CN103293962A - Planet gravity-assist low-thrust trajectory optimization method based on decomposition and coordination strategy - Google Patents

Abstract

The invention relates to a planet gravity-assist low-thrust trajectory optimization method based on a decomposition and coordination strategy and belongs to the technical field of aerospace technologies. The planet gravity-assist low-thrust trajectory optimization method based on the decomposition and coordination strategy comprises firstly decomposing a planet gravity-assist low-thrust transfer trajectory optimization problem into a system-level optimization problem and two second-level optimization sub-problems with planet gravity-assist positions serving as nodes; and then utilizing the system-level optimization problem solving as a main iteration for coordinating status matching of the planet gravity-assist positions of the optimization sub-problems, and utilizing the second-level optimization sub-problem solving as an auxiliary iteration for determining thrust control laws of every subsection trajectory until the main iteration and the auxiliary iteration are both converged. The planet gravity-assist low-thrust trajectory optimization method based on the decomposition and coordination strategy reduces the complexity of an optimization model and the sensitivity of the trajectory constraint to optimized parameters, and improves the convergence efficiency of the transfer trajectory optimization problem.

Description

A kind of planet based on the composition decomposition strategy is borrowed power low-thrust trajectory optimization method

Technical field

The present invention relates to a kind of planet based on the composition decomposition strategy and borrow power low-thrust trajectory optimization method, belong to field of aerospace technology.

Background technology

The development of advanced Push Technology and the discovery of the new mechanism of celestial mechanics, for the flying method of deep space probe has brought technical renovation, typical representative is to borrow the branch mode of power technology in conjunction with low thrust propulsion system and planet, has plurality of advantages such as emitted energy is low, fuel consumption is few, the technology realization is simple.Simultaneously, the introducing of these two new technologies has also brought problems such as dynamics of orbits is non-linear by force, optimization model complexity, causes the optimal design convergence difficulty of transfer orbit.Optimal design is the gordian technique that planet is borrowed the research of power low thrust transfer orbit, seeks the main path that the reasonable optimizing method is raising problem convergence efficiency, is one of hot issue of current scientific and technical personnel's concern.

Borrow in the power low-thrust trajectory optimization method at the planet that has developed, technology [1] (McConaghy T T formerly, Debban T J, Petropoulos A E, Longuski J M.Design and Optimization of Low-Thrust Trajectories with Gravity Assists[J] .Journal of Spacecraft and Rockets, 2003,40 (3): 380-387.), proposed a kind of optimization method based on the pulse hypothesis.This method is decomposed into a plurality of discrete segmental arcs with low-thrust trajectory, and the combined action of thrust on each section track is assumed to the pulse that is applied to this track mid point, thereby the Orbit Optimized problem is converted into the optimizing problem that discrete pulse and planet are borrowed force parameter of finding the solution.The advantage of this method is by the pulse hypothesis, has effectively reduced the optimization number of parameters, and shortcoming is that the pulse hypothesis has reduced computational accuracy, and optimizing algorithm still needs to calculate simultaneously discrete pulse and planet is borrowed force parameter, and convergence efficiency is lower.

Technology [2] (Fanghua Jiang formerly, Hexi Baoyin, Junfeng Li.Practical Techniques for Low-Thrust Trajectory Optimization with Homotoptic Approach[J] .Journal of Guidance, Control, and Dynamics, 2012,35 (1): 245-258.), proposed a kind of indirect Orbit Optimized method based on Homotopy Transform.This method is utilized Pang De lia king extremum principle that the Orbit Optimized problem is converted into and is found the solution boundary value problem, in conjunction with technology such as particle optimization, Homotopy Transform, realizes finding the solution of optimum solution.The solution that the advantage of this method is tried to achieve by indirect method satisfies the single order optimality condition, shortcoming is not have the association of concrete physical meaning state variable owing to having introduced, borrow power, consider complicated low thrust transfer orbit optimization problem such as path constraint for planet repeatedly, this method is very responsive to initial value, convergence is relatively poor, the practicality deficiency.

Summary of the invention

The present invention provides a kind of planet based on the composition decomposition strategy to borrow power low-thrust trajectory optimization method for solving the problem to initial value sensitivity, poor astringency that existing survey of deep space planet borrows power low thrust transfer orbit optimization method to exist.

The present invention is achieved through the following technical solutions: at first borrowing the power place with planet is node, borrows power low thrust transfer orbit optimization problem to be decomposed into a system-level optimization problem and two 2-level optimization subproblems in planet; Be solved to main iteration with system-level optimization problem then, the planet that is used for coordinating sub-optimization problem is solved to time iteration by means of power place state matches with the 2-level optimization subproblem, is used for determining the thrust control law of each segmentation track, all restrains until main iteration and inferior iteration.Below concrete steps are elaborated.

Step 1, the Orbit Optimized model decomposes

Detector is under the effect of thrustor, follow celestial body A, through borrowing Lixing star B, arrive target celestial body C, be that node is decomposed into two sections with whole transfer orbit to borrow Lixing star B: borrow before the power track BC section after the track AB section and the power of borrowing, by optimizing the model decomposition transfer orbit optimization problem is decomposed into a system-level optimization problem and two 2-level optimization subproblems, three optimization problem models are as described below.

1) AB section 2-level optimization subproblem model

Optimize parameter

$X_{\mathrm{AB}}=[U_{\mathrm{AB}}\left(t\right),V_{\mathrm{AB}}^{\∞-}]$

Wherein: U _AB(t) be the low thrust control law of AB section track,

For the detector of AB section 2-level optimization subproblem correspondence enters the hyperbolic curve hypervelocity with respect to planet B.

Performance index

$J_{\mathrm{AB}}=\left|\right|V_{\mathrm{AB}}^{\∞-}-V_S^{\∞-}\left|\right|\→\min$

Wherein:

Be the optimization parameter of system-level optimization problem, the physical significance of sign is that the detector of system-level optimization problem correspondence enters hyperbolic curve hypervelocity with respect to planet B.

Constraint condition

${\mathrm{\Φ}}_{\mathrm{AB}}=\left(\begin{array}{c}\left|\right|r_{\mathrm{AB}}\left(t_B\right)-r_B\left(t_B\right)\left|\right|\\ \left|\right|U_{\mathrm{AB}}\left(t\right)\left|\right|-U_P\end{array}\right)=0$

Wherein: r _ABBe the heliocentric position vector of AB section track detector, r _BBe respectively the heliocentric position vector of planet B, t _BFor planet B borrows power constantly, U _PBe thrustor thrust size.

2) BC section 2-level optimization subproblem model

Optimize parameter

$X_{\mathrm{BC}}=[U_{\mathrm{BC}}\left(t\right),V_{\mathrm{BC}}^{\∞+}]$

Wherein: U _BC(t) be the low thrust control law of BC section track,

Be the detector of the BC section 2-level optimization subproblem correspondence hyperbolic curve hypervelocity of setting out with respect to planet B.

Performance index

$J_{\mathrm{BC}}=\left|\right|V_{\mathrm{BC}}^{\∞+}-V_S^{\∞+}\left|\right|\→\min$

Wherein:

Be the optimization parameter of system-level optimization problem, the physical significance of sign is that the detector of system-level optimization problem correspondence is with respect to the hyperbolic curve hypervelocity of setting out of planet B.

Constraint condition

${\mathrm{\Φ}}_{\mathrm{BC}}=\left(\begin{array}{c}\left|\right|r_{\mathrm{BC}}\left(t_B\right)-r_B\left(t_B\right)\left|\right|\\ \left|\right|U_{\mathrm{BC}}\left(t\right)\left|\right|-U_P\end{array}\right)=0$

Wherein: r _BCHeliocentric position vector for BC section track detector.

3) system-level optimization problem model

Optimize parameter

$X_S=[t_A,t_B,t_C,V_S^{\∞-},V_S^{\∞+}]$

Wherein: t _AFor detector from celestial body A constantly, t _CArrive the moment of celestial body C for detector.

Performance index

J _S=t _C-t _A→min

Constraint condition

${\mathrm{\Φ}}_{S1}=\left(\begin{array}{c}\left|\right|V_S^{\∞-}\left|\right|-\left|\right|V_S^{\∞+}\left|\right|\\ \left|\right|V_{\mathrm{AB}}^{\∞-}-V_S^{\∞-}\left|\right|\\ \left|\right|V_{\mathrm{BC}}^{\∞+}-V_S^{\∞+}\left|\right|\end{array}\right)=0$

Φ _S2=r _P-R _P-h _min≥0

Wherein: R _PFor borrowing the radius of Lixing star, h _MinFor the minimum of planet B is borrowed power height, r _PBorrow the minor increment of Lixing star barycenter for detector distance.

r _PObtain by finding the solution following equation

$\arccos \left(\frac{V_S^{\∞-}\·V_S^{\∞+}}{\left|\right|V_S^{\∞-}\left|\right|\left|\right|V_S^{\∞+}\left|\right|}\right)-2\arcsin \left(\frac{{\mathrm{\μ}}_B}{{\mathrm{\μ}}_B+r_P\left|\right|V_S^{\∞-}\left|\right|}\right)=0$

Wherein: μ _BGravitational constant for planet B.

Step 2 arranges the optimization problem initial value

In departure time that launch mission requires, time of arrival scope, be respectively system-level optimization parameter X _S, two 2-level optimization's subproblem parameter X _ABAnd X _BCInitialize.

Step 3 is found the solution the 2-level optimization subproblem

Current state X based on system-level optimization parameter _S, adopt standard point collocation and seqential quadratic programming algorithm respectively two 2-level optimization subproblems to be found the solution, reach convergence respectively until the seqential quadratic programming algorithms of two 2-level optimization subproblems, obtain two performance index J _ABAnd J _BC

Step 4, solving system level optimization problem

Two performance index J that step 3 is obtained _ABAnd J _BCThe system-level optimization problem model of substitution adopts seqential quadratic programming algorithm solving system level optimization problem.If algorithm is not restrained, then press the correction principle of sequence quadratic programming algorithm to current system-level optimization parameter X _SRevise, with revised X _SAs new current state, recomputate step 3 to step 4.Reach convergence as if algorithm, then the X of current correspondence _S, X _ABAnd X _BCBe optimum planet and borrow power low-thrust trajectory parameter, termination of iterations.

Beneficial effect

The inventive method borrows power low-thrust trajectory optimization problem to be decomposed into a system-level optimization problem and a plurality of 2-level optimizations subproblem in the planet of complexity, wherein the 2-level optimization subproblem is used for finding the solution the thrust control law of segmentation track, and system-level optimization problem then retrains the matching and coordination of realizing between the 2-level optimization subproblem by the planet power of borrowing.Compare with former optimization problem, the optimization parameter of three optimization problems after a decomposition and constraint condition number average reduces, and has reduced complexity and the track restrained susceptibility to the optimization parameter of optimizing model, has improved the convergence efficiency of transfer orbit optimization problem.

Description of drawings

Fig. 1 is that the planet that the present invention is based on the composition decomposition strategy is borrowed power low-thrust trajectory optimization method process flow diagram.

Embodiment

With from the earth, utilize the Mars power of borrowing to carry out Jupiter intersection detection track and be example below, embodiments of the present invention are elaborated.

The concrete steps of present embodiment are as follows:

Step 1, the Orbit Optimized model decomposes

It is that node is decomposed into two sections with complete transfer orbit with Mars: the earth-Mars transfer leg EM section and Mars-Jupiter transfer leg MJ section, utilize the composition decomposition strategy to make up a system-level optimization problem and two 2-level optimization subproblems respectively, the model of three optimization problems is as follows:

1) EM section 2-level optimization subproblem

Optimize parameter

$X_{\mathrm{EM}}=[U_{\mathrm{EM}}\left(t\right),V_{\mathrm{EM}}^{\∞-}]$

Wherein: U _EM(t) be the low thrust control law of EM section track,

Detector exceeds the speed limit with respect to the hyperbolic curve that enters of Mars when borrowing power for Mars.

Performance index

$J_{\mathrm{EM}}=\left|\right|V_{\mathrm{EM}}^{\∞-}-V_S^{\∞-}\left|\right|\→\min$

Wherein:

Be the optimization parameter of system-level optimization problem, the physical significance of sign be Mars when borrowing power detector with respect to the system-level hyperbolic curve hypervelocity that enters of planet B.

Constraint condition

${\mathrm{\Φ}}_{\mathrm{EM}}=\left(\begin{array}{c}\left|\right|r_{\mathrm{EM}}\left(t_M\right)-r_M\left(t_M\right)\left|\right|\\ \left|\right|U_{\mathrm{EM}}\left(t\right)\left|\right|-U_P\end{array}\right)=0$

Wherein: r _EMBe the heliocentric position vector of EM section track detector, r _MBe the heliocentric position vector of Mars, t _MFor Mars borrows power constantly, U _PBe thrustor thrust size.

2) MJ section 2-level optimization subproblem model

Optimize parameter

$X_{\mathrm{MJ}}=[U_{\mathrm{MJ}}\left(t\right),V_{\mathrm{MJ}}^{\∞+}]$

Wherein: U _MJ(t) be the low thrust control law of MJ section track,

Detector is with respect to the hyperbolic curve hypervelocity of setting out of Mars when borrowing power for Mars.

Performance index

$J_{\mathrm{MJ}}=\left|\right|V_{\mathrm{MJ}}^{\∞+}-V_S^{\∞+}\left|\right|\→\min$

Wherein:

Be the optimization parameter of system-level optimization problem, the physical significance of sign be Mars when borrowing power detector with respect to the system-level hyperbolic curve hypervelocity of setting out of Mars.

Constraint condition

${\mathrm{\Φ}}_{\mathrm{MJ}}=\left(\begin{array}{c}\left|\right|r_{\mathrm{MJ}}\left(t_M\right)-r_M\left(t_M\right)\left|\right|\\ \left|\right|U_{\mathrm{MJ}}\left(t\right)\left|\right|-U_P\end{array}\right)=0$

Wherein: r _MJHeliocentric position vector for MJ section track detector.

3) system-level optimization problem model

Optimize parameter

$X_S=[t_E,t_M,t_J,V_S^{\∞-},V_S^{\∞+}]$

Wherein: t _EFor detector from the earth constantly, t _JArrive the moment of Jupiter for detector.

Performance index

J _S=t _J-t _E→min

Constraint condition

${\mathrm{\Φ}}_{S1}=\left(\begin{array}{c}\left|\right|V_S^{\∞-}\left|\right|-\left|\right|V_S^{\∞+}\left|\right|\\ \left|\right|V_{\mathrm{EM}}^{\∞-}-V_S^{\∞-}\left|\right|\\ \left|\right|V_{\mathrm{MJ}}^{\∞+}-V_S^{\∞+}\left|\right|\end{array}\right)=0$

Φ _S2=r _PM-R _M-h _min≥0

Wherein: R _MBe the radius of Mars, h _MinFor minimum Mars is borrowed power height, r _PMMinimum distance for detector distance Mars barycenter.

r _PMObtain by finding the solution following equation

$\arccos \left(\frac{V_S^{\∞-}\·V_S^{\∞+}}{\left|\right|V_S^{\∞-}\left|\right|\left|\right|V_S^{\∞+}\left|\right|}\right)-2\arcsin \left(\frac{{\mathrm{\μ}}_M}{{\mathrm{\μ}}_M+r_P\left|\right|V_S^{\∞-}\left|\right|}\right)=0$

Wherein: μ _MGravitational constant for Mars.

Step 2 arranges the optimization problem initial value

Be respectively system-level optimization parameter X _S, EM section 2-level optimization subproblem parameter X _EM, and MJ section 2-level optimization subproblem parameter X _MJInitialize.

Step 3 is found the solution the 2-level optimization subproblem

Current state X based on system-level optimization parameter _S, adopt standard point collocation and seqential quadratic programming algorithm respectively two 2-level optimization subproblems to be found the solution, reach convergence until the seqential quadratic programming algorithm.

Step 4, solving system level optimization problem

Two performance index J that calculate based on step 3 _EMAnd J _MJ, adopt seqential quadratic programming algorithm solving system level optimization problem.If algorithm reaches convergence, iteration stops, then the X of current correspondence _S, X _EMAnd X _MJBe optimum Mars and borrow power low-thrust trajectory parameter.If algorithm is not restrained, to current system-level optimization parameter X _SRevise, and calculation procedure three again.

For present embodiment, the seqential quadratic programming algorithm adopts the SNOPT software package of Stanford Univ USA's exploitation, under given same design variable initial condition, result of calculation is: when optimization problem not being carried out composition decomposition, optimizing the algorithm iteration number of times is 383 times, when adopting composition decomposition strategy of the present invention that optimization problem is handled, the iterations of optimizing algorithm is 165 times, and planet borrows the convergence efficiency of power low-thrust trajectory optimization problem to be significantly improved.

Claims (1)

1. the planet based on the composition decomposition strategy is borrowed power low-thrust trajectory optimization method, it is characterized in that: specifically comprise the steps:

Step 1, the Orbit Optimized model decomposes

Detector is under the effect of thrustor, follow celestial body A, through borrowing Lixing star B, arrive target celestial body C, be that node is decomposed into two sections with whole transfer orbit to borrow Lixing star B: borrow before the power track BC section after the track AB section and the power of borrowing, by optimizing the model decomposition transfer orbit optimization problem is decomposed into a system-level optimization problem and two 2-level optimization subproblems, three optimization problem models are as described below;

1) AB section 2-level optimization subproblem model

Optimize parameter

$X_{\mathrm{AB}}=[U_{\mathrm{AB}}\left(t\right),V_{\mathrm{AB}}^{\∞-}]$

Wherein: U _AB(t) be the low thrust control law of AB section track,

For the detector of AB section 2-level optimization subproblem correspondence enters the hyperbolic curve hypervelocity with respect to planet B;

Performance index

$J_{\mathrm{AB}}=\left|\right|V_{\mathrm{AB}}^{\∞-}-V_S^{\∞-}\left|\right|\→\min$

Wherein:

Be the optimization parameter of system-level optimization problem, the physical significance of sign is that the detector of system-level optimization problem correspondence enters hyperbolic curve hypervelocity with respect to planet B;

Constraint condition

${\mathrm{\Φ}}_{\mathrm{AB}}=\left(\begin{array}{c}\left|\right|r_{\mathrm{AB}}\left(t_B\right)-r_B\left(t_B\right)\left|\right|\\ \left|\right|U_{\mathrm{AB}}\left(t\right)\left|\right|-U_P\end{array}\right)=0$

Wherein: r _ABBe the heliocentric position vector of AB section track detector, r _BBe respectively the heliocentric position vector of planet B, t _BFor planet B borrows power constantly, U _PBe thrustor thrust size;

2) BC section 2-level optimization subproblem model

Optimize parameter

$X_{\mathrm{BC}}=[U_{\mathrm{BC}}\left(t\right),V_{\mathrm{BC}}^{\∞+}]$

Wherein: U _BC(t) be the low thrust control law of BC section track,

Be the detector of the BC section 2-level optimization subproblem correspondence hyperbolic curve hypervelocity of setting out with respect to planet B;

Performance index

$J_{\mathrm{BC}}=\left|\right|V_{\mathrm{BC}}^{\∞+}-V_S^{\∞+}\left|\right|\→\min$

Wherein: Be the optimization parameter of system-level optimization problem, the physical significance of sign is that the detector of system-level optimization problem correspondence is with respect to the hyperbolic curve hypervelocity of setting out of planet B;

Constraint condition

${\mathrm{\Φ}}_{\mathrm{BC}}=\left(\begin{array}{c}\left|\right|r_{\mathrm{BC}}\left(t_B\right)-r_B\left(t_B\right)\left|\right|\\ \left|\right|U_{\mathrm{BC}}\left(t\right)\left|\right|-U_P\end{array}\right)=0$

Wherein: r _BCHeliocentric position vector for BC section track detector;

3) system-level optimization problem model

Optimize parameter

$X_S=[t_A,t_B,t_C,V_S^{\∞-},V_S^{\∞+}]$

Wherein: t _AFor detector from celestial body A constantly, t _CArrive the moment of celestial body C for detector;

Performance index

J _S=t _C-t _A→min

Constraint condition

${\mathrm{\Φ}}_{S1}=\left(\begin{array}{c}\left|\right|V_S^{\∞-}\left|\right|-\left|\right|V_S^{\∞+}\left|\right|\\ \left|\right|V_{\mathrm{AB}}^{\∞-}-V_S^{\∞-}\left|\right|\\ \left|\right|V_{\mathrm{BC}}^{\∞+}-V_S^{\∞+}\left|\right|\end{array}\right)=0$

Φ _S2=r _P-R _P-h _min≥0

Wherein: R _PFor borrowing the radius of Lixing star, h _MinFor the minimum of planet B is borrowed power height, r _PBorrow the minor increment of Lixing star barycenter for detector distance;

r _PObtain by finding the solution following equation

$\arccos \left(\frac{V_S^{\∞-}\·V_S^{\∞+}}{\left|\right|V_S^{\∞-}\left|\right|\left|\right|V_S^{\∞+}\left|\right|}\right)-2\arcsin \left(\frac{{\mathrm{\μ}}_B}{{\mathrm{\μ}}_B+r_P\left|\right|V_S^{\∞-}\left|\right|}\right)=0$

Wherein: μ _BGravitational constant for planet B;

Step 2 arranges the optimization problem initial value

In departure time that launch mission requires, time of arrival scope, be respectively system-level optimization parameter X _S, two 2-level optimization's subproblem parameter X _ABAnd X _BCInitialize;

Step 3 is found the solution the 2-level optimization subproblem

Current state X based on system-level optimization parameter _S, adopt standard point collocation and seqential quadratic programming algorithm respectively two 2-level optimization subproblems to be found the solution, reach convergence respectively until the seqential quadratic programming algorithms of two 2-level optimization subproblems, obtain two performance index J _ABAnd J _BC

Step 4, solving system level optimization problem

Two performance index J that step 3 is obtained _ABAnd J _BCThe system-level optimization problem model of substitution adopts seqential quadratic programming algorithm solving system level optimization problem; If algorithm is not restrained, then press the correction principle of sequence quadratic programming algorithm to current system-level optimization parameter X _SRevise, with revised X _SAs new current state, recomputate step 3 to step 4; Reach convergence as if algorithm, then the X of current correspondence _S, X _ABAnd X _BCBe optimum planet and borrow power low-thrust trajectory parameter, termination of iterations.

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