Emergent behavior of the Cucker–Smale model with inherent dynamics under unit-speed constraint

This paper studies the emergent behavior of Cucker–Smale flocks with inherent dynamics and unit-speed constraints under both complete and directed interaction topologies. We present two sufficient frameworks that guarantee flocking, depending on the initial conditions and system parameters. Specifically, for interaction topologies represented by complete graphs, we show that exponential convergence occurs when the initial velocity angles between agents are less than π/2 and the inherent dynamics are orthogonal to the agents’ velocities. For rooted digraph interaction topologies, we provide analogous sufficient conditions that also ensure the convergence of flocking. Finally, numerical simulations are performed to illustrate and validate the theoretical results.