A novel approach for Swarm's synergic behaviors on manifolds based on Riemannian Geometry

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.