Finite-time convergence control for acyclic persistent formations

In this paper, we propose a distance-based control law for acyclic persistent formations of mobile agents. The proposed normalized gradient law, which can be implemented distributively by using local measurements, allows agents to achieve their desired formation shape specified by inter-agent distance constraints in finite time, with local but not global con-vergence. We show some local finite-time convergence properties including an upper bound for the convergence time. Further the existence of attractive incorrect equilibrium formations is demonstrated. Simulation results are provided for illustration.