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Branching improved Deep Q Networks for solving pursuit-evasion strategy solution of spacecraft

  • * Corresponding author: Bingyan Liu, Academy of Military Science of the People's Liberation Army, Beijing 100091, PR China

    * Corresponding author: Bingyan Liu, Academy of Military Science of the People's Liberation Army, Beijing 100091, PR China 
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  • With the continuous development of space rendezvous technology, more and more attention has been paid to the study of spacecraft orbital pursuit-evasion differential game. Therefore, we propose a pursuit-evasion game algorithm based on branching improved Deep Q Networks to obtain a space rendezvous strategy with non-cooperative target. Firstly, we transform the optimal control of space rendezvous between spacecraft and non-cooperative target into a survivable differential game problem. Next, in order to solve this game problem, we construct Nash equilibrium strategy and test its existence and uniqueness. Then, in order to avoid the dimensional disaster of Deep Q Networks in the continuous behavior space, we construct a TSK fuzzy inference model to represent the continuous space. Finally, in order to solve the complex and timeconsuming self-learning problem of discrete action sets, we improve Deep Q Networks algorithm, and propose a branching architecture with multiple groups of parallel neural Networks and shared decision modules. The simulation results show that the algorithm achieves the combination of optimal control and game theory, and further improves the learning ability of discrete behaviors. The algorithm has the comparative advantage of continuous space behavior decision, can effectively deal with the continuous space chase game problem, and provides a new idea for the solution of spacecraft orbit pursuit-evasion strategy.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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  • Figure 1.  Coordinate diagram of spacecraft and non-cooperative target

    Figure 2.  Schematic diagram of direction angle of behavior control quantity

    Figure 3.  TSK fuzzy inference model of pursuit-evasion behavior

    Figure 4.  Branching Deep Q Networks architecture

    Figure 5.  Sharing behavior decision diagram based on improved Deep Q Networks

    Figure 6.  The interactive flow of pursuit-evasion game

    Figure 7.  The error function value comparison of the two algorithms

    Figure 8.  The reward value comparison of the two algorithms

    Figure 9.  The pursuit-evasion trajectory after learning 0 times

    Figure 10.  The pursuit-evasion trajectory after learning 400 times

    Figure 11.  Probability distribution of pursuit-evasion behavior

    Figure 12.  The pursuit-evasion trajectory after learning 800 times

    Table 1.  The initial state of the spacecraft and the non-cooperative target

    x y z $ \dot{x} $ $ \dot{y} $ $ \dot{z} $
    (km) (km) (km) (km/s) (km/s) (km/s)
    P 0 0 0 -0.0563 0.0418 0
    E 70 70 0 -0.0425 0.0314 0
     | Show Table
    DownLoad: CSV

    Table 2.  Experimental environment parameters

    computing platform environment configuration
    CPU Intel Core i5-7300H QCPU @2.50GHz
    RAM 8 GB
    System Windows 10
    Programming language Python 3.6
    Compiling environment Pycharm 2018
    Deep Learning framework TensorFlow 0.12.0
     | Show Table
    DownLoad: CSV
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