Spacecraft body-fixed hovering over a tumbling object with equivalent regulator

Relative hovering of spacecraft is a new type of close-proximity operation. This work deals with the body-fixed hovering over a tumbling object. Initially, the dynamics of the virtual hovering point over the tumbling object in local-vertical-local-horizon(LVLH) frame is derived with considering the rotation of the object. Then, the body-fixed hovering control is converted into an optimal tracking control problem. Based on the state-dependent Riccati equation(SDRE), the equivalent regulator is put up with as nearly optimal regulator, and compared with the modified servo controller. Numerical simulation results show that the equivalent regulator achieves near 50% higher tracking accuracy and 2.5% lower total fuel consumption than modified servo controller with the same state and control weights.