On the Formation Rejoin Problem*

We consider the problem of a maneuvering vehicle performing a rejoin to close formation with another maneuvering vehicle. The dynamics of relative position and velocity is shown to be governed by a linear time varying dynamics. Using rotationally invariant potential functions to exploit the symmetry present in the dynamics, we are able to construct Lyapunov functions that, along with their time derivative, are independent of time allowing us to conclude, in the case of linear feedback, exponential stability of the time varying closed loop system. The situation with nonlinear feedback is somewhat more delicate, requiring the use of Matrosov's theorem to prove uniform global asymptotic stability. Performance of the approach is illustrated by rejoining to an aggressively maneuvering flight leader using a saturating control law.