Control Of Low Earth Orbit Spacecraft Formation Flying

This thesis discusses some issues related to the low earth orbit spacecraft formation flying. These issues include the formation flying orbit design, the formation establishment, reconfiguration, and keeping. The main work is summarized as follows.1. The formation flying orbit design problem is discussed using the kinematics method. The relative motion equations of spacecraft formation in circular or slightly elliptical orbits and in eccentric orbits are proposed respectively. These equations are expressed by six orbit elements and they can be used directly for the formation flying orbit design. Several typical relative motions are analyzed and several special formations are suggested. Whose effectiveness is verified by the computer simulation results.2. The fuel optimal impulse control of the formation establishment is studied based on the Hill's equations. The analytical, two-impulse optimal solutions are proposed for transferring a deputy from the reference point to a class of elliptical relative orbits and to the pendulum relative orbit, and an analytical, three-impulse optimal solution is proposed for achieving the desired general elliptical relative orbit. The priority of these analytical solutions is: given a desired relative orbit, the optimal impulse control scheme can be easily implemented using onboard computational resources. Based on these analytical solutions, the equations of the optimal transfer trajectory are obtained, and the relationship among this trajectory, the desired relative orbit, and the optimal impulses is shown. At the formation level, an asynchronous control scheme for the formation establishment is developed, in which the fuel consumption is optimal,the calculation load is lower, and the security is better.3. Several kinds of typical formation reconfigurations are discussed respectively, including an elliptical formation transfering to another elliptical one, a pendulum one to another pendulum one, an elliptical one to a pendulum one and a pendulum one to an elliptical one. After the mathematic models of these formation reconfigurations are presented, a necessary condition of the elliptical formation reconfiguration with fuel optimal control is proved. The condition indicates the relationship between the formation establishment and reconfiguration, which is later used to obtain the analytical and fuel optimal solutions of the elliptical formation reconfiguration and the pendulum formation reconfiguration. The optimal transfer trajectory equations of these two formation reconfigurations are proposed, and the relationship among the trajectory, the desired relative orbit, and the optimal impulses is shown. The multi-impulse suboptimal solutions are presented for the formation reconfigurations between the elliptical formation and the pendulum formation, and the control scheme can be obtained directly from the initial and the desired relative orbits by using these solutions, at the same time the fuel consumption is suboptimal. An asynchronous control scheme for the formation reconfiguration is developed at the formation level, and the advantages of the control scheme are shown by the simulation results.4. The problem of formation keeping with two-impulse and continuous thrust is discussed. Under the two-impulse control scheme, the control of formation keeping is similar to that of the formation reconfiguration, and at the formation level, the asynchronous control scheme can be used to the formation keeping too. Based on the author's work on controlling the quintuple inverted pendulum, a fuzzy control method with continuous thrust is suggested for the formation keeping, the fuzzy controller is designed by the LQR (Linear Quadratic Regulator) theory and 2-ary piecewise interpolation function. Comparing to the traditional fuzzy controller, the number of the inference rules is decreased dramatically, so that the controller can be easily implemented on-line. The validation of the proposed method is verified by the simulation results.