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Optimal deterministic guidance for bounded-thrust spacecrafts

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Abstract

The minimum-propellant deterministic guidance law for bounded-thrust, constant jetexhaust velocity, spacecrafts is developed using the neighboring extremal theory. Minimization of the first-order variation in cost between a multi-burn nominal extremal and the perturbed trajectory eliminates all correction strategies except small changes in the nominal thrust-on, thrust-off times and small rotations of the thrust vector. Optimal values of these corrective controls for fixed values of initial state deviations, δx 0, are found by minimizing the second variation in cost subject to the variational state and adjoint equations — an accessory minimum problem. The solution takes the linear feedback form δu=A −1 22 A 21δx 0, where the matricesA 22 andA 21 are functions only of transition matrices calculated along the nominal trajectory. The solution is applied to a three-burn Earth-Mars transfer.

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Authors and Affiliations

  1. Dept. of Aerospace Engineering and Mechanics, Univ. of Minnesota, Minneapolis, Minn., USA

    Alain L. Kornhauser (Assistant Professor)

  2. Dept. of Aerospace and Mechanical Sciences, Princeton Univ., Princeton, N.J., USA

    Paul M. Lion (Associate Professor)

Authors
  1. Alain L. Kornhauser
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  2. Paul M. Lion
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Kornhauser, A.L., Lion, P.M. Optimal deterministic guidance for bounded-thrust spacecrafts. Celestial Mechanics 5, 261–281 (1972). https://doi.org/10.1007/BF01228429

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  • DOI: https://doi.org/10.1007/BF01228429

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