Dynamic Altitude Synchronization Using Graph Theory

Abstract

The Q-structure formation control is useful for motion planning at the kinematics level. For formation control that takes into account the dynamics of helicopters, a different approach is proposed. Chapter 8 presents synchronized altitude tracking control of helicopters with unknown dynamics by graph theory, while the desired trajectory is available to a portion of the team. Since only the neighbors’ information is available to the helicopter, we use the weighted average of neighbors’ states as the reference state of the helicopter in the control design. We prove that if the extended communication graph contains a spanning tree with the virtual vehicle as its root, then its Laplacian will be positive definite. This property is essential for the stability proven and it also makes the proof of the stability for the results easy and direct. The mathematical stability proof, which makes use of the positive definite property of the graph Laplacian, is provided for both full-state and output feedback cases.