Abstract
The minimum time interception problem with a tangent impulse whose direction is the same as the satellite’s velocity direction is studied based on the relative motion equations of elliptical orbits by the combination of analytical, numerical, and optimization methods. Firstly, the feasible domain of the true anomaly of the target under the fixed impulse point is given, and the interception solution is transformed into a univariate function only with respect to the target true anomaly by using the relative motion equation. On the basis of the above, the numerical solution of the function is obtained by the combination of incremental search and the false position method. Secondly, considering the initial drift when the impulse point is freely selected, the genetic algorithm-sequential quadratic programming (GA-SQP) combination optimization method is used to obtain the minimum time interception solution under the tangent impulse in a target motion cycle. Thirdly, under the high-precision orbit prediction (HPOP) model, the Nelder-Mead simplex method is used to optimize the impulse velocity and transfer time to obtain the accurate interception solution. Lastly, the effectiveness of the proposed method is verified by simulation examples.
Highlights
For the orbital interception problem under the two-body model, the Lambert method can be used to solve it when the initial orbital elements of a satellite and a target are known [1]
The main innovation of this paper is to provide an accurate method to solve the interception solution of the minimum time tangent impulse under relative motion by combining analytical, numerical, and optimization methods
− a tan 2 c4, c5 − π2 + π1 + f1 6. It can be seen from the above conclusion that the feasible domain of the tangent interception solution corresponding to the satellite impulse point is f2 ∈ f2,s1, f2,s2, in which, when f2 ∈ f2,s4, f2,s2, the flight transfer angle of the projectile is greater than π and the interception orbit is hyperbolic
Summary
For the orbital interception problem under the two-body model, the Lambert method can be used to solve it when the initial orbital elements of a satellite and a target are known [1]. When the impulse point and the interception point are given, the orbital transfer time can be obtained by the Kepler equation, and the initial velocity required for the orbital transfer can be solved by expressing the transfer time as a univariate function of other parameters [2, 3]. When the relative distance between the satellite and the target is small, the state transition matrix can be constructed to solve the initial velocity required for the orbital transfer. For the Lambert problem considering J2 perturbation, under the premise of setting the terminal precision, the state transitionsensitive matrix of the two-body model is often used to iteratively obtain the required initial velocity by the shooting method [16]. The relative motion model based on an elliptic orbit is used to transform the interception solution into a univariate function only about the true anomaly of the target. Considering the initial drift segment, the GA-SQP combination optimization
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