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A Lagrangian-based Swarming Behavior in the Absence of Obstacles

Vanualailai, Jito and Sharma, Bibhya N. (2010) A Lagrangian-based Swarming Behavior in the Absence of Obstacles. [Conference Proceedings]

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Lagrangian swarm models consider long-range attraction and short-range repulsion between individuals, moving with the velocity of the swarm’s centroid, as a seed in the formation of the swarm itself and its behavior. By constructing a Lyapunov function based on this heuristic rule, we create a relatively simple gradient system which surprisingly exhibits complex emergent or self-organized motions in the absence of fixed or moving obstacles. The Lyapunov function contains an inter-individual collisionavoidance component; hence the component is bounded, yet it guarantees collision avoidance. Three parameters are utilized, and which we call cohesion parameter, coupling parameter, and convergence parameter. They are, respectively, a measure of the strengths of the cohesion of the swarm, the interaction between any two individuals and the instantaneous velocity of an individual with respect to the swarm centroid. By varying these parameters in a precise way, computer simulations show that for a sufficiently large number of individuals, our proposed model generates four types of swarming-like behaviors. They are (1) the cruise formation (linear or nonlinear) reminiscent of a cruising and leaderless school of fish, or a moving herd of land animals with a leader (leader-following), (2) random walks similar to the swarming behavior of fruit flies Drosophila melanogaster, (3) constant arrangements requiring individuals to aggregate and stop, as in fruiting body formation by bacteria, and (4) circular motions reminiscent of the behavior of a school of fish when threatened by a predator.

Item Type: Conference Proceedings
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Technology and Environment (FSTE) > School of Computing, Information and Mathematical Sciences
Depositing User: Ms Shalni Sanjana
Date Deposited: 15 Apr 2014 04:36
Last Modified: 23 Sep 2016 02:59

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