A Physics-Informed Deep Learning Framework for Spacecraft Pursuit-Evasion Task Assessment

Qualitative spacecraft pursuit-evasion problem which focuses on feasibility is rarely studied because of high-dimensional dynamics, intractable terminal constraints and heavy computational cost. In this paper, A physics-informed framework is proposed for the problem, providing an intuitive method for spacecraft threat relationship determination, situation assessment, mission feasibility analysis and orbital game rules summarization. For the first time, situation adjustment suggestions can be provided for the weak player in orbital game. First, a dimension-reduction dynamics is derived in the line-of-sight rotation coordinate system and the qualitative model is determined, reducing complexity and avoiding the difficulty of target set presentation caused by individual modeling. Second, the Backwards Reachable Set (BRS) of the target set is used for state space partition and capture zone presentation. Reverse-time analysis can eliminate the influence of changeable initial state and enable the proposed framework to analyze plural situations simultaneously. Third, a time-dependent Hamilton-Jacobi-Isaacs (HJI) Partial Differential Equation (PDE) is established to describe BRS evolution driven by dimension-reduction dynamics, based on level set method. Then, Physics-Informed Neural Networks (PINNs) are extended to HJI PDE final value problem, supporting orbital game rules summarization through capture zone evolution analysis. Finally, numerical results demonstrate the feasibility and efficiency of the proposed framework.