  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 criteria and achieve a prescribed reconfiguration. Though
the methodology is applicable to any linear time-variant system, this paper
leverages 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 sub-optimal 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 simulation environment.
