Fast optimization of interplanetary low-thrust transfer trajectory based on gauss pseudospectral algorithm

In this paper, we have proposed a fast gauss pseudospectral approach for optimization of interplanetary low-thrust transfer trajectory. First, the optimization model of interplanetary low-thrust trajectory was established using modified equinoctial elements. Then, through parameterizing the optimization model by gauss pseudospectral strategy, the low-thrust trajectory optimization problem was translated into a large-scale parameters optimization problem with multi-constraints, in which the thrust direction and planetary ephemeris constrains were treated as path and event constraints respectively. Furthermore, in order to improve the efficiency and precision, the analytical jacobian matrix of performance index and constraints equations were derived. Taking the Mars and Mercury mission as the examples, the proposed gauss pseudospectral approach was validated. The numerical result demonstrates that, comparing to traditional numerical algorithm, the computation efficiency can be improved 67.78% using analytic jacobian matrix.