Preliminary Results of Vehicle Formation Control Using Dynamic Inversion

Results are presented from a preliminary study to determine the potential benefits of utilizing dynamic inversion inspired by a structural analogy for formation control of a system of vehicles. Vehicles are modeled as unconstrained mass particles under the influence of control forces in an inertial reference frame. For a system of particles restricted to motion in one dimension only, equations of motion are developed, and a corresponding dynamic inversion control law is proposed. A dissipative mechanical structure analogy is used to establish a family of feedback controllers. The conditions for global asymptotic stability are presented, and information requirements are discussed. It is shown that a stable system can be generated with each particle obtaining measurements for the mass center location of the system, and the position of the particles immediately next to it. A simulation of the response of a system to initial errors and desired trajectories using the proposed control law is presented yielding satisfactory results. INTRODUCTION Formation control, in recent years, has been a topic of significant interest to researchers. Of particular interest is the control of cooperative teams of vehicles to perform tasks such as reconnaissance missions and cooperative strikes. More specifically, the advantages of formation flight of air vehicles, manned or unmanned, include the increased capability of performing missions that would otherwise be more difficult for a single, larger aircraft. Additionally, it is known that formation flight yields a reduction in the total drag of a wing, or follower, aircraft trailing behind a lead aircraft. A significant amount of work has been devoted to designing control systems for aircraft in formation. In particular, Pachter et al. have developed a linear controller for formation flight, while Singh et al. have developed an adaptive feedback linearizing controller. More recently, the work of Olfati-Saber and Murray provides a theoretical framework for stability analysis and distributed control of multi-agent formations in two or three dimensions. Giulietti et al. developed a controller in which the flight vehicles retain their distance with respect to an imaginary point in the formation. Most of the controllers described above rely on the existence of a leader, whose actions are followed by other vehicles. Instead of using a leader or an imaginary point to guide the formation, this paper explores the advantages of using the mass center of the system, in essence a virtual formation, as the guide. The case of one-dimensional formation control is investigated, equations of motion are developed using a Lagrangian approach, and a corresponding dynamic inversion control law is generated. Lastly, stability characteristics and information requirements are analyzed. ONE-DIMENSIONAL FORMATION CONTROL This section presents the application of the proposed approach to a system of particles constrained to move in one dimension only. Equations of motion for the system are developed, and the stability of the formulation is studied. Equations of Motion As with any dynamical system, the equations describing the dynamics of the system need to be developed. First, a coordinate system is defined as presented in figure 1. Figure 1. One-Dimensional Coordinate System __________________ Graduate Research Assistant, Aerospace Engineering Department. Student Member AIAA. Professor and Director, Flight Simulation Laboratory, Aerospace Engineering Department. Associate Fellow AIAA. Distinguished Professor, George J. Eppright Chair, and Director, Center for Mechanics and Control. Aerospace Engineering Department. Fellow AIAA. In figure 1, there exist n particles that are collocated in one-dimensional space, and can only move in a straight line. This system could be representative of a line of vehicles following each other. The mass of each particle is denoted as mi, the inertial position of each particle as xi, and the control force acting on each particle as ui. The position state of the system can be described with the 1 American Institute of Aeronautics and Astronautics 42nd AIAA Aerospace Sciences Meeting and Exhibit 5 8 January 2004, Reno, Nevada AIAA 2004-295 Copyright © 2004 by R. Caicedo, J. Valasek and J.L. Junkins. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. vector x and the control forces with the vector u as follows: 1