This paper proposes a flexible multi-layer and multi-controller architecture for a dynamic navigation in the formation of a group of autonomous vehicles in constrained environments. The main objectives of this architecture are to ensure reliable navigation in the formation of the vehicles and to guarantee the stable and smooth reconfiguration of the fleet shape. A precise review and analysis of the main used leader-follower modeling for the control of a fleet of autonomous vehicles is conducted. After highlighting their advantages and drawbacks, an appropriate leader-follower approach based on deformable shape is proposed. At each sample time, the leader's state (pose and velocity), defined as the main dynamic target, is taken as a reference to guide the overall fleet dynamic. In addition, an analytic formulation of the maximum linear and angular velocities of the leader is proposed in order to guarantee the asymptotic stability of the navigation in formation as well as the fleet reconfiguration phases (between different formation shapes). An important focus of this paper corresponds to the proposition of a reliable strategy for the fleet reconfiguration, according to the environmental context (when, for instance, obstacles are detected). The safety of the fleet is formally demonstrated using an appropriate reconfiguration matrix, which takes into account the vehicles' set-points inter-distances to avoid any inter-vehicles collisions. In addition, an estimation of the formation parameters, according to an authorized minimum distance between the vehicles, is given. Simulations and experiments in different scenarios are performed to demonstrate the flexibility, reliability, and efficiency of the proposed dynamic navigation of a fleet of vehicles in formation.