A multi-impulse extended method for low-thrust trajectory optimization

The low-thrust trajectory optimization is replaced by a multi-impulse one. After the multi-impulse trajectory was obtained by solving a nonlinear programming problem, the multi-impulse is extended directly to the low-thrust by Q-guidance. Starting with the first segment of the multi-impulse trajectory, the thrust direction is set to consist with the impulse direction. The thrust magnitude is at its maximum. By propagating the initial state with the thrust for 1.0 day, the state of the spacecraft will update to a new one. A new impulse is obtained by solving the Lambert's problem between the new state and the final state. The process is then repeated until the impulse reduces to zero. Finally, the multi-impulse trajectory is converted to the low-thrust one by applying this process to all the other segments. Numerical results for two rendezvous missions fully validate the availability and efficiency of the Multi-Impulse Extended method.