1. Decentralized Multi-Robot ROS 2 Topology
In real multi-agent fleets (e.g. TurtleBot4, Crazyflie swarms), each robot runs an isolated ROS 2 node under a dedicated namespace (`/robot_0`, `/robot_1`). Inter-agent communication is achieved via local Wi-Fi mesh or DDS multicast discovery (CycloneDDS / Zenoh) without a single point of failure.
2. Virtual Spring-Damper Formation Dynamics
To maintain rigid geometry without centralized synchronization, each follower robot computes virtual spring forces to its target coordinate in the leader's local frame:
F_formation = -k * (p_i - p_desired) - c * (v_i - v_leader)
When an obstacle enters the formation, the repulsive obstacle force temporarily stretches the virtual springs, allowing robots to stream around pillars and snap back smoothly.
3. Distributed Consensus Rendezvous
Uncoordinated robots with no central GPS agree on a common meeting point via Laplacian consensus:
dx_i / dt = Σ a_ij * (x_j - x_i)
where a_ij = 1 if robot j is within communication range R_perc. As long as the communication graph remains connected, the swarm provably converges to the geometric centroid.