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Lyapunov-Based Control for a Swarm of Planar Nonholonomic Vehicles

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Abstract

In this paper, we develop a planar Lagrangian swarm model using the Direct Method of Lyapunov to construct the instantaneous velocity of each individual in the swarm. The velocity controllers ensure the cohesion and therefore the stability of the swarm. We introduce novel Lyapunov functions which allow the swarm to navigate in obstacle-free and obstacle-cluttered environments. We apply the methodology to a swarm of planar nonholonomic vehicles. Via computer simulations, we illustrate several self-organizations such as parallel formation, emergent leader, split/rejoin maneuver, and tunnelling for obstacle avoidance.

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Authors and Affiliations

  1. School of Mathematical and Computing Sciences, Fiji National University, Suva, Fiji

    Sandeep Ameet Kumar

  2. School of Computing, Information and Mathematical Sciences, University of the South Pacific, Suva, Fiji

    Jito Vanualailai & Bibhya Sharma

Authors
  1. Sandeep Ameet Kumar
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  2. Jito Vanualailai
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  3. Bibhya Sharma
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Correspondence to Sandeep Ameet Kumar.

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Kumar, S.A., Vanualailai, J. & Sharma, B. Lyapunov-Based Control for a Swarm of Planar Nonholonomic Vehicles. Math.Comput.Sci. 9, 461–475 (2015). https://doi.org/10.1007/s11786-015-0243-z

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  • DOI: https://doi.org/10.1007/s11786-015-0243-z

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