{
  "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 ($\\sim$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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30388",
  "author_total": 4,
  "authors": [
    {
      "name": "Qian Zhang"
    },
    {
      "name": "Shanqing Liu"
    },
    {
      "name": "Jerome Darbon"
    },
    {
      "name": "George Karniadakis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ym6yj943xemr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30388",
  "fulltext_url": null,
  "id": "3ym6yj943xemr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30388",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1707|Robotic Path Planning Algorithms"
    ]
  ],
  "openalex": "W7223402770",
  "pdf_url": "https://arxiv.org/pdf/2610.30388",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ym6yj943xemr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30388",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30388"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Transformer-based Approach for Real-time Multi-agent Path Planning with Varying Initial/Final Conditions",
  "title_text": "A Transformer-based Approach for Real-time Multi-agent Path Planning with Varying Initial/Final Conditions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/3ym6yj943xemr",
  "venue": "arXiv",
  "versions": []
}