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Gaussian Smoothing Technique for Eclipse-Constrained Cislunar Multi-Mode Trajectory Optimization
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DOI：10.34133/space.0441.png)
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Abstract
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The presence of discontinuous path constraints and optimal bang-bang control profiles in indirect trajectory optimization may lead to integral discontinuities and exacerbate the sensitivity problem of the initial costate. In this manuscript, we incorporate a multimode electric propulsion system into a low-thrust trajectory optimization problem subject to shadow constraints in cislunar space. The forced engine shutdown in shadowing and the rapid switching between different propulsion modes exacerbate the nonlinearity of the optimization problem. An indirect optimal control formulation for the multimode propulsion system is derived, and a control smoothing method based on the Gaussian error function is proposed. The 13-type minimum-fuel transfer problem between 4 cislunar periodic orbits under all possible shadowing conditions is resolved through the utilization of a set of parameterized S-shaped curves, which gradually approximate the discontinuity profiles. A comparative analysis was conducted to demonstrate the effectiveness of the technique, and the distribution of the arc segments and the embedding pattern of the shadow arcs were discussed.
Keywords:
trajectory optimization
bang-bang control
shadow constraints
multimode propulsion
Gaussian smoothing
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