Optimal design and simulation of long-range orbital rendezvous based on direct collocation method

The application of direct collocation method to space vehicle long-range orbital rendezvous with finite thrust optimization problem was introduced. Firstly, the model of long-range orbital rendezvous optimization control problem was established, while motion equation of the state variables was built in geocentric-equatorial inertial coordinate system. Performance was selected to minimize the total fuel consumption. The control variables are thrust, azimuth angle and elevation angle. Terminal state variable constraints are position and velocity constraints. Then, the optimal control problem was transformed into nonlinear programming problem (NLP) using direct collocation method. And the state variables and control variables were selected as optimal parameters at all collocation nodes. At last, parameter optimization problem was solved using the SNOPT software package. The simulation results demonstrate that direct collocation method is not sensitive to orbital rendezvous initial conditions; they also show that the optimal solutions of long-range orbital rendezvous optimization problem are fairly good in robustness.