Direct Approach for Computing Near-Optimal Low-Thrust Earth-Orbit Transfers

Optimization of low-thrust many-revolution transfers and Lyapunov-based guidance

“…Furthermore, the perturbations and shadowing can be easily included by using orbital averaging. The parameterized control law is in the form of true optimal control, which is different from other parameterized control law such as the blended control [5], and the near-optimal control law [7], which are all theoretically not optimal. The use of equinoctial elements eliminates the singularity when either eccentricity or inclination is zero, which is not considered in Refs.…”

“…The use of equinoctial elements eliminates the singularity when either eccentricity or inclination is zero, which is not considered in Refs. [5,7] where the control laws with intuitive physical meaning are all expressed in classical orbital elements. A periapsis-and apoapsis-centered burn structure is introduced for solving fuel-saving orbit transfers, which is empirical but simple and effective.…”

“…In order to alleviate the computational burden, orbital averaging (also used in SEPSPOT) is employed by several researchers. Kluever [5] developed a method combining the orbital averaging method and a blended control strategy to efficiently solve minimumtime Earth-orbit transfers. Geffroy and Epenoy [6] solved orbit transfer problems under constraints by using the orbital averaging method.…”

Optimal strategy for low-thrust spiral trajectories using Lyapunov-based guidance

“…Compared with the indirect method, the direct method usually exhibits a larger convergence domain [5,6] . In the hybrid method, the time histories of costate variables are directly parameterized and the optimal solution is obtained through the NLP methods [7,8] .…”

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

“…Craig A. Kluever [10] developed a near-optimal direct method for minimum-time Earth-orbit transfer problems of solar electric propulsion spacecraft. The optimal thrust direction time history is computed by the blend of three external feedback control laws.…”