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<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-interdisciplinary-mathematics</journal-id>
      <journal-title-group>
        <journal-title>Journal of Interdisciplinary Mathematics</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-012X</issn>
      <issn publication-format="print">0972-0502</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JIM-2817</article-id>
      <title-group>
        <article-title>Hybrid dynamical system models for human–robot interaction</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Wani</surname>
            <given-names>Tanveer Ahmad</given-names>
          </name>
          <aff>Department of Physics, Noida International University, Greater Noida, Uttar Pradesh, 201312, India</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Bhardwaj</surname>
            <given-names>Nitish</given-names>
          </name>
          <aff>Department of Computer Engineering &amp; Applications, GLA University, Mathura, Uttar Pradesh, 281406, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Tolani</surname>
            <given-names>Smita</given-names>
          </name>
          <aff>Faculties Engineering, Sciences and Humanities, St. Vincent Pallotti College of Engineering &amp; Technology, Nagpur, Maharashtra, 441108, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Oli</surname>
            <given-names>Sanjay</given-names>
          </name>
          <aff>Department of Mathematics, Dayananda Sagar College of Engineering, Bangalore, Karnataka, 560111, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Nayak</surname>
            <given-names>Praveen  Priyaranjan</given-names>
          </name>
          <aff>Department of Electronics and Communication Engineering, Institute of Technical Education and Research, Siksha ‘O’ Anusandhan (Deemed to be University), Bhubaneswar, Odisha, 751030, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <given-names>Loganathan</given-names>
          </name>
          <aff>Department of Humanities and Sciences, Aarupadai Veedu Institute of Technology, Vinayaka Mission’s Research Foundation (Deemed to be University), Paiyanur, Tamil Nadu, 603104, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname> Likhith</surname>
            <given-names>S.  R.</given-names>
          </name>
          <aff>Presidency School of Computer Science and Engineering, Presidency University, Bangalore, Karnataka, 560119, India</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>10</issue>
      <fpage>3033</fpage>
      <lpage>3046</lpage>
      <pub-date date-type="pub">
        <day>27</day>
        <month>10</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>With the increasing popularity of human–robot interaction (HRI), control systems are becoming more and more interesting and complicated because they need to coordinate continuous human movements and discrete robot decision-making in dynamic environments. The current strategies tend to be less flexible when working collaboratively, take longer to react and become less stable in interaction. This study presents a hybrid nonlinear state-space model, hybrid automata, Model Predictive Control (MPC), Extended Kalman Filter (EKF) and Adaptive Hybrid Interaction Algorithm (AHIA) based Hybrid Dynamical Human–Robot Interaction (HD-HRI) framework for real-time human intent estimation and robot motion planning. The framework is assessed based on the accuracy of interaction, prediction of intent, trajectory tracking error, response latency, collision avoidance rate and task completion success. Experimental results confirm that 95.8% of the interactions are accurate, 94.9% of intents are correctly predicted, 21.6% of trajectory tracking errors is reduced, 18.4% of response latency is reduced, 97.3% of collisions are avoided, and 95.6% of the tasks are completed. The results prove that the proposed hybrid dynamical framework can be effectively implemented in practical applications, which can be reliable, stable, and efficient for human–robot collaboration.</p>
      </abstract>
      <kwd-group>
        <kwd>Dark matter density reconstruction</kwd>
        <kwd>Galaxy rotation curves</kwd>
        <kwd>Jeans equation</kwd>
        <kwd>Bayesian inverse modeling</kwd>
        <kwd>Tikhonov regularization</kwd>
        <kwd>Nonlinear least-squares optimization</kwd>
      </kwd-group>
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          <meta-value>open</meta-value>
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  </front>
</article>
