Nonlinear optimal attitude control of spacecraft using novel state-dependent coefficient parameterizations

This paper addresses the attitude stabilization problem with the optimization objective regarding system performance and energy consumption for rigid spacecraft. Novel state-dependent coefficient (SDC) parameterizations are developed to reduce the optimization problem to solving the state-dependent Riccati equation (SDRE). To be explicit, a proper SDC parameterization is selected for the stabilization mission among infinite feasible SDC representations by utilizing an improved guideline. Subsequently, a novel analytical SDC reconstruction is evoked alternatively at the mission breakdown region in which the derived SDC parameterization fails to operate. Behind the scenes, the anti-unwinding behavior is supported by the explicit sampling SDC forms derived for the scalar part of the unit quaternion. The novelty of two developed SDC parameterizations lies in that they not only render the maximal pointwise controllable space to facilitate the control mission, but also cover the whole maneuvering domain without any breakdowns. Moreover, the computational burdens for online SDRE solvability checking and numerical SDC reconstruction are alleviated significantly. Finally, comparative numerical simulations are implemented to highlight the superior performance of the presented scheme.