{
  "abstract": "Optimal path parameterization (OPP) is a fundamental problem for planning trajectories along a prescribed geometric path under kinodynamic constraints and task-dependent objectives. Among existing OPP works, it remains challenging to simultaneously achieve feasibility guarantees, general-objective optimality certificates, and online-compatible computation in a unified framework, especially for third-order OPP (OPP3) with non-convex constraints. This paper proposes reachability-augmented dual dynamic programming (RDDP), a state-grid-free and objective-aware dynamic programming (DP) framework for OPP. The key idea is to replace the relatively complete recourse assumption used in classical dual DP (DDP) with OPP-specific backward reachable sets, and then generate both value-function cuts and trial trajectories only inside these reachable sets. For convex and non-convex OPP, we prove global optimality and Karush-Kuhn-Tucker convergence of RDDP under OPP-specific conditions, respectively. Efficient instantiations are developed for second-order OPP (OPP2) and OPP3. Experiments show that RDDP achieves objective values comparable to convex-optimization baselines with speedups of approximately 15.3 and 4.9 times over the fastest of 4 tested solvers for OPP2 and OPP3, respectively. RDDP also achieves faster convergence than grid-based DP. Compared with reachability-analysis methods, RDDP retains the reachability mechanism while replacing local maximum-control propagation with value-function-guided control selection, thereby enabling objectives beyond traversal time. In summary, RDDP addresses a key capability gap in OPP by unifying certifiable general-objective optimization, reachability-based feasibility preservation, and online-compatible low-dimensional DP computation in a single framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.19089",
  "author_total": 4,
  "authors": [
    {
      "name": "Yunan Wang"
    },
    {
      "name": "Jizhou Yan"
    },
    {
      "name": "Chuxiong Hu"
    },
    {
      "name": "Zeyang Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/da6815gj53xzf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.19089",
  "fulltext_url": null,
  "id": "da6815gj53xzf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.19089",
  "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.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1707|Robotic Path Planning Algorithms"
    ]
  ],
  "openalex": "W7161846414",
  "pdf_url": "https://arxiv.org/pdf/2605.19089",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/da6815gj53xzf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2605.19089",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.19089"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Reachability-Augmented Dual Dynamic Programming for Optimal Path Parameterization",
  "title_text": "Reachability-Augmented Dual Dynamic Programming for Optimal Path Parameterization",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/da6815gj53xzf",
  "venue": "arXiv",
  "versions": []
}