A mesh adaptive refinement method for solving trajectory optimization problem by using direct method based on second-generation wavelets was proposed to deal with the conflict between accuracy and efficiency. The original trajectory optimization problem was transformed into a nonlinear programming problem that was solved by standard nonlinear programming codes. Then the wavelet transformation of control or state function was performed

and the wavelet coefficients were obtained. A new node could be determined based on the magnitude of coefficients and the relationship between wavelet coefficients and dyadic nodes. The results demonstrate that the proposed method can balance accuracy of the solution and speed of computations by setting appropriate threshold of wavelet coefficients. Compared with the Gauss pseudospectral method software package

the number of nodes are reduced by 10% approximately

and the optimality accuracy is increased by an order of magnitude by using the method.