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原文摘要

Finite-time formation transitions are useful for coordinating multi-agent systems in time-critical missions, but convergence to a prescribed formation in finite time does not guarantee collision avoidance or communication connectivity during the transition. Existing approaches address finite-time coordination and safety-constrained formation control, yet explicit connections between disagreement during transitions, formation geometry, and coupling-gain selection need to be developed for certifying safe maneuvers. This paper develops a disagreement-based framework for certifying transient safety and connectivity during finite-time tracking of arbitrary prescribed formation trajectories. Local feedback guarantees exact finite-time tracking with a graph-independent settling-time bound, while a graph-dependent disagreement bound is used to derive sufficient geometric conditions for collision avoidance and connectivity preservation. These conditions further yield an offline coupling-gain selection rule based on the available geometric clearance. Numerical simulations illustrate the trade-off between convergence rate and control effort as the coupling gain increases. They also demonstrate the effectiveness and conservatism of the proposed certificates.