Point return orbit design and characteristics analysis for manned lunar mission

Shen, Hong-Xin; Zhou, Jianping; Peng, Qibo; Li, Haiyang

doi:10.1007/s11431-012-4969-4

Cited by 15 publications

(21 citation statements)

References 7 publications

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“…Provided a tentative solution is given, the equations of motion and adjoint differential equations are integrated to determine the errors on the boundary conditions. The initial values of the unknown constants that rule the state equations (Δ t 1 , Δ t 2 , Δ v r 1 , Δ v θ 1 ) are easily estimated from their physical meaning; one only needs to ensure that they are within reasonable ranges (Section 6), which can be determined according to the existing literature . Therefore, in this paper, attention is focused on estimating only the initial adjoints, as finding appropriate values is a quite difficult task.…”

Section: Indirect Optimization Methodsmentioning

confidence: 99%

“…The optimal trajectory with minimal Δ v is depicted in Figure . By referring to the results of and , the ranges for the unknown constants to estimate the initial adjoints are assumed as

0.25 h \leq Δ {italict}_{1} \leq 0.75 h, 2.5 day \leq Δ {italict}_{2} \leq 4.5 day, Δ {italicv}_{r 1} = 0, 0.8 km / s \leq Δ {italicv}_{θ 1} \leq 1 km / s

and the procedures usually provide a suitable initial guess for any set of values within these ranges. In the following example, Δ t 1 = 0.5 h, Δ t 2 = 4 day, Δ v r 1 = 0, and Δ v θ 1 = 0.85 km/s are used.…”

Section: Validationmentioning

confidence: 99%

“…Because the initial LLO is almost circular with respect to the Moon, velocity at point 1 is approximately horizontal, that is, v r1 ≈ 0. By means of (18), one also has that the magnitude of the velocity adjoint vector at the points where the impulses are applied is unit. Thus, the estimation of velocity adjoints at point 1 is…”

Section: Initial Adjoints Estimation With Adjoint Control Transformationmentioning

confidence: 99%

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Adjoints estimation methods for impulsive Moon-to-Earth trajectories in the restricted three-body problem

Shen

Casalino

2014

Optim. Control Appl. Meth.

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SUMMARYA study of optimal impulsive Moon-to-Earth trajectories is presented in a planar circular restricted threebody framework. Two-dimensional return trajectories from circular lunar orbits are considered, and the optimization criterion is the total velocity change. The optimal conditions are provided by the optimal control theory. The boundary value problem that arises from the application of the theory of optimal control is solved using a procedure based on Newton's method. Motivated by the difficulty of obtaining convergence, the search for the initial adjoints is carried out by means of two different techniques: homotopic approach and adjoint control transformation. Numerical results demonstrate that both initial adjoints estimation methods are effective and efficient to find the optimal solution and allow exploring the fundamental tradeoff between the time of flight and required ΔV.

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Section: Indirect Optimization Methodsmentioning

confidence: 99%

“…The optimal trajectory with minimal Δ v is depicted in Figure . By referring to the results of and , the ranges for the unknown constants to estimate the initial adjoints are assumed as

0.25 h \leq Δ {italict}_{1} \leq 0.75 h, 2.5 day \leq Δ {italict}_{2} \leq 4.5 day, Δ {italicv}_{r 1} = 0, 0.8 km / s \leq Δ {italicv}_{θ 1} \leq 1 km / s

Section: Validationmentioning

confidence: 99%

Section: Initial Adjoints Estimation With Adjoint Control Transformationmentioning

confidence: 99%

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Adjoints estimation methods for impulsive Moon-to-Earth trajectories in the restricted three-body problem

Shen

Casalino

2014

Optim. Control Appl. Meth.

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“…The spacecraft velocity is either free or related to the maximum permitted value of velocity v reentry at the atmosphere boundary r reentry , which is usually set at 122 km above the Earth's surface. () Using the patched‐conic approximation, the hyperbolic excess velocity on entering the Earth's sphere of influence becomes

(‖‖, {bold-italicv}_{\infty f}) = (‖‖, v_{f} - v_{\oplus} ((), t_{f})) = \sqrt{v_{reentry}^{2} - 2 \frac{{normalμ}_{\oplus}}{r_{reentry}},}

where μ ⊕ is the gravitational parameter of the Earth. The maximum incoming hyperbolic excess velocity is assumed to be 6 km/s, resulting in entry velocity v reentry around 12.6 km/s, which is slightly smaller than the corresponding limited value used for NASA's Stardust mission…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…The spacecraft velocity is either free or related to the maximum permitted value of velocity v reentry at the atmosphere boundary r reentry , which is usually set at 122 km above the Earth's surface. 23,24 Using the patched-conic approximation, the hyperbolic excess velocity on entering the Earth's sphere of influence becomes…”

Section: Statement Of the Problemmentioning

confidence: 99%

No‐guess indirect optimization of asteroid mission using electric propulsion

Shen

2018

Optim Control Appl Methods

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Summary This paper researches the optimal opportunities and trajectories for an asteroid‐Earth return mission and compares different options in terms of time length and reentry velocity. High specific impulse and steering capabilities of solar electric propulsion are exploited to perform deep space maneuvers. An indirect method based on the theory of optimal control is applied to find the trajectory that maximizes the final mass. The boundary value problem that arises from the application of the optimal control theory is solved by means of a shooting procedure based on Newton's method. In particular, the best opportunities to reach the Earth are first analyzed by searching a time‐free transfer that intercepts the Earth's orbit at the most favorable point; suitable launch windows are then determined. This technique shows significant benefit to define the initial solution that is required to start the optimization process so that no initial guess of adjoints is required for the optimization. Mission opportunities returning from asteroid Bennu (101955) are presented.

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Indirect Optimization of Three-Dimensional Multiple-Impulse Moon-to-Earth Transfers

Shen¹,

Casalino

2014

J of Astronaut Sci

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Point return orbit design and characteristics analysis for manned lunar mission

Cited by 15 publications

References 7 publications

Adjoints estimation methods for impulsive Moon-to-Earth trajectories in the restricted three-body problem

Adjoints estimation methods for impulsive Moon-to-Earth trajectories in the restricted three-body problem

No‐guess indirect optimization of asteroid mission using electric propulsion

Indirect Optimization of Three-Dimensional Multiple-Impulse Moon-to-Earth Transfers

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