Direct Optimization of Low-Thrust Transfers Using Averaging Techniques Based on Fourier Series Expansion

Low-thrust transfers in the central gravitational field involve a large number of orbital revolutions, which poses a real challenge to trajectory optimization. This article uses an orbital averaging technique based on Fourier series Expansion to describe the trajectory dynamics: the low-thrust profile is transformed in Fourier space, and secular dynamics equations are represented as functions of these thrust Fourier coefficients. The Chebyshev pseudo spectral and the Sequence Quadratic Planning method are used to convert the optimal low-thrust transfer problem to a parameter optimization one and obtain the optimal control solutions. Maximum inclination transfer problem for the low-thrust vehicle in arbitrary elliptic Earth orbits is presented, and it shows that the direct method using averaging techniques based on Fourier series Expansion can determine the low-thrust optimal control solutions accurately and reduce computational requirements significantly.