{
  "abstract": "Residual tracking errors may persist in actuator-limited quadrotors after the main transient has decayed, particularly when motor lag, dead-zone behavior, thrust saturation, rotor drag, and partial motor-effectiveness loss weaken corrective action near the sliding surface. This study develops a friction-mode residual reaching law (FRMRL) for robust attitude–altitude control of a quadrotor UAV. The law retains the smoothness of a bounded sliding-mode reaching function and adds a residual-activated term that becomes effective when the sliding variable remains nonzero while the corresponding angular or vertical rate is small. It therefore strengthens the reaching action in the low-rate residual regime without increasing switching authority across the full operating range. The controller is formulated for a cascaded quadrotor architecture in which the directly actuated attitude–altitude channels are modeled as matched-input second-order subsystems subject to lumped perturbations and actuator nonlinearities. Lyapunov analysis establishes uniform ultimate boundedness under bounded perturbations and asymptotic convergence in the nominal case; it also shows a stronger local descent rate than the smooth reaching baseline in the residual regime. FRMRL is evaluated against PID, constant-rate SMC, exponential-reaching-law SMC, adaptive SMC, and a gain-matched smooth-reaching-law ablation baseline across six scenarios: nominal tracking, matched disturbances, wind-like disturbances, parameter uncertainty, actuator saturation with dead-zone, and partial motor-effectiveness loss. FRMRL achieves the lowest study-specific journal-oriented quality score in all six scenarios. Its mean score is 13.2%, 19.7%, 49.9%, and 78.4% lower than the corresponding mean scores for ERL-SMC, ASMC, CRL-SMC, and PID, respectively. Across the six scenarios, FRMRL also yields a mean total IAE of 15.5468 and a mean peak-to-peak control ripple of 0.3783. The gain-matched ablation indicates that residual activation, rather than differences in baseline gains, accounts for the improvement in residual-error suppression and control smoothness.",
  "abstract_shown": true,
  "affiliations": [
    "Faculty of Electrical and Electronics Engineering, Ho Chi Minh City University of Technology and Engineering, Ho Chi Minh City, Vietnam.",
    "Department of Electrical Engineering, National Cheng Kung University, Tainan City, Taiwan."
  ],
  "article_type": "Research Article",
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Thanh-Lam Le",
      "orcid": "0009-0008-8562-2031"
    },
    {
      "affs": [
        1
      ],
      "name": "Min-Fu Hsieh",
      "orcid": "0000-0002-5514-3397"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/77fhk6vwng2r3.bib",
  "cited_by": 0,
  "doi": "10.1371/journal.pone.0360921",
  "fulltext_url": "https://europepmc.org/articles/PMC13726998",
  "id": "77fhk6vwng2r3",
  "issns": [
    "1932-6203"
  ],
  "landing_url": "https://doi.org/10.1371/journal.pone.0360921",
  "language": "eng",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "heading",
      "Actuators"
    ],
    [
      "heading",
      "Aerodynamics"
    ],
    [
      "heading",
      "Classical Mechanics"
    ],
    [
      "heading",
      "Continuum Mechanics"
    ],
    [
      "heading",
      "Drag"
    ],
    [
      "heading",
      "Dynamics"
    ],
    [
      "heading",
      "Engineering and Technology"
    ],
    [
      "heading",
      "Fluid Dynamics"
    ],
    [
      "heading",
      "Fluid Mechanics"
    ],
    [
      "heading",
      "Inertia"
    ],
    [
      "heading",
      "Mechanical Engineering"
    ],
    [
      "heading",
      "Moment of Inertia"
    ],
    [
      "heading",
      "Motion"
    ],
    [
      "heading",
      "Physical Sciences"
    ],
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      "heading",
      "Physics"
    ],
    [
      "heading",
      "Research Article"
    ],
    [
      "heading",
      "Rotors"
    ],
    [
      "heading",
      "Thrust"
    ],
    [
      "heading",
      "Torque"
    ],
    [
      "openalex",
      "2207|Adaptive Control of Nonlinear Systems"
    ],
    [
      "plos",
      "/Engineering and technology/Mechanical engineering/Actuators"
    ],
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      "plos",
      "/Engineering and technology/Mechanical engineering/Rotors"
    ],
    [
      "plos",
      "/Physical sciences/Physics/Classical mechanics/Continuum mechanics/Fluid mechanics/Fluid dynamics/Drag"
    ],
    [
      "plos",
      "/Physical sciences/Physics/Classical mechanics/Dynamics/Aerodynamics"
    ],
    [
      "plos",
      "/Physical sciences/Physics/Classical mechanics/Motion/Inertia"
    ],
    [
      "plos",
      "/Physical sciences/Physics/Classical mechanics/Motion/Inertia/Moment of inertia"
    ],
    [
      "plos",
      "/Physical sciences/Physics/Classical mechanics/Motion/Torque"
    ],
    [
      "plos",
      "/Physical sciences/Physics/Classical mechanics/Thrust"
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  "pdf_url": "https://europepmc.org/articles/PMC13726998?pdf=render",
  "pmcid": "PMC13726998",
  "pmid": "42970559",
  "published": "2026-11-02",
  "publisher": "Public Library of Science",
  "ris": "https://research.draconitic.com/paper/77fhk6vwng2r3.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:16Z",
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  "subjects": [
    {
      "field": "physics",
      "origin": "plos:fluid dynamics",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Residual-activated smooth sliding-mode control for actuator-limited quadrotor UAV attitude–altitude tracking",
  "title_text": "Residual-activated smooth sliding-mode control for actuator-limited quadrotor UAV attitude–altitude tracking",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T12:22:48Z",
  "url": "https://research.draconitic.com/paper/77fhk6vwng2r3",
  "venue": "PLOS One",
  "versions": []
}