Fixed-time near-optimal control for repointing maneuvers of a spacecraft with nonlinear terminal constraints

Repointing maneuvers of a spacecraft in staring mode are investigated where the optical axis is required to align with the target orientation. Different from traditional three-axis reorientation maneuvers, the rotation about the optical axis is free of constraints for repointing maneuvers. Both static target observation and moving target detection constraints are considered. The problem is then formulated as a finite-time horizon optimal control problem with nonlinear terminal constraints. A simple and efficient state-dependent Riccati equation(SDRE) based dynamic programming approach is applied to tackle this nonlinear optimal control problem. The convergence of the attitude from initial conditions to the desired terminal constraint is rigorously proved for the first time. Considering the inability of the SDRE method to deal with the problem of large angle maneuvers, an improved SDRE approach combined with a waypoint is proposed to enhance control performance. Finally, numerical investigations are conducted and compared with the real optimal solutions obtained by using the optimization software.