Obstacle avoidance dynamics on Riemannian manifolds

We propose a second‐order dynamical model driven by obstacle avoidance forces. Under the proposed dynamics, each agent independently reacts to a set of given obstacles, which may be either static or moving, through repulsive forces, and no interaction among agents is considered. The model is first formulated in the Euclidean space to understand its basic behavior. We then extend the dynamics to general Riemannian manifolds by employing intrinsic geometric tools, thereby enabling obstacle avoidance in curved environments. Analytical properties of the system are investigated, and numerical simulations are performed to support and compare with the theoretical results.