Multi-phase relative trajectory planning using high-order expansion and neural network

This paper focuses on the end-to-end design and autonomous planning of multi-phase relative trajectory in on-orbit service (OOS) mission. The strong coupling among transfer phases typically requires manual tuning or repeated optimization during trajectory design, leading to substantial computational burden and limiting responsiveness in time-critical or autonomous scenarios. A data-efficient machine learning framework based on differential-algebra (DA) method is proposed to learn the mapping between mission constraints and maneuver sequences. Starting from a prior maneuver strategy, we develop a DA-based multi-phase trajectory expansion scheme that constructs transition polynomials for reference trajectories while preserving constraint consistency across phases. These polynomials enable large-scale dataset generation through inexpensive polynomial evaluations, thereby avoiding repeated and computationally intensive numerical propagation. A deep neural network is then trained via backpropagation to infer maneuver sequences directly from constraint variables, while simultaneously compensating for deficiencies in the prior strategy. Once trained, the network produces maneuver sequences instantaneously for varying constraints, eliminating manual tuning and iterative computation in trajectory planning. The proposed framework integrates data-driven learning with dynamical priors to substantially reduce data-generation cost and improve planning efficiency. We validate the method on a representative multi-phase OOS scenario and assess data-generation efficacy under two distinct prior maneuver strategies, one analytical and one numerical. Simulations demonstrate that DA-based data generation reduces computation time by >90 %, and confirm the effectiveness of the proposed approach for multi-phase relative trajectory planning.