Finite Time Distance-based Rigid Formation Stabilization and Flocking

Most of the existing results on distributed distance-based rigid formation control establish asymptotic and often exponentially asymptotic convergence. To further improve the convergence rate, we explain in this paper how to modify existing controllers to obtain finite time stability. For point agents modeled by single integrators, the controllers proposed in this paper drive the whole formation to converge to a desired shape with finite settling time. For agents modeled by double integrators, the proposed controllers allow all agents to both achieve the same velocity and reach a desired shape in finite time. All controllers are totally distributed. Simulations are also provided to validate the proposed control.