Practical Constraints for the Applied Lambert Problem

Thompson, B.; Rostowfske, Luke J.

doi:10.2514/1.g004765

Cited by 5 publications

(3 citation statements)

References 8 publications

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“…We use the penalty function method to deal with the constraint conditions; that is, when the constraint is not satisfied, a penalty term is added to the objective function, and the size of the penalty term is proportional to the value of the part beyond the limit, as shown in Equation (5).…”

Section: Solution Algorithm Frameworkmentioning

confidence: 99%

“…Huang et al characterized apogee and perigee height constraints as the lateral component range of eccentricity vector, and the solution of multirevolution transfer can be selected in advance to meet the constraints [4]. Thompson et al made the dynamic transformation of height constraints of apogee and perigee and determined the input direction of flight, transfer time, and cycle range by semimajor axis versus transfer time graph [5]. According to the demand of Moon-to-Earth transfer, Luo et al effectively transformed the dynamic characterization of the original Lambert problem for the quasi-Lambert problem with limited departure flight-direction angle but free transfer angle and gave a fast iterative solution [6].…”

Section: Introductionmentioning

confidence: 99%

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Multisatellite Flyby Inspection Trajectory Optimization Based on Constraint Repairing

et al. 2021

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With the rapid development of on-orbit services and space situational awareness, there is an urgent demand for multisatellite flyby inspection (MSFI) that can obtain information about a large number of space targets with little fuel consumption in a short time. There are two kinds of constraints, namely inspection constraints (ICs) at each flyby point and transfer process constraints (TPCs) in the actual mission. Further considering the influence of discrete and continuous variables such as inspection sequence, time, and maneuver scheme, it is complex and difficult to solve MSFI. To optimize it efficiently, the task flow and the problem model are defined firstly. Then, the algorithm framework based on constraint repairing is given, which contains repair methods of the ICs and the TPCs. Finally, the proposed method is compared with the nonrepair optimization method in two numerical examples. The results indicate that when the constraints are hard to meet, it is better and more efficient than the nonrepair method.

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Section: Solution Algorithm Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multisatellite Flyby Inspection Trajectory Optimization Based on Constraint Repairing

et al. 2021

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“…A typical way of solving the Lambert problem is to establish a connection between the transfer time and a Kepler element [12][13][14]. It is also common to convert the Lambert problem into an optimization problem by adding constraints [15][16][17] to achieve the optimal solution to the interception problem [18,19]. Unfortunately, these methods are sensitive to an initial value for iteration, and thus, the b-spline interpolation function is introduced to provide the selection strategy of the initial value [20].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution for the Single-Impulse Flyby Co-Orbital Spacecraft Problem

Su¹,

Dong²,

Liu³

et al. 2022

Aerospace

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The traversal inspection of satellites in satellite constellations or geosynchronous orbits has been a focus of research. A large number of variable orbit requirements in the “single-to-single” mode severely affects the efficiency of inspections. To address this problem, this study investigated the problem of a single-impulse flyby co-orbiting two spacecraft and proposed a derivative-free numerical solution method that used the geometric relationship between the two intersections of the target and transfer orbits of the flyby problem in order to transform them into a nonlinear equation in a single variable for a given impulse time. The validity of the proposed method was verified using numerical examples. While the Lambert problem is one of the bases for solving the variable orbit problem, on-star intelligent control also raises the requirements for speed. To address this problem, this study also investigated the Lambert problem in a single-impulse flyby co-orbiting two spacecraft and determined the iterative initial value by constructing a quadratic interpolation equation between the inverse of the transfer time and the vertical component of the eccentric vector, the derivative-free quadratic interpolation cut-off method was proposed. Using 100,000 random tests showed that computational efficiency was improved by more than one order of magnitude compared with commonly used methods, with a calculation error of less than 10−6.

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Lambert’s Problem with Multiple Constraints

Zhang

Liu

2022

J. Aerosp. Eng.

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Practical Constraints for the Applied Lambert Problem

Cited by 5 publications

References 8 publications

Multisatellite Flyby Inspection Trajectory Optimization Based on Constraint Repairing

Multisatellite Flyby Inspection Trajectory Optimization Based on Constraint Repairing

Numerical Solution for the Single-Impulse Flyby Co-Orbital Spacecraft Problem

Lambert’s Problem with Multiple Constraints

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