Integrated nonlinear optimal control of spacecraft in proximity operations

Abstract

This article proposes an integrated optimal control strategy for a servicing spacecraft in proximity operations on a target in space. The relative position vector between the servicing spacecraft and the target is required to direct towards the docking port of the target while the attitude of the two bodies must be synchronised without exciting large flexible vibrations. The control of translational, rotational and flexible motions is formulated in one unified optimal control framework in which the tracking errors in relative position and attitude, and flexible structure vibrations can be minimised simultaneously using one cost function. This formulation results in a highly nonlinear system that poses a challenging control problem. The nonlinear optimal control technique is employed to design a closed-form feedback control law for this nonlinear control problem by finding an approximate solution to the Hamilton–Jacobi–Bellman (HJB) equation through a perturbation process. The closed-form controller offered by this approach is easy to implement onboard especially for this problem with a large state-space. Numerical simulations including the six degrees-of-freedom rigid body dynamics and coupled flexible structure dynamics are performed to demonstrate the effectiveness of this control formulation even under large moment of inertia uncertainties.