Solar sail trajectory optimization of multi-asteroid rendezvous mission

Abstract An interplanetary trajectory optimization of the multi-asteroid rendezvous is investigated for a solar sail-based spacecraft. The optimal control problem is formulated using the calculus of variations and Pontryagin's maximum principle and the first order necessary conditions for optimality of the problem are derived. To achieve the optimal solution, the indirect method transforms the optimal control problem into a multiple point boundary value problem and solves it via shooting method, and the pseudospectral method discretizes the state and control variables and solves the NLP problem. In this paper, a numerical method combining the global optimization algorithm and a nonlinear equation solver is proposed to get the optimal solution of the indirect method. Additionally, costates are estimated to validate the optimality of the solution obtained via the pseudospectral method. Finally, numerical examples are given to verify the effectiveness of the proposed methods. The results indicate that the optimal solutions to the problems with two and three targets can be solved using the proposed indirect method algorithm. As the number of visiting targets is more than three, the direct method will be more efficient.