{
  "abstract": "Longitudinal spacing models describe the speed--spacing states that vehicles maintain, while longitudinal controllers regulate vehicle motion through spacing and speed errors. Less explicit is how one spacing state should be connected to another through a finite, physically meaningful vehicle transition. This paper develops such a connection through r-Safety and Adaptive Kinematic Smoothing (AKS). The r-Safety relation represents speed-dependent spacing through a braking-normalized reserve, whose change, together with leader motion, determines the follower displacement required during a transition. AKS then converts this displacement into a low-dimensional analytical trajectory with consistent position, speed, spacing, and acceleration. Experiments using controlled platoons and NGSIM trajectories identify r-Safety values of 0.307 and 0.249--0.281, respectively, and show that AKS can both represent observed transitions and generate prospective references under prescribed endpoint states, transition horizons, and leader motion. In same-controller ablations, adding AKS reduces integrated acceleration effort by 21--47% and integrated squared jerk by 73--81% across the controlled and naturalistic datasets. FHWA ACC/CACC trajectories further provide an empirical illustration of finite-horizon execution under automated following, showing how spacing adjustment can continue beyond the prescribed speed transition. The framework therefore provides a direct path from a speed--spacing relation to an analytical finite transition and its use as a longitudinal control reference.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28676",
  "author_total": 2,
  "authors": [
    {
      "name": "Xuesong Zhou"
    },
    {
      "name": "Ziyi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/752506nthzygp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28676",
  "fulltext_url": null,
  "id": "752506nthzygp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28676",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Traffic control and management"
    ]
  ],
  "openalex": "W7214276724",
  "pdf_url": "https://arxiv.org/pdf/2609.28676",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/752506nthzygp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.28676",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28676"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "The r-Safety Reserve and Adaptive Kinematic Smoothing for Car-Following Transitions",
  "title_text": "The r-Safety Reserve and Adaptive Kinematic Smoothing for Car-Following Transitions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/752506nthzygp",
  "venue": "arXiv",
  "versions": []
}