In this work, we establish a novel dynamical model to address the aggregation problem of the multi-agent system on manifolds. At first, with the help of local coordinate charts, we describe the multi-agent system as a manifold, which is part of the ambient space. Then, we convert the aggregation problem of agents into an optimization issue to minimize the volume of a virtual manifold, and we show that evolving along its mean curvature field can minimize the virtual manifold's volume. Finally, we implement our approach for the multi-agent system on the sphere and non-homogeneous manifold. Several numerical simulations are also performed to verify our theoretical analysis.
In this paper, we gave a geometric description of the synergic behaviors' features. Then we established a second-order dynamic model to address aggregation, collision evasion, obstacle avoidance and target pursuit problems of a swarm moving on a Riemannian manifold. Finally, the large-time behaviors of a swarm (consisted of 100 particles) on unit sphere and a complex manifold with obstacles and target were simulated using our model.
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