Minimum-fuel low-thrust trajectory optimization using adaptive wavelet collocation and sequential convex programming

The minimum-fuel transfer problem is a common challenge encountered in low-thrust orbit trajectory optimization, typically solved with Bang-Bang control solution. This paper proposes a novel approach to solve the optimization problem by employing an adaptive wavelet collocation method for grid refinement and a synergistic integration of sequential convex programming, which results in an effective and precise solution methodology. The method introduces a spline wavelet to convert the infinite-dimensional state and control variable into finite dimensions. The dynamic nonlinear programming (NLP) problem is then convexified and linearized into a second-order cone programming (SOCP) problem using a small perturbation method, which can be rapidly solved by convex optimization tools. By iteratively solving the sequential SOCP problems, state and control variables converge quickly and accurately to the optimal control solution. A numerical simulation of a low-thrust transfer trajectory from Earth to Mars is performed to demonstrate the effectiveness of the proposed method. The results show that the adaptive method achieves higher accuracy in determining the switching time compared to conventional methods.