Optimal multiple-impulse time-fixed rendezvous between circular orbits

Prussing, John E.; Chiu, J. H.

doi:10.2514/6.1984-2036

Cited by 11 publications

(7 citation statements)

References 6 publications

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“…The numerical results show that the largest gain for the velocity variation (Δ ) does not imply the largest gain in energy (Δ ), which is a consequence of (11) to (13). Note that the variation in energy has an extra term (sin( )), affecting the magnitude of the change in energy and not the magnitude of the change in velocity.…”

Section: Swing-by Withmentioning

confidence: 85%

“…It is necessary to remember that the variation of energy obtained from the swing-by has a strong dependence on the geometry of the close approach, a fact that is expressed by the angle of approach in the analytical equations (11) to (13). The eccentricity of the primaries has a direct impact in this geometry, with lower values for the eccentricity generating trajectories for 3 that reaches 2 in approaches that are near parallel to the trajectory of 2 .…”

Section: Swing-by Withmentioning

confidence: 99%

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The Study of the Asymmetric Multiple Encounters Problem and Its Application to Obtain Jupiter Gravity Assisted Maneuvers

Santos

Prado

Rocco

2013

Mathematical Problems in Engineering

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The Multiple Encounters Problem is described in the literature as the problem of finding trajectories for a spacecraft that leaves from a mother planet, describes a trajectory in the interplanetary space, and then goes back to the mother planet. The present paper extends the literature and the departure and arrival angles of the spacecraft are generalized to be nonsymmetrical. The solutions are shown in terms of the true (]) and eccentric anomaly ( ). The velocity variation (Δ ) required for the transfer is also shown. Then, this study is generalized to consider the possibility that the spacecraft makes a close approach with the mother planet to change its energy in the return trip. The velocity (Δ ) and energy variation (Δ ) due to this passage are obtained. The topics studied here can be applied in missions that leave and come back to the Earth, with the goal of studying the interplanetary space, as well as for missions whose objective is to make an alteration in the energy of the space vehicle through a swing-by with the mother body.

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Section: Swing-by Withmentioning

confidence: 85%

Section: Swing-by Withmentioning

confidence: 99%

The Study of the Asymmetric Multiple Encounters Problem and Its Application to Obtain Jupiter Gravity Assisted Maneuvers

Santos

Prado

Rocco

2013

Mathematical Problems in Engineering

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“…The single-target time-constrained rendezvous is a wellknown problem in spaceflight mechanics. Several optimization methods have been proposed assuming either finite [21] or impulsive thrust [22,23]. In the latter case, four burns permit the achievement of the optimal solution [24].…”

Section: Introductionmentioning

confidence: 99%

Evolutionary Optimization of Multirendezvous Impulsive Trajectories

Federici

Zavoli

Colasurdo

2021

International Journal of Aerospace Engineering

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This paper investigates the use of evolutionary algorithms for the optimization of time-constrained impulsive multirendezvous missions. The aim is to find the minimum- Δ V trajectory that allows a chaser spacecraft to perform, in a prescribed mission time, a complete tour of a set of targets, such as space debris or artificial satellites, which move on the same orbital plane at slightly different altitudes. For this purpose, a two-level design approach is pursued. First, an outer-level combinatorial problem is defined, dealing with the simultaneous optimization of the sequence of targets and the rendezvous epochs. The suggested approach is first tested by assuming that all transfer legs last exactly the same amount of time; then, the time domain is discretized over a finer grid, allowing a more appropriate sizing of the time window allocated for each leg. The outer-level problem is solved by an in-house genetic algorithm, which features an effective permutation-preserving solution encoding. A simple, but fairly accurate, heuristic, based on a suboptimal four-impulse analytic solution of the single-target rendezvous problem, is used when solving the combinatorial problem for a fast guess at the transfer cost, given the departure and arrival epochs. The outer-level problem solution is used to define an inner-level NLP problem, concerning the optimization of each body-to-body transfer leg. In this phase, the encounter times are further refined. The inner-level problem is tackled through an in-house multipopulation self-adaptive differential evolution algorithm. Numerical results for case studies including up to 20 targets with different time grids are presented.

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“…The power-limited thrust is a continuously variable thrust or a constant thrust. For the optimal rendezvous problem with continuously variable thrust , there are some important results [15–19]. For the problem with constant thrust , the thrust of engine is assumed to be constant in magnitude and controllable in direction.…”

Section: Introductionmentioning

confidence: 99%

An improved two-manoeuvre method for orbit rendezvous with constant thrust

Zhang

Zhou

2011

Proceedings of the Institution of Mechanical Engineers, Part G:

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An improved two-manoeuvre method to the two-point boundary value problem for arbitrary non-coplanar elliptic orbital rendezvous with constant thrust is proposed. The initial required velocity is obtained by solving Lambert's problem. A new method is proposed to determine the optimal thrust direction to nullify the velocity variation. The optimal direction is close to the direction of the velocity-to-be-gained vector. Therefore, the velocity-to-be-gained guidance method is adopted in both the first and the second engine manoeuvres. The total rendezvous process requires a closed-loop feedback control in the first manoeuvre and an open-loop control in the second one. Compared with existing methods based on the linear relative motion equations, this new approach can be used in the cases of far relative ranges and long rendezvous times. Numerical simulations show that the proposed method is feasible.

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Optimal multiple-impulse time-fixed rendezvous between circular orbits

Cited by 11 publications

References 6 publications

The Study of the Asymmetric Multiple Encounters Problem and Its Application to Obtain Jupiter Gravity Assisted Maneuvers

The Study of the Asymmetric Multiple Encounters Problem and Its Application to Obtain Jupiter Gravity Assisted Maneuvers

Evolutionary Optimization of Multirendezvous Impulsive Trajectories

An improved two-manoeuvre method for orbit rendezvous with constant thrust

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