Naval Postgraduate School, Monterey, California, & Politecnico di Torino, Torino, Italy
Analytical-numerical method for the Time-Optimal Maneuver of a Spacecraft in Proximity of a Reference Orbit
The time-optimal maneuver is considered for a fourth-order 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 fourth-order system is equivalent, via a well-known state vector transformation, to the Hill-Clohessy-Wiltshire 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 fourth-order linear speed of response problem, Journal of Applied Mathematics and Mechanics, 1996) to determine the change in the minimum-time control to the state-space origin as the initial state is variated, and Romano and Curti’s method (M. Romano and F. Curti, Time-optimal control of linear time invariant systems between two arbitrary states, Automatica, 2020) to determine the minimum-time 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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Analytical-numerical method for the Time-Optimal Maneuver of a Spacecraft in Proximity of a Reference Orbit
