Abstract
A decentralized closed-loop optimization based on the difference of convex programming is proposed to assemble large telescopes autonomously in-orbit. This study focuses on assembly problems of mirror satellites with six degrees of freedom. Firstly, the hp-Radau pseudospectral collocation method is adopted to increase computational efficiency. Subsequently, the nonconvex constraints are convexified by applying undominated decomposition and sequential convex programming. Additionally, the fixed trajectory assumption enables the translational optimization problem to be a decentralized problem with convergence-guaranteed proof. The six degrees of freedom optimization problem is decoupled by utilizing the proposed algorithm in translational and rotational planning, and coupled by thruster allocation method. To improve the robustness of the system, the algorithm is wrapped in the model predictive control framework, and the recursive feasible property is ensured using the outer-bounding tube. Therefore, the closed-loop optimal control is robust under additive uncertainties. In the numerical experiments, mirror satellites are released from a high-accuracy fitting carrier satellite to accomplish the assembly, and these satellites are utilized to verify the high-speed algorithm and the effectiveness of the closed-loop optimization.
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