We investigate the close-range relative motion and control of a spacecraft approaching a tumbling target. Unlike the traditional rigid-body dynamics with translation and rotation about the center of mass (CM), the kinematic coupling between translation and rotation is taken into consideration to directly describe the motion of the spacecraft's sensors or devices which are not coincident with the CM. Thus, a kinematically coupled 6 degrees-of-freedom (DOF) relative motion model for the instrument (feature point) is set up. To make the chaser spacecraft's feature point track the target's, an optimal tracking problem is defined and a control law with a feedback-feedforward structure is designed. With quasi-linearization of the nonlinear dynamical system, the feedforward term is computed from a specified constraint about the dynamical system and the reference model, and the feedback action is derived starting from the state-dependent Ricca equation (SDRE). The proposed controller is compared with an existing suboptimal tracking controller, and numerical simulations are presented to illustrate the effectiveness and superiority of the proposed method.

Collision prediction and avoidance are critical for satellite proximity operations, and the key is the treatment of satellites' motion uncertainties and shapes, especially for ultra-close autonomous systems. In this paper, the zonotope-based reachable sets are utilized to propagate the uncertainties. For satellites with slender structures (such as solar panels), their shapes are simplified as cuboids which is a special class of zonotopes, instead of the classical sphere approach. The domains in position subspace influenced by the uncertainties and shapes are determined, and the relative distance is estimated to assess the safety of satellites. Moreover, with the approximation of the domains, the worst-case uncertainties for path constraints are determined, and a robust model predictive control method is proposed to deal with the line of sight and obstacle avoidance constraints. With zonotope representations of satellites, the proposed robust model predictive control is capable of handling the shapes of the satellite and obstacle simultaneously. Numerical simulations demonstrate the effectiveness of the proposed methods with an elliptic reference orbit. 1

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