Formation Control for Multiple Vehicles Based on Motion Planning Approach

Abstract: The paper studies the problem of finite time formation control for multiple vehicles based on the motion planning approach. The vehicle is modeled as the full actuated rigid body with the dynamics evolving on the tangent bundle of Euclidean group, both the formation time which is finite and the geometric structure of the formation are assumed to be specified by the task. For the required formation, an open optimal control law is derived by using Pontryagins minimum principle. In order to overcome the deficiency that the open control law is sensitive to disturbances, the open control law is converted to the closed form by feeding the current state back and initializing the control law at the current time, under the assumption that the mode of communication between the vehicles is all-to-all. For the demonstration of the result, some numerical examples of formation for planar vehicles are included.