Abstract
Formation keeping and motion coordination are key problems in cooperative robotics. As a solution to these problems, the concept of a virtual structure is considered. Based on this idea, we have developed a new flexible virtual structure approach, describing the dynamic model of n vehicles in formation. The developed model is linear, simple to command without need to linearization tools. Note that, for 2D and 3D space navigation, only a rigid virtual structure was proposed in the literature. Further, the problem was limited to a kinematic behavior of the structure. Hence, the flexible virtual structure in dynamic modeling of mobile robots formation presented, gives more capabilities to the formation to avoid obstacles in hostile environment while keeping formation and avoiding inter-agent collision. The stability of the system in the neighborhood of the the desired configuration is studied and sufficient conditions to recall robots to the desired shape of the formation over time are developed. Smooth trajectories of the formation are generated. These trajectories joining an initial configuration to a final desired one, are generated in an hostile environment with presence of obstacles. The flexible virtual structure guarantees an inter-agent collision free motion while keeping formation and avoiding obstacles.