Sundman-Transformed Differential Dynamic Programming with Modified Equinoctial Elements

Previous efforts addressed the challenge of low-thrust many-revolution trajectory optimization by applying a Sundman transformation to change the independent variable of the spacecraft equations of motion to an orbit anomaly and performing the optimization with differential dynamic programming (DDP). The approach may be enhanced by representing the spacecraft state with orbital elements rather than position and velocity coordinates. This paper shows how the modified equinoctial element state representation enters the DDP algorithm. Example transfers from geostationary transfer orbit (GTO) to geosynchronous orbit (GEO) demonstrate how gains in computational efficiency are possible with minimal impact to solution quality. Those gains are leveraged to compute the Pareto front of time versus delivered mass for a benchmark orbit transfer from the literature.

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