A second-order solution to the two-point boundary value problem for rendezvous in eccentric orbits

Zhang, Gang; Zhou, Di

doi:10.1007/s10569-010-9269-3

Cited by 13 publications

(2 citation statements)

References 25 publications

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“…From q 2 J/q 2 > 0 by equation (18), it is known that the solution of is almost equal to zero. Note that ¼ 0 is an approximate optimal solution to minimize the cost function J in equation (14) when the sampling period t is small enough, although ¼ 0 does not exactly satisfy equation (16). Obviously, the optimal manoeuvre strategy is close to the velocity-to-be-gained guidance scheme.…”

Section: Fig 2 Geometry Of Thrust Directionmentioning

confidence: 99%

“…When the state transition matrix of these equations is obtained [ 13 ], it will be easy to obtain an analytical expression for the required relative velocity. Using the perturbation method, Zhang and Zhou [ 14 ] proposed a second-order solution to the two-point boundary value problem for elliptical orbital rendezvous, while accounting for J 2 perturbation.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Fig 2 Geometry Of Thrust Directionmentioning

confidence: 99%

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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Optimal two-impulse rendezvous using constrained multiple-revolution Lambert solutions

Zhang

Zhou

Mortari

2011

Celest Mech Dyn Astr

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A solution to the fixed-time minimum-fuel two-impulse rendezvous problem for the general non-coplanar elliptical orbits is provided. The optimal transfer orbit is obtained using the constrained multiple-revolution Lambert solution. Constraints consist of lower bound for perigee altitude and upper bound for apogee altitude. The optimal time-free twoimpulse transfer problem between two fixed endpoints implies finding the roots of an eighth order polynomial, which is done using a numerical iterative technique. The set of feasible solutions is determined by using the constraints conditions to solve for the short-path and long-path orbits semimajor axis ranges. Then, by comparing the optimal time-free solution with the feasible solutions, the optimal semimajor axis for the two fixed-endpoints transfer is identified. Based on the proposed solution procedure for the optimal two fixed-endpoints transfer, a contour of the minimum cost for different initial and final coasting parameters is obtained. Finally, a numerical optimization algorithm (e.g., evolutionary algorithm) can be used to solve this global minimization problem. A numerical example is provided to show how to apply the proposed technique.

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