Convergence properties analysis of the indirect optimization techniques for solar sail trajectory optimization

Abstract

The indirect method is commonly used for solving the solar sail spacecraft trajectory optimization problem. However, the convergence difficulty usually tends to happen due to the sensitivity of the initial costates. In order to improve the numerical convergence properties, many indirect optimization techniques, such as the normalization of the costate vector, have been proposed in the research of deep space trajectory optimization problem. However, there is little literature focused on the analysis of the convergence properties for different indirect optimization techniques. This paper takes the asteroid rendezvous mission with solar sail spacecraft as background, and analyzes the relationship between the indirect optimization techniques which includes the normalization of the costate vector, the homotopic approach and different coordinate systems (the Cartesian and the Spherical coordinate system) for solar sail dynamic models and the convergence properties. First, dynamic models based on different indirect optimization techniques are developed. The shooting method is used to solve for the optimal costates. Then, the convergence properties of the three techniques are compared and analyzed according to the times of initial guesses and the accuracy of the guessed costates. The results of the numerical simulations show that the homotopic approach can achieve the highest accuracy of initial guesses and the best convergence properties.