Synchronization and Collision Avoidance in Non-Linear Flocking Networks of Autonomous Agents

We introduce and discuss two novel second-order consensus networks with state-dependent couplings of CuckerSmale type. The first scheme models flocking to synchronization over a network of agents where the alignment of the agent’s states occurs over a non-trivial limit orbit that is generated by the internal dynamics of each individual agent. The second scheme models the speed alignment of a group of agents which avoid approaching each other closer than a prescribed distance. While seemingly different, both of these systems can be analyzed using the same mathematical methods. We rigorously analyze both examples and reveal their striking similarities. We arrive at sufficient conditions that relate the initial configurations and the systems’ parameters that give rise to a collective common behavior. Simulation examples are presented to support our theoretical conclusions