A high-order fully actuated predictive control approach for spacecraft flying-around

Under the framework of high-order fully actuated (HOFA) system theory, this study investigates a spacecraft flying-around problem in a sight coordinate system. In this sight coordinate system, a nonlinear HOFA system model is applied to establish the relative dynamics of spacecraft flying-around, such that the presented flying-around mission can be transformed into a tracking control problem of nonlinear HOFA systems. A HOFA predictive control approach is correspondingly proposed to deal with this problem. Concretely, the nonlinearities can be eliminated to construct a linear HOFA system by utilising full actuation characteristic, and then a linear incremental HOFA (LIHOFA) prediction model is constructed by applying a Diophantine equation to replace a reduced-order prediction model. Based on this LIHOFA prediction model, multi-step ahead predictions are developed to optimise the tracking control performance, so that the realisation of the presented flying-around mission can be guaranteed. A sufficient and necessary condition is derived in the in-depth discussion to maintain the stability and tracking control performance of closed-loop systems. Furthermore, numerical simulation and comparison about spacecraft flying-around in circular and elliptical orbits are provided to verify the feasibility of the HOFA predictive control approach. To highlight its practicability, an experimental verification via air-bearing spacecraft (ABS) simulator is shown for the implementation of flying-around mission.