Impulsive orbit correction using second-order Gauss’s variational equations

Zhang, Gang; Mortari, Daniele

doi:10.1007/s10569-019-9949-6

Cited by 3 publications

(4 citation statements)

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“…Looking at the three 2D planes separately, reconfigurations can be categorized based on whether they can be achieved with one or two maneuvers by determining the times ∈ T where S(c, t) intersects the boundary of S * (c, T), where S and S * are computed with Eqs. (8) and (9), respectively. The reachable sets for eccentric orbits ( Fig.…”

Section: Analysis Of Reachable Sets In Roe Spacementioning

confidence: 99%

“…6a for an arbitrary 2D case and can be easily deduced by substituting (1 + )δu u u in place of δu u u in the definitions of the reachable sets given in Eqs. (7), (8), and (9), where the pseudo-state is linear in delta-v. In all figures in this section, the solid lines indicate S * (c, T), the convex hull of the reachable set, and the dashed lines indicate S(c, t), the reachable set at an arbitrary time in the reconfiguration span.…”

Section: Maneuver Execution Errorsmentioning

confidence: 99%

“…In addition, it was assumed that the in-plane and out-of-plane control problems were decoupled. Zhang and Mortari [8] removed the need for the transcendental equation in Chernick's closed-form solution and used it as initial guess to derive both single-and multi-impulse minimum norm solutions through a nonlinear least-squares iterative method using the second order Gauss Variational Equations. Vaddi et al [9] proposed analytical solutions to the optimal reconfiguration problem, but only for control of the in-plane orbital elements in near-circular orbits.…”

mentioning

confidence: 99%

“…In addition, it was assumed that the in-plane and out-of-plane control problems were decoupled. Zhang and Mortari [8] removed the need for the transcendental equation in Chernick's closed-form solution and used it as initial guess to derive both single-and multi-impulse minimum norm solutions through a nonlinear least-squares iterative Given an initial set of chief orbital elements (OE), α α α c,0 , and an initial set of ROE, δα α α 0 , the fixed-time, fixed-end conditions relative orbit reconfiguration problem is defined by a desired final set of ROE, δα α α f ∈ R 6 , and a reconfiguration time span T. With these reconfiguration parameters, the optimal control problem to be solved in this paper is…”

mentioning

confidence: 99%

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New Closed-Form Solutions for Optimal Impulsive Control of Spacecraft Relative Motion

Chernick

D’Amico

2018

Journal of Guidance, Control, and Dynamics

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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 timevariant 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.

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Section: Analysis Of Reachable Sets In Roe Spacementioning

confidence: 99%

Section: Maneuver Execution Errorsmentioning

confidence: 99%

mentioning

confidence: 99%

“…In addition, it was assumed that the in-plane and out-of-plane control problems were decoupled. Zhang and Mortari [8] removed the need for the transcendental equation in Chernick's closed-form solution and used it as initial guess to derive both single-and multi-impulse minimum norm solutions through a nonlinear least-squares iterative Given an initial set of chief orbital elements (OE), α α α c,0 , and an initial set of ROE, δα α α 0 , the fixed-time, fixed-end conditions relative orbit reconfiguration problem is defined by a desired final set of ROE, δα α α f ∈ R 6 , and a reconfiguration time span T. With these reconfiguration parameters, the optimal control problem to be solved in this paper is…”

mentioning

confidence: 99%

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