This paper addresses the spacecraft relative orbit reconfiguration problem of minimizing the delta- cost of impulsive control actions while achieving a desired state in fixed time. The problem is posed in relative orbit element (ROE) space, which yields insight into relative motion geometry and allows for the straightforward inclusion of perturbations in linear time-variant form. Reachable set theory is used to translate the cost-minimization problem into a geometric path-planning problem and formulate the reachable delta- minimum, a new metric to assess optimality and quantify reachability of a maneuver scheme. Next, this paper presents a methodology to compute maneuver schemes that meet this new optimality criterion and achieve a prescribed reconfiguration. Though the methodology is applicable to any linear time-variant system, this paper uses a state representation in ROE to derive new globally optimal maneuver schemes in orbits of arbitrary eccentricity. The methodology is also used to generate quantifiably suboptimal solutions when the optimal solutions are unreachable. Further, this paper determines the mathematical impact of uncertainties on achieving the desired end state and provides a geometric visualization of those effects on the reachable set. The proposed algorithms are tested in realistic reconfiguration scenarios and validated in a high-fidelity computational simulation environment.
Closed-Form Optimal Impulsive Control of Spacecraft Formations Using Reachable Set Theory
Journal of Guidance, Control, and Dynamics ; 44 , 1 ; 25-44
2020-11-09
20 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
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