Finite time optimal formation control for multiple vehicles

The paper studies the problem of finite time formation control for multiple vehicles. The vehicle is modeled as the full actuated rigid body, both the formation time and the geometric structure of the formation are specified by the task. An open optimal control law is derived by using Pontryagins minimum principle, and is converted to the closed form by feeding the current state back under the assumption that the mode of communication between the vehicles is all-to-all. For the demonstration of the result, a numerical example of formation for planar vehicles is included.