Connectivity-Preserving Similar Formation via Dual–Threshold Common-Mode Switching
摘要
We study leaderless similar formation control for planar multi-agent systems with limited communicating range by proposing a dual-threshold common-mode controller. Driven by two thresholds strictly inside the communication radius, a switching signal partitions the controller into two modes. In the formation mode, the agents follow a similarity formation flow that moves the state toward the subspace determined by the predetermined shape; in the consensus mode, a distance weighted consensus flow is activated only when any inter-agent distance nears the boundary, contracts those distances, and returns control to the formation mode once all edges reenter a safe band, thus avoiding rapid toggling and preserving connectivity. With edge weights that keep the similarity subspace invariant and diagonal gains that stabilize motion transverse to it, a single Lyapunov function guarantees convergence to a steady formation within the similarity family, with only finitely many switches; the resulting scale is set by the two thresholds. The steady-state formation scale is tunable through the two thresholds. Simulations with five single-integrator agents confirm connectivity preservation, post-switch exponential convergence, and effective scale regulation.