Abstract
In this paper we give an analytic study to construct a command for a group of vehicles to reach a target in an hostile environment. A consensus between different agents is established. This work is an extension to a previous one(El) Kamel et al. (2009) to the case of multi-vehicle. The vector which contains all the velocity fields is considered as a feedback control law. We developed a new technique which decompose the vector of velocities to a sum of two parts; an attractive part that guarantees the convergence toward the target and a repulsive part that ensures obstacle avoiding. Our approach is based on LaSalle's theorem. The feedback control law ensures also that each vehicle/agent choose the optimal trajectory in front of the obstacle without neither switching control nor tracking trajectory. We introduce the consensus algorithm with a constant reference state using graph theoretical tools to create an hierarchical formation. The stability of the formation is realized when all agents converge to the desired configuration in neighborhood of the target.