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This article presents an efficient Bi-LSTM-MPSP integrated framework to address the cooperative trajectory optimization problem for multiple gliding vehicles. This study establishes a novel two-stage optimization framework specifically designed for collaborative gliding vehicles, which are characterized by highly nonlinear dynamics, parameter uncertainties, and coupled constraints, featuring a dual-phase computational architecture: (1) offline initial solution generation and (2) online numerical iteration refinement. The developed Bi-LSTM neural network that simultaneously learns forward and backward temporal dependencies in trajectory sequences, significantly enhancing both learning efficiency and output precision for high-dimensional continuous control vectors. The proposed adaptive-step MPSP algorithm effectively handles numerical optimization on multiple gliding trajectories, simultaneously enforcing time-sensitive coordination, spatial positioning, and terminal angular constraints while strictly complying with flight path boundaries. Bi-LSTM hybrid MPSP algorithm is used to quickly solve control vector sequences with better performance indicators. Numerical simulations demonstrate the proposed method’s dual advantages in computational efficiency and multi-constraint satisfaction performance. The proposed solution achieves the real-time performance with computation times below 100 ms in embedded computing environments, demonstrating potential for engineering implementation.

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An Efficient Collaborative Trajectory Optimization Approach for Gliding Vehicles Using Bi-LSTM-MPSP

  • 会议论文

  • 发表日期：

    2026年

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  • Qian Zhang,
  • Hao Li,
  • Guanwei Yan,
  • Ruihai Chen,
  • Qinyong Zeng

摘要

This article presents an efficient Bi-LSTM-MPSP integrated framework to address the cooperative trajectory optimization problem for multiple gliding vehicles. This study establishes a novel two-stage optimization framework specifically designed for collaborative gliding vehicles, which are characterized by highly nonlinear dynamics, parameter uncertainties, and coupled constraints, featuring a dual-phase computational architecture: (1) offline initial solution generation and (2) online numerical iteration refinement. The developed Bi-LSTM neural network that simultaneously learns forward and backward temporal dependencies in trajectory sequences, significantly enhancing both learning efficiency and output precision for high-dimensional continuous control vectors. The proposed adaptive-step MPSP algorithm effectively handles numerical optimization on multiple gliding trajectories, simultaneously enforcing time-sensitive coordination, spatial positioning, and terminal angular constraints while strictly complying with flight path boundaries. Bi-LSTM hybrid MPSP algorithm is used to quickly solve control vector sequences with better performance indicators. Numerical simulations demonstrate the proposed method’s dual advantages in computational efficiency and multi-constraint satisfaction performance. The proposed solution achieves the real-time performance with computation times below 100 ms in embedded computing environments, demonstrating potential for engineering implementation.