A Transformer-based Approach for Real-time Multi-agent Path Planning with Varying Initial/Final Conditions
Abstract
We address the problem of real-time multi-agent path planning under prescribed initial and final configurations, formulated as a high-dimensional optimal control problem subject to inter-agent collision avoidance and obstacle constraints. Classical solvers based on the Hamilton--Jacobi--Bellman equation or Pontryagin's maximum principle (PMP) become computationally intractable as the number of agents grows, due to the curse of dimensionality and the non-convexity introduced by interaction constraints. We propose OCFormer, a transformer-based neural network that parameterizes the inverse of a coordinate transformation mapping a simple, analytically tractable latent space, in which agents evolve independently under a decoupled Hamiltonian, to the physical space of the coupled, interacting system. The model is trained by minimizing a physics-informed loss comprising the Hamiltonian ODE residual from the PMP and a boundary matching term, without requiring pre-computed trajectory data. The self-attention mechanism endows OCFormer with permutation equivariance over agents, a structural symmetry that prior symplectic network approaches do not natively enforce. When trained on a distribution of boundary conditions, the amortized OCFormer produces near-optimal trajectories for unseen initial and final configurations in a single forward pass (∼220ms), enabling real-time inference without retraining. We further introduce a lightweight transfer learning framework that adapts a pretrained OCFormer to out-of-distribution perturbations in seconds via L-BFGS fine-tuning. Numerical experiments on two- and three-dimensional multi-agent navigation with up to 128 agents demonstrate the scalability and efficiency of the proposed approach.
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BibTeX
@misc{zhang2026transformerbased,
title = {{A Transformer-based Approach for Real-time Multi-agent Path Planning with Varying Initial/Final Conditions}},
author = {Qian Zhang and Shanqing Liu and Jerome Darbon and George Karniadakis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30388},
eprint = {2610.30388},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30388},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Transformer-based Approach for Real-time Multi-agent Path Planning with Varying Initial/Final Conditions
AU - Qian Zhang
AU - Shanqing Liu
AU - Jerome Darbon
AU - George Karniadakis
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30388
UR - https://arxiv.org/abs/2610.30388
AB - We address the problem of real-time multi-agent path planning under prescribed initial and final configurations, formulated as a high-dimensional optimal control problem subject to inter-agent collision avoidance and obstacle constraints. Classical solvers based on the Hamilton--Jacobi--Bellman equation or Pontryagin's maximum principle (PMP) become computationally intractable as the number of agents grows, due to the curse of dimensionality and the non-convexity introduced by interaction constraints. We propose OCFormer, a transformer-based neural network that parameterizes the inverse of a coordinate transformation mapping a simple, analytically tractable latent space, in which agents evolve independently under a decoupled Hamiltonian, to the physical space of the coupled, interacting system. The model is trained by minimizing a physics-informed loss comprising the Hamiltonian ODE residual from the PMP and a boundary matching term, without requiring pre-computed trajectory data. The self-attention mechanism endows OCFormer with permutation equivariance over agents, a structural symmetry that prior symplectic network approaches do not natively enforce. When trained on a distribution of boundary conditions, the amortized OCFormer produces near-optimal trajectories for unseen initial and final configurations in a single forward pass (∼220ms), enabling real-time inference without retraining. We further introduce a lightweight transfer learning framework that adapts a pretrained OCFormer to out-of-distribution perturbations in seconds via L-BFGS fine-tuning. Numerical experiments on two- and three-dimensional multi-agent navigation with up to 128 agents demonstrate the scalability and efficiency of the proposed approach.
ER -