Optimal Relative Attitude Tracking Control for Spacecraft Proximity Operation

Optimal control for relative attitude alignment and angular velocity tracking is discussed in this paper. The spacecraft relative attitude kinematics and dynamics based on quaternions are established during the spacecraft proximity operation. Then the attitude tracking problem is formulated as a nonlinear optimal control problem. After transform the relative attitude kinematics and dynamics into the state dependent coefficient form, with the consideration of nonlinear and time-varying properties lie in the model, the State Dependent Riccati Equation (SDRE) controller and theta-D controller are derived respectively. Numerical simulations through Matlab are made to validate the effectiveness of the model and the control law, it can be shown from the results that even though the solution of the SDRE method is more effective and the energy consumption is lower, the theta-D controller has an advantage in terms of computational efficiency, which can be solved in a fast manner.