Study On Bounds Model And Control For Spacecraft Cluster

Spacecraft cluster（SC） is a new and important research field of the distributed spacecraft system, which will be used to many possible space missions like spaceborne Earth observation, on-orbit service, deep space small planet exploring, etc., as an enabling technology. Taking the necessary condition as the main concern, the thesis proposes the concept of boundedness for SC, and gives a completed research on the boundedness condition, the boundedness achieving method, the bounds modeling, and the bounds controlling. According to some real missions’ requirements, the relative hovering control and inner-formation flying contro l problems are also studied. The main results achieved in this dissertation are summarized below.The bounds model for spacecraft relative motion and SC is developed. Firstly, based on the periodical spacecraft relative motion equations, the upper and lower bounds of the relative position coordinates are obtained by using the extreme value theory. Then, the analytical upper and lower bounds model for the inter-satellite distance in the cases of fly-around relative motion and in-plane relative motion are derived. Next, using the bounds model for a pair of satellites, and by adopting the concepts of enclosing cube and ball, the bounds model for SC are further built up.The analytical boundedness conditions for SC are developed. Firstly, the relation between boundedness and periodicity of relative motion in the central force field is analyzed. the methods of periodicity matching and energy matching for constructing the boundedness conditions are summarized. Secondly, the equivalency of boundedness and J₂-invaraince in the J₂ perturbed relative motion case is proved. the J₂-invariance conditions in the cases of mean osculated and non-osculated orbital elements are improved obviously. the simplified J₂-invaraince conditions for three cases such as near-polar orbits, frozen orbits and equatorial orbits are proposed too. Thirdly, the spatial geometrical property of the strict J₂-invariant relative orbits is analyzed. the conditions for the self- intersection and its number for the J₂-invaraint relative orbits are derived.The initialization control methods for achieving the boundedness condition for SC are proposed. Firstly, the initialization methods for achieving the first-order or second-order boundedness by using one, two or three directional velocity increments are obtained. Then, the single velocity increment method for initializing a SC in the case of J₂ perturbed environments is further developed. Next, the problem of SC initializing by a group of small satellites which are injected into orbits from a common mo ther spacecraft platform is also studied. Finally, a kind of relative motion equations which are expressed as the functions of the releasing velocities of the small satellites are derived too. then, the corresponding control methods are further proposed.The bounds controlling methods for SC are proposed. Firstly, a two-steps scheme is firstly designed for the problem of bounds control, where the first step is used to transform the expected bounds to the expected orbital elements of the follower satellite, and the second step is used to achieve the expected orbital elements from the current orbital elements. Secondly, the problem of orbital elements adjustment is divided into two parts, i.e. the in-plane control and the outside-plane control. Furthermore, an optimal control algorithm by using only four pulses for in-plane control is suggested. Thirdly, as for the problem of limited directional control, the bounds control methods for fly-around and in-plane relative motion is further studied. Next, the concept of virtual reference satellite is proposed. Finally, the optimal control method for bounded SC is developed.According to the above theory, two possible missions related to the bounds constraint are analyzed. The first one is the spacecraft relative hovering control problem. In this paper, a general hovering control model including the J₂ perturbation is developed. The minimum/maximum force and fuel-cost orientations are analytically obtained. The second one is the control problem of inner- formation flying system. As for the classical inner-formation flying system which contains only one inner satellite, the nonlinear relative motion equations which consider the small eccentricity effects are adopted. then, according to the Lyapunov control theory for the time varying dynamical system, four kinds of nonlinear control algorithms are developed. The mass variation due to the fuel cost, the dynamical model’s inaccuracy and the disturbances’ uncertainty are analyzed. Then, a robust controller by using μ-synthesis is designed. Thirdly, considering the possibility that the system contains two inner-satellites, a coordinative control algorithm with parameters self-adaptive estimator is designed too.The dynamical mechanism of SC is systematically analyzed. The concept of boundedness is proposed, which extends the research range of the traditional formation fly and provides a theoretical foundation for SC. The bounds model, boundedness condition, initialization and bounds adjustment control methods in this thesis provide the practical mathematical tools for SC. The control algorithms for relative hovering and inner-formation flying give the optimal solution for the related space missions.