Modeling and controlling 3D formations and flocking behavior of unmanned air vehicles

This paper deals with the problem of modeling and controlling dynamic formations and flocking behavior of unmanned air vehicles. Dynamic formations are modeled using 3D kinematic models combined with dynamic graph structures. The leader-follower and co-leader interconnections are described by time-varying matrices that consist of a binary connectivity matrix and shape matrices. The control laws allowing to maintain the formation with stable motion are decentralized and reactive. They consist of linear navigation laws with deviation terms. These laws are used to generate trajectories to reach the goal and/or switch from one configuration to another. All geometric shapes are obtained from a basic shape that consists of a triangle. Thus any formation is a collection of triangles. To simplify the modeling and control tasks, a cylindric coordinate system is used and the three dimensional workspace is resolved into horizontal and vertical planes. The vehicles are then controlled in the horizontal and vertical planes separately.