A new optimal control approach, Theta-D technique, is employed to control the position and altitude of a spacecraft accurately m order to capture and remove large space targets. Spacecrafts are required to be able to perform large position and angle maneuvers: their dynamics are highly nonlinear. To control this highly nonlinear dynamic system, we formulate it as a nonlinear optimal regulator problem. The proposed Theta-D technique can give an approximately closed-form suboptimal controller in the sense that it obtains an approximate solution to the Hamilton-Jacobi-Bellman (HJB) equation through a perturbation method. By adjusting perturbation terms, asymptotic stability can be achieved in the large and the system transient performance can also be tuned in a flexible way. Compared with the popular SDRE technique, this approach does not need on-line computations of algebraic Riccati equation. With high-dimensioned systems, this feature presents a tremendous implementation advantage. A six degree of freedom simulation of the spacecraft and target are used to demonstrate the effectiveness of the Theta-D controller
