Spacecraft formation reconfiguration requires the generation of fuel-efficient maneuver sequences that transfer a deputy spacecraft between prescribed relative orbital configurations while respecting orbital dynamics and operational constraints. When formulated in the relative orbital elements (ROE) space, the reconfiguration problem admits compact linearized dynamics and naturally supports multi-impulse control strategies, making it particularly attractive for formation flying applications. Classical analytical methods provide closed-form solutions with low computational cost and clear physical interpretability; however, in the context of multi-impulse trajectory generation with diverse boundary conditions, the construction of a compact and interpretable analytic maneuver structure, together with an efficient mapping from mission boundaries to its parameters, remains an open challenge.
  This paper proposes a physics-informed neural network (PINN) framework for fast multi-impulse trajectory generation in spacecraft formation reconfiguration. Rather than directly predicting a high-dimensional sequence of discrete impulsive maneuvers, the proposed approach introduces a low-dimensional analytic parameterization of the radial–tangential–normal (RTN) components of the velocity increments. The maneuver profiles in each direction are represented using sinusoidal basis functions with a small number of coefficients, capturing the dominant structure observed in optimal multi-impulse solutions while significantly reducing the dimensionality of the control space. The resulting parameterization preserves physical interpretability and enables smooth, structured maneuver profiles.
  A neural network is trained to learn the nonlinear mapping from the initial and final ROE boundary conditions to the parameters of the analytic maneuver model. To ensure physical consistency, the training process employs a hybrid loss function that combines supervised learning from offline optimized trajectories with physics-informed terms. The physics-informed loss enforces the discrete-time ROE dynamics and terminal boundary conditions by propagating the network-predicted maneuver sequence through the orbital dynamics during training. This formulation encourages the learned model to generate dynamically consistent trajectories while maintaining the flexibility and generalization capability of data-driven learning.
  The linear structure of the ROE dynamics further leads to a scaling property of the multi-impulse reconfiguration problem, whereby scaling the desired changes in the eccentricity and inclination vectors results in a proportional scaling of the optimal velocity increments. This property is transferred to the analytic maneuver parameterization and exploited to construct a simple scaling-based out-of-distribution extension.   The proposed extension enables the trained PINN to generate feasible maneuver sequences for reconfiguration tasks whose magnitudes exceed the nominal training range, while preserving relative accuracy.
Numerical simulations demonstrate that the proposed PINN framework can generate dynamically consistent multi-impulse trajectories with small terminal ROE errors and near-optimal fuel consumption at negligible online computational cost. The results indicate that physics-informed learning combined with analytic control parameterization provides an effective and practical approach for rapid trajectory generation in autonomous spacecraft formation reconfiguration.