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摘要:
为保证在轨机动实时性和高精度的要求，提出了一种基于机器学习的在轨实时机动决策方法。通过优化算法离线获得摄动下的精确解，减去二体解得到速度增量差，将其投影到轨道坐标系获得速度增量摄动修正项，以此作为神经网络输出，设计网络参数并训练得到摄动修正网络、组合应用摄动修正网络和二体解实现高精度的在轨实时轨道机动决策。仿真结果表明：卫星按照该决策机动完成后的终端位置偏差与按照优化算法给出的决策机动完成后终端位置偏差精度一致，且前者决策耗时仅为后者决策耗时的0.01%左右。所提轨道机动决策方法兼顾了精度与实时性，适用于星上决策。
Abstract:In order to ensure the real-time maneuverability and high-precision requirements of orbital maneuver, a real-time maneuver decision-making method based on machine learning is proposed. The optimal solution under perturbation is obtained offline through the optimization algorithm. The two-body solution is subtracted to obtain the speed increment difference, which is projected onto the orbital system to obtain the speed increment perturbation correction term, which is used as the output of the neural network. The network parameters are designed and trained to obtain perturbation correction network. The combination of perturbation correction network and two-body solution is used to achieve high-precision real-time orbital maneuver decision. The simulation results show that the terminal position deviation after the completion of the maneuver according to the decision is consistent with the accuracy of the terminal position deviation after the completion of the decision maneuver according to the optimization algorithm, and the former decision time is only about 0.01% of the latter decision time. The orbital maneuver decision-making method proposed in this paper takes into account both accuracy and real-time performance, and is suitable for on-board decision-making.
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Key words:
- orbital maneuver /
- neural networks /
- machine learning /
- Lambert maneuver /
- perturbation correction
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表 1 样本点到样本中心点最远距离
Table 1. The farthest distance from sample point to sample center point
参数 数值 δr1x/m 1 000 δr1y/m 1 000 δr1z/m 1 000 δv1x/(m·s-1) 1 δv1y/(m·s-1) 1 δv1z/(m·s-1) 1 δr2x/m 1 000 δr2y/m 1 000 δr2z/m 1 000 δv2x/(m·s-1) 1 δv2y/(m·s-1) 1 δv2z/(m·s-1) 1 
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表 2 网络结构参数取值
Table 2. Parameter value of network structure
神经网络参数 数值 网络隐层数 1，2，3，4 隐层节点数 8，16，32，64，128
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表 3 不同层数、节点数和激活函数的速度增量网络的性能
Table 3. Performance of speed increment networks with different layers, units and activation functions
隐层层数/节点数 MSE logsig softmax poslin purelin tansig 1/8 9.95×10-6 8.38×10-5 8.23×10-9 2.06×10-9 5.76×10-6 1/16 3.05×10-6 1.81×10-5 5.42×10-6 2.02×10-9 1.45×10-6 1/32 6.40×10-6 2.20×10-6 2.17×10-9 2.02×10-9 3.83×10-6 1/64 6.41×10-6 7.47×10-6 2.73×10-7 2.01×10-9 4.27×10-6 1/128 2.46×10-4 2.62×10-6 7.91×10-6 2.02×10-9 2.97×10-6 2/8 2.26×10-5 5.98×10-5 2.86×10-5 2.02×10-9 3.10×10-5 2/16 5.66×10-6 2.69×10-5 3.86×10-6 2.02×10-9 3.70×10-6 2/32 2.60×10-6 4.37×10-6 6.06×10-5 2.02×10-9 8.53×10-6 2/64 3.33×10-4 1.54×10-6 5.09×10-4 2.02×10-9 6.34×10-5 2/128 1.89×10-3 2.91×10-6 5.29×10-3 2.02×10-9 9.91×10-4 3/8 2.94×10-5 1.18×10-4 2.96×10-1 2.02×10-9 8.34×10-6 3/16 3.23×10-6 1.60×10-5 4.88×10-5 2.01×10-9 4.08×10-6 3/32 5.15×10-6 1.64×10-5 2.43×10-3 2.03×10-9 3.28×10-6 3/64 4.24×10-4 9.36×10-6 5.23×10-3 2.02×10-9 1.25×10-4 3/128 2.90×10-3 2.93×10-6 9.91×10-2 2.02×10-9 3.13×10-3 4/8 4.02×10-5 2.98×10-1 2.96×10-1 2.02×10-9 2.57×10-5 4/16 2.45×10-6 3.03×10-1 1.05×10-2 2.02×10-9 8.95×10-6 4/32 5.82×10-6 1.31×10-5 7.84×10-3 2.03×10-9 9.21×10-6 4/64 4.66×10-4 1.13×10-5 1.35×10-1 2.02×10-9 2.91×10-4 4/128 2.65×10-3 2.98×10-1 1.50 2.02×10-9 2.94×10-3
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表 4 不同层数、节点数和激活函数的摄动偏差网络的性能
Table 4. Performance of perturbation deviation networks with different layers, units and activation functions
隐层层数/节点数 MSE logsig softmax poslin purelin tansig 1/8 2.80×10-6 1.04×10-6 1.91×10-6 6.11×10-6 5.50×10-6 1/16 1.62×10-6 1.04×10-6 2.24×10-6 5.87×10-6 4.11×10-6 1/32 3.60×10-6 1.34×10-6 8.77×10-6 1.87×10-6 4.86×10-6 1/64 3.27×10-6 1.19×10-6 7.61×10-6 2.58×10-6 3.04×10-6 1/128 8.65×10-6 2.26×10-6 8.98×10-6 7.81×10-7 7.07×10-6 2/8 2.08×10-6 1.30×10-6 3.33×10-6 3.96×10-6 4.73×10-6 2/16 3.13×10-6 2.07×10-6 4.83×10-6 8.44×10-7 4.59×10-6 2/32 3.20×10-6 1.78×10-6 4.35×10-6 3.59×10-7 3.19×10-6 2/64 1.86×10-6 8.88×10-7 5.48×10-6 1.09×10-7 2.16×10-6 2/128 5.23×10-6 5.71×10-7 3.04×10-6 1.52×10-8 2.02×10-6 3/8 6.12×10-6 5.85×10-7 1.61×10-6 9.80×10-7 2.06×10-6 3/16 5.45×10-6 8.64×10-7 2.22×10-6 4.71×10-7 2.32×10-6 3/32 2.44×10-6 7.58×10-7 3.87×10-6 8.09×10-8 2.74×10-6 3/64 2.49×10-6 2.02×10-6 3.55×10-6 2.98×10-9 2.52×10-6 3/128 2.43×10-6 7.33×10-7 9.31×10-7 4.11×10-10 2.98×10-6 4/8 7.63×10-7 1.52×10-6 9.29×10-7 1.03×10-6 9.74×10-7 4/16 9.66×10-7 8.19×10-7 3.84×10-6 4.16×10-7 2.02×10-6 4/32 1.99×10-6 1.24×10-6 3.53×10-6 6.47×10-9 1.12×10-6 4/64 1.84×10-6 1.51×10-6 3.57×10-7 1.06×10-10 1.57×10-6 4/128 1.87×10-6 3.99×10-7 6.99×10-7 8.84×10-12 1.18×10-6
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表 5 不同层数, 节点数和激活函数的摄动修正网络的性能
Table 5. Performance of perturbation correction networks with different layers, units and activation functions
隐层层数/节点数 MSE logsig softmax poslin purelin tansig 1/8 9.44×10-7 3.87×10-7 3.16×10-6 2.70×10-6 5.14×10-6 1/16 2.29×10-6 9.71×10-7 6.09×10-6 3.01×10-6 1.83×10-6 1/32 1.64×10-6 1.36×10-6 7.63×10-6 3.61×10-6 4.02×10-6 1/64 2.87×10-6 7.55×10-7 4.58×10-6 3.67×10-6 9.22×10-6 1/128 7.44×10-6 2.81×10-7 6.37×10-6 5.56×10-7 7.38×10-6 2/8 1.24×10-6 2.06×10-6 2.71×10-6 2.29×10-6 1.21×10-6 2/16 9.09×10-7 6.05×10-7 4.78×10-6 2.10×10-6 1.84×10-6 2/32 2.73×10-6 1.26×10-6 1.99×10-6 1.02×10-6 4.42×10-6 2/64 1.89×10-6 1.08×10-6 5.50×10-6 6.50×10-8 2.95×10-6 2/128 4.18×10-6 9.30×10-7 5.67×10-6 2.20×10-8 3.87×10-6 3/8 3.00×10-7 2.51×10-6 1.52×10-6 1.51×10-6 1.16×10-6 3/16 2.18×10-6 1.81×10-6 4.38×10-6 1.00×10-6 1.05×10-6 3/32 1.65×10-6 1.10×10-6 5.48×10-6 1.01×10-7 2.51×10-6 3/64 2.15×10-6 1.40×10-6 4.15×10-6 4.33×10-9 1.95×10-6 3/128 2.95×10-6 9.17×10-7 2.87×10-6 5.72×10-10 2.33×10-6 4/8 4.20×10-6 7.73×10-7 1.46×10-6 1.55×10-6 1.26×10-6 4/16 7.32×10-7 1.25×10-6 2.00×10-6 3.41×10-7 1.65×10-6 4/32 8.72×10-7 1.00×10-6 1.85×10-6 5.47×10-9 2.16×10-6 4/64 2.11×10-6 1.54×10-6 1.93×10-6 1.14×10-10 1.54×10-6 4/128 2.63×10-6 1.00×10-6 3.29×10-7 7.28×10-12 2.03×10-6
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表 6 终端位置偏差统计
Table 6. Statistics of terminal position deviation
方法 dmax/m dmin/m dmean/m 优化算法(样本) 3.864 0×10-3 2.340 0×10-4 2.008 0×10-3 最优速度增量网络 2.892 5×10-1 3.076 0×10-3 7.396 2×10-2 最优摄动偏差网络 1.192 3×10-2 6.240 0×10-4 4.751 9×10-3 最优摄动修正网络 1.117 8×10-2 3.150 0×10-4 4.175 8×10-3
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