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SCIENTIA SINICA Physica, Mechanica & Astronomica, Volume 49, Issue 8: 084509(2019) https://doi.org/10.1360/SSPMA-2019-0104

Design and optimization of low thrust transfer trajectory for engineering constraints

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  • ReceivedApr 4, 2019
  • AcceptedMay 10, 2019
  • PublishedMay 31, 2019
PACS numbers

Abstract

Multimode electric propulsion system is widely used in deep space exploration. Its thrust is output in stages with the change of input power, which also means that continuous power changes lead to discontinuous thrust changes. In the design and optimization of low-thrust trajectory, the discontinuity of thrust is often neglected and regarded as a continuous parameter. The optimal design of low-thrust transfer trajectory constrained by multimode electric propulsion is studied, and the influence of thrust grading characteristics on the trajectory is analyzed in this paper. A specific optimization strategy is proposed, including three main steps: model discretization based on direct method, fast generation of initial value based on particle swarm optimization (PSO), and optimization based on sequential quadratic programming (SQP). The dynamic model and optimization model of low-thrust transfer trajectory is established. Then, the optimization model is discretized based on the direct method and the original optimal control problem is transformed into a parameter optimization problem in the form of nonlinear programming (NLP). A hybrid optimization algorithm based on PSO and SQP is proposed to solve the new NLP problem. PSO is used to search the initial value efficiently and guarantee the global performance of the initial value and SQP is used for local optimization based on initial value, which can give full play to the excellent global optimization performance of PSO and the outstanding local optimization performance of SQP. The effectiveness of the proposed optimization strategy is verified by a simulation example of the main belt asteroid Metis (1974 QU2) rendezvous mission with once Mars gravity assist. The results show that the optimal control curve obtained is in accordance with the optimal control form of bang-bang control derived from the theory, and the thruster has just two situations at any time: shutdown or startup with maximum thrust. In the working power range, increasing the number of thrust stages can improve the rate of energy utilization, thereby improving the efficiency of thruster, shortening the startup time and reducing fuel consumption. Meanwhile, ineffective grading should be avoided in the non-working power range.


Funded by

科工局民用航天“十三五”技术预先研究项目(D030102)

上海市科委科研计划(18DZ2272300)


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  • Figure 1

    (Color online) The procedure of optimization.

  • Figure 2

    (Color online) Power change process under different thrust grading conditions. (a) 2 grades; (2) 3 grades; (c) 5 grades; (d) 11 grades.

  • Figure 3

    (Color online) Optimal transfer trajectory of 11 grading condition.

  • Figure 4

    (Color online) Change of thrust vector. (a) Thrust amplitude; (b) thrust longitude; (c) thrust latitude.

  • Figure 5

    (Color online) Flight process. (a) Heliocentric distance; (b) heliocentric velocity; (c) semimajor axis; (d) eccentricity; (e) inclination.

  • Table 1   Parameters of PSO Algorithm

    参数

    数值

    粒子个数n

    40

    迭代次数cmax

    2000

    运行次数

    5

    惯性权重上限wmax

    0.9

    惯性权重下限wmin

    0.4

    局部学习因子上限c1max

    2.5

    局部学习因子下限c1min

    0.5

    全局学习因子上限c2max

    2.5

    全局学习因子下限c2min

    0.5

    最大学习速度vmax

    0.8

  • Table 2   Orbit parameters of metis (MJD=58000.0)

    参数

    数值

    半长轴 (AU)

    2.3863

    偏心率

    0.1220

    轨道倾角 (°)

    5.5743

    平近点角 (°)

    68.9317

    升交点黄经 (°)

    74.9285

    近日点幅角 (°)

    265.8840

  • Table 3   Optimization results under different thrust grading conditions

    工作档数

    分档工况

    总速度增量 (km/s)

    燃料消耗量 (kg)

    开机时间 (d)

    飞行时间 (d)

    2档

    P≥4000 W, 133 m N

    2000 W≤P≤4000 W, 67 m N

    6.4896

    258.5700

    1496

    2000

    3档

    P≥4000 W, 133 m N

    3000 W≤P<4000 W, 100 m N

    2000 W≤P<3000 W, 67 m N

    6.1108

    244.7840

    1321

    2000

    5档

    P≥4000 W,133 m N

    推力随着功率的变化线性减小

    每相差500 W为一档

    P<2000 W不工作

    5.8380

    234.7610

    1201

    2000

    11档

    P≥4000 W,133 m N

    推力随着功率的变化线性减小

    每相差200 W为一档

    P<2000 W不工作

    5.7297

    230.7598

    1118

    2000

  • Table 4   Orbit parameters of 11 grading condition

    描述量

    结果

    地球出发时刻 (YY.MM.DD)

    2022.08.22

    地球出发C3 (km2/s2)

    17.0057

    火星借力时刻 (YY.MM.DD)

    2023.07.20

    火星借力高度 (km)

    500

    借力提供速度增量 (km/s)

    3.1911

    颖神星到达时刻 (YY.MM.DD)

    2028.02.12

    总飞行时间 (d)

    2000

    总速度增量需求 (km/s)

    5.7297

    总燃料消耗 (kg)

    230.7610

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