Lyapunov-Based Control for a Swarm of Planar Nonholonomic Vehicles

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 al...

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Bibliographic Details
Published in:Mathematics in computer science 2015-12, Vol.9 (4), p.461-475
Main Authors: Kumar, Sandeep Ameet, Vanualailai, Jito, Sharma, Bibhya
Format: Article
Language:English
Subjects:
Computer Science
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1661-8270
1661-8289
DOI:10.1007/s11786-015-0243-z