The primer vector on fixed-time impulsive trajectories

Handelsman, M.; Lion, P. M.

doi:10.2514/6.1967-54

Cited by 9 publications

(12 citation statements)

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“…The optimality conditions for problems of this form are described in [20] and [21] and summarized breifly in the following. Suppose c * is an optimal solution to (14). Because S * (c * ) is compact and convex, there must exist a non-empty set…”

Section: Reformulation Of the Energy-optimal Control Problemmentioning

confidence: 99%

“…Using this method, the optimal control problem is cast as a two-point boundary value problem where an optimal solution must satisfy a set of analytical conditions on the evolution of the primer vector. This approach has been studied continuously for over fifty years [14]- [19], but the resulting algorithms are subject to substantial limitations. For example, Roscoe's algorithm [18] is known to have a limited radius of convergence from the initial estimate of the times of optimal control inputs.…”

Section: Introductionmentioning

confidence: 99%

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Fast Algorithm for Fuel-Optimal Impulsive Control of Linear Systems With Time-Varying Cost

Koenig

D’Amico

2021

IEEE Trans. Automat. Contr.

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This paper presents a new computationally efficient and robust algorithm that provides energy-optimal impulsive control input sequences that drive a linear timevariant system to a desired state at a specified time. This algorithm is applicable to a broad class of problems where the cost is expressed as a time-varying norm-like function of the control input. This degree of generality enables inclusion of complex, time-varying operational constraints in the control planning problem. First, optimality conditions for this problem are derived using reachable set theory, which provides a simple geometric interpretation of the meaning of the dual variables. Next, an optimal impulsive control algorithm is developed that iteratively refines an estimate of the dual variable until the optimality criteria are satisfied to within a user-specified tolerance. The iteration procedure simultaneously ensures global convergence and minimizes computation cost by discarding inactive constraints. The algorithm is validated through implementation in challenging example problems based on the recently proposed Miniaturized Distributed Occulter/Telescope small satellite mission, which requires periodic formation reconfigurations in a perturbed orbit with time-varying attitude constraints. Additionally, it is demonstrated that the algorithm can be implemented with run times more than an order of magnitude faster than other approaches.

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Section: Reformulation Of the Energy-optimal Control Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fast Algorithm for Fuel-Optimal Impulsive Control of Linear Systems With Time-Varying Cost

Koenig

D’Amico

2021

IEEE Trans. Automat. Contr.

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“…When the magnitude of the thrust is not very low, the orbit transfer can be approximated as a multi-impulse model. Numerous studies on impulsive orbit rendezvous of two-body models have been conducted [2][3][4][5][6][7]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

“…For certain particular orbits, an analytical solution of multiple impulses can be derived [3,4]. The optimization methods typically include indirect method using prime vector theory [5] and direct method using parameter optimization [6,7]. The optimization of the two-body dynamics model does not require inordinate time because the equations are analytical.…”

Section: Introductionmentioning

confidence: 99%

Fast optimization of impulsive perturbed orbit rendezvous using simplified parametric model

Huang

Luo

2021

Astrodyn

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A novel simplified parametric model for long-duration impulsive orbit rendezvous is proposed. Based on an existing fast estimation method, the optimal impulses and trajectory can be expressed by only ten parameters whose initial values can be easily determined.Then, these parameters are used to predict orbital deviations with a target orbit. A simple correction process is designed to sequentially update the parameters based on the J2 perturbed analytical dynamic equations of circular orbits. Finally, an iteration loop is formed to obtain the precise parameters and optimal trajectory. The simulation results confirm that the simplified parametric optimization method can be applied to elliptical orbits of small eccentricity and adapts well to both analytical and high-precision dynamics.The deviations could always converge within five iterations and the calculation was more efficient than the existing methods.

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“…The most well-known multiple impulsive maneuver for coplanar orbits was first proposed by Walter Hohmann [1] in year 1925. Then, Lion et al [2] have utilized the primer vector for optimal impulsive time-fixed approaches. The primer vector has been implemented for both circular and elliptical orbits [3,4].…”

Section: Introductionmentioning

confidence: 99%

A new shape-based multiple-impulse strategy for coplanar orbital maneuvers

2019

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A new shape-based geometric method (SBGM) is proposed for generation of multi-impulse transfer trajectories between arbitrary coplanar oblique orbits via a heuristic algorithm. The key advantage of the proposed SBGM includes a significant reduction in the number of design variables for an Nimpulse orbital maneuver leading to a lower computational effort and energy requirement. The SBGM generates a smooth transfer trajectory by joining a number of confocal elliptic arcs such that the intersections share common tangent directions. It is proven that the well-known classic Hohmann transfer and its bi-elliptic counterpart between circular orbits are special cases of the proposed SBGM. The performance and efficiency of the proposed approach is evaluated via computer simulations whose results are compared with those of optimal Lambert maneuver and traditional methods. The results demonstrate a good compatibility and superiority of the proposed SBGM in terms of required energy effort and computational efficiency.

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The primer vector on fixed-time impulsive trajectories

Cited by 9 publications

References 1 publication

Fast Algorithm for Fuel-Optimal Impulsive Control of Linear Systems With Time-Varying Cost

Fast Algorithm for Fuel-Optimal Impulsive Control of Linear Systems With Time-Varying Cost

Fast optimization of impulsive perturbed orbit rendezvous using simplified parametric model

A new shape-based multiple-impulse strategy for coplanar orbital maneuvers

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