This research presents a Lagrangian swarm model for the control of a planar swarm model that has a target. The Direct Method of Lyapunov is used to ensure cohesion of the swarm and stability at the target point. The model proposed can address obstacle-free and obstacle-cluttered environments. Emergent patterns such as split/rejoin, tunnelling maneuver and emergent leader are some of the achievable results, which we apply to nonholonomic planar vehicles.