This paper addresses the spacecraft relative orbit reconfiguration problem of minimizing the delta- v 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- v 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.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Closed-Form Optimal Impulsive Control of Spacecraft Formations Using Reachable Set Theory


    Contributors:

    Published in:

    Publication date :

    2020-11-09


    Size :

    20 pages




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English





    Optimal Continuous/Impulsive Control for Lorentz-Augmented Spacecraft Formations

    Sobiesiak, Ludwik A. / Damaren, Christopher J. | AIAA | 2014




    NEW CLOSED-FORM SOLUTIONS FOR OPTIMAL IMPULSIVE CONTROL OF SPACECRAFT RELATIVE MOTION

    Chernick, Michelle / D Amico, Simone | British Library Conference Proceedings | 2016