Aggregation of Multi-Agent System on Manifolds With Riemannian Geometry

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.