Chaotically Paced Transit of an Embedded-Leader Swarm with Local Spring-Damper Formation Control

Abstract

This paper treats planar swarm transit along a fixed route when no ground station streams the reference in flight. One embedded leader stores the deployment point and the destination, generates the reference onboard, and drives its progress rate with a saturated coordinate of a Chua oscillator; the saturation keeps the rate inside a prescribed positive band, which gives explicit bounds on the reference arrival time. This leader broadcasts the one scalar rate to the other leaders; every leader adds it as a velocity feedforward and holds its station by single-pinned consensus on position error, while followers use only relative position and velocity feedback through a spring-damper network. For kinematic leaders and double-integrator followers on fixed graphs with ideal information exchange, the leader errors decay exponentially, the follower errors are bounded, and the whole swarm eventually stays inside the destination area whenever the final formation fits strictly inside it. Ten simulations with 30 agents compare the chaotic rate with a constant rate. The reference arrivals satisfy the analytical bounds, and the chaotic rate raises the error of a constant-velocity predictor at all three tested horizons, at the cost of a larger but bounded follower error. The analysis does not address internal link failures or model-aware observers.