This paper presents a method for string stable formation control and formation position assignment for several unmanned air vehicles. The model addresses two main issues of formation control; (a) stability analysis of the interconnected system, (b) vehicle position assignment and switching. The vehicles move along a given trajectory in a specified formation shape. This allows us to decouple the formation shape problem from the motion of the group along a given path. Each vehicle maintains its position relative to an inertial waypoint, and its position relative to its neighbors. Thus, we are developing a leaderless formation control scheme. A specific leader is not desirable, because it may lead to instability of the interconnected system in the case of an error associated with the leader vehicle, and is not fault tolerant. We include an analysis of the error dynamics of the system for a V-shaped formation. This specific shape was selected as birds use it frequently and NASA has shown that this formation is energy efficient. Our system is mesh stable and spacing errors do not exacerbate downstream of the origin. When planes fly in V-formation, the front plane uses more energy and, therefore, more fuel. The trailing planes benefit from the vortex created by the wings of the plane in front of them and use less energy to maintain a cruising speed. For the purposes of maximizing fuel efficiency in an entire team of UAVs, the model uses a simple proximity algorithm to assign the vehicles’ positions and determine when and which vehicles to switch. The only physical variables that need to be observed are the positions of each plane relative to an arbitrary virtual leader position, and the velocities and fuel reserves of each plane, and a small number of other indicial variables. The fuel burnt by the front plane determines when to signal for a switch in position and the geometry of the formation in combination with the fuel levels of the remaining planes controls the decision making process. The different aspects of the model are all meant to work together and individually. Matlab simulation plots of path motion and error convergence are shown as proof of concept.
Distributed Consensus-Based Robust Adaptive Formation Control for Nonholonomic Mobile Robots with Partial Known Dynamics
