Naval Postgraduate School, Monterey, California, & Politecnico di Torino, Torino, Italy
Analyticalnumerical method for the TimeOptimal Maneuver of a Spacecraft in Proximity of a Reference Orbit
The timeoptimal maneuver is considered for a fourthorder system, that consists of a double integrator and a harmonic oscillator, coupled by one control channel. The boundary conditions are arbitrarily set initial and final states. That fourthorder system is equivalent, via a wellknown state vector transformation, to the HillClohessyWiltshire Dynamics of a Spacecraft relative to a reference circular orbit, subjected to a continuous thrust parallel to the orbital velocity vector. A new combination is presented here of Belousova and Zarkh’s method (Y. R. Belousova and M.A. Zarkh, The synthesis of optimal control in a fourthorder linear speed of response problem, Journal of Applied Mathematics and Mechanics, 1996) to determine the change in the minimumtime control to the statespace origin as the initial state is variated, and Romano and Curti’s method (M. Romano and F. Curti, Timeoptimal control of linear time invariant systems between two arbitrary states, Automatica, 2020) to determine the minimumtime control between two arbitrary states based upon the knowledge of the minimum time control between an arbitrary state and the origin. A perspective is given toward the application of the proposed method for the more general case of elliptical reference orbit (Tschauner model).
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Analyticalnumerical method for the TimeOptimal Maneuver of a Spacecraft in Proximity of a Reference Orbit
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