Terminal-guidance Based Reinforcement-learning for Orbital Pursuit-evasion Game of the Spacecraft
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摘要: 针对脉冲推力航天器轨道追逃博弈问题, 提出一种基于强化学习的决策方法, 实现追踪星在指定时刻抵近至逃逸星的特定区域, 其中两星都具备自主博弈能力. 首先, 充分考虑追踪星和逃逸星的燃料约束、推力约束、决策周期约束、运动范围约束等实际约束条件, 建立锥形安全接近区及追逃博弈过程的数学模型; 其次, 为了提升航天器面对不确定博弈对抗场景的自主决策能力, 以近端策略优化 (Proximal policy optimization, PPO) 算法框架为基础, 采用左右互搏的方式同时训练追踪星和逃逸星, 交替提升两星的决策能力; 在此基础上, 为了在指定时刻完成追逃任务, 提出一种终端诱导的奖励函数设计方法, 基于CW (Clohessy Wiltshire)方程预测两星在终端时刻的相对误差, 并将该预测误差引入奖励函数中, 有效引导追踪星在指定时刻进入逃逸星的安全接近区. 与现有基于当前误差设计奖励函数的方法相比, 所提方法能够有效提高追击成功率. 最后, 通过与其他学习方法仿真对比, 验证提出的训练方法和奖励函数设计方法的有效性和优越性.Abstract: This paper addresses the problem of orbital pursuit-evasion of two multi-impulse satellites with strong maneuver ability. A reinforcement-learning based approach is proposed to train two satellites such that the pursuer can reach to a specific region adjacent to the evader at the appointed time. First, by taking fuel limits, control force limits, control frequency, and range of motion into consideration, the model for conical approach region and orbital dynamics of relative motion between two satellites is established. Based on this model, to enhance the ability of confronting with the situations with high uncertainties, the proximal policy optimization (PPO) scheme is adopted to train the pursuer and the evader alternately. Moreover, to accomplish the pursuit or evasion at the appointed time, a new kind of reward function is designed based on the final predicted error, which guides the pursuer to approach the evader approximately at the prescribed time. Compared with existing reward function design methods based on the current error, the proposed method in this paper can effectively enhance the success rate of pursuit. Finally, the simulation comparisons are conducted to show the superiority of the terminal-guidance reward function proposed in this paper over traditional reward function design approaches.
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图 3 两星训练框架示意图
Fig. 3 The schematic diagram for training framework of the two spacecraft
图 8 训练过程中两星终端相对距离
Fig. 8 The final distance between pursuer and evader during the training
图 9 训练过程中终端时刻两星与安全接近区域中心线夹角
Fig. 9 The final angle between the pursuer-evader direction and the conic center axis during the training
图 10 基于本文奖励函数设计方法的多局打靶结果
Fig. 10 The Monte-Carlo results for the reward function design method in this paper
图 11 本文奖励函数对应的一局轨迹
Fig. 11 The trajectory in one episode based on the reward function designed in this paper
图 12 基于传统奖励函数设计方法的多局打靶结果
Fig. 12 The Monte-Carlo results for the traditional reward function design method
表 1 追踪星和逃逸星参数设置
Table 1 Parameters of the pursuer and evader
博弈对象 决策周期 (s) 各轴推质比(N/kg) 各轴单次速度增量上限 (m/s) 总速度增量上限 (m/s) 追踪星 600 20/500 1.6 320 逃逸星 600 20/500 1.6 240 
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表 2 PPO算法相关参数
Table 2 Parameters for the PPO algorithm
参数描述 参数数值 学习率 $\alpha_{lr}=0.0002$ 损失函数相关参数 $\varepsilon=0.1, c_1=0.5, c_2=0.01$ 训练所需轨迹条数 $\mathrm{Batch_{-}n=128}$ 追踪星奖励函数参数 $\delta_{c1}=1$, $\delta_{c2}=0.1$, $\alpha_c=4\times10^{-6}$, $\beta_c=1/\pi$, $\lambda_c=0.5$ 逃逸星奖励函数参数 $\delta_{t1}=1$, $\delta_{t2}=0.1$, $\alpha_t=4\times10^{-6}$, $\beta_t=1/\pi$, $\lambda_t=5/6$
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表 3 不同追逃策略的追踪成功率
Table 3 Success rate of the pursuer for different pursuing and evasion strategies
逃逸星 追踪星 PPO+本文奖励 PPO+传统奖励 SAC+本文奖励 零控脱靶量法 PPO+本文奖励 $97{\text{%}}$ $89{\text{%}}$ $0{\text{%}}$ $92{\text{%}}$ PPO+传统奖励 $99{\text{%}}$ $92{\text{%}}$ $2{\text{%}}$ $98{\text{%}}$ SAC+本文奖励 $100{\text{%}}$ $61{\text{%}}$ $7{\text{%}}$ $100{\text{%}}$ 零控脱靶量法 $99{\text{%}}$ $99{\text{%}}$ $9{\text{%}}$ $98{\text{%}}$
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