportional-differential (PD) control is introduced for large position errors. And PD control works when relative position errors come up to a certain threshold. Finally, numerical simulations show the comparison between PD-fuzzy and fuzzy control method, and the results demonstrate the validity of PD-fuzzy control which possesses both control methodʹs advantages.