Stable motions of vehicle formations

We investigate stable maneuvers for a group of autonomous vehicles while moving in formation. The allowed decentralized feeback laws are factored through the Laplacian matrix of the communication graph. We show that such laws allow for stable circular or elliptical motions for certain vehicle dynamics. We find necessary and sufficient conditions on the feedback gains and the dynamic parameters for convergence to formation. In particular, we prove that for undirected graphs there exist feedback gains that stabilize rotational (or elliptical) motions of arbitrary radius (or eceentricity). In the directed graph case we provide necessary and sufficient conditions on the curvature that guarantee stability for a given choice of feedback gains. We also investigate stable motions involving reorientation of the formation along the direction of motion.

[1]  T. Samad,et al.  Formations of formations: hierarchy and stability , 2004, Proceedings of the 2004 American Control Conference.

[2]  J. A. Fax.  Optimal and Cooperative Control of Vehicle Formations , 2002 .

[3]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[4]  Petter Ögren,et al.  Obstacle avoidance in formation , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[5]  George J. Pappas,et al.  Stable flocking of mobile agents part I: dynamic topology , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[6]  Wei Zhang,et al.  Vehicle networks: achieving regular formation , 2003, Proceedings of the 2003 American Control Conference, 2003..

[7]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[8]  Gerardo Lafferriere,et al.  Flocks and Formations , 2005 .

[9]  Richard M. Murray,et al.  Information flow and cooperative control of vehicle formations , 2004, IEEE Transactions on Automatic Control.

[10]  George J. Pappas,et al.  Stable flocking of mobile agents, part I: fixed topology , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[11]  Randal W. Beard,et al.  Decentralized Scheme for Spacecraft Formation Flying via the Virtual Structure Approach , 2004 .

[12]  Gerardo Lafferriere,et al.  Decentralized control of vehicle formations , 2005, Syst. Control. Lett..

[13]  Randal W. Beard,et al.  A decentralized scheme for spacecraft formation flying via the virtual structure approach , 2003, Proceedings of the 2003 American Control Conference, 2003..

[14]  Naomi Ehrich Leonard,et al.  Virtual leaders, artificial potentials and coordinated control of groups , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[15]  Kathryn Fraughnaugh,et al.  Introduction to graph theory , 1973, Mathematical Gazette.

[16]  Randal W. Beard,et al.  A decentralized approach to formation maneuvers , 2003, IEEE Trans. Robotics Autom..

[17]  George J. Pappas,et al.  Flocking in Fixed and Switching Networks , 2007, IEEE Transactions on Automatic Control.

[18]  G. Lafferriere,et al.  Graph theoretic methods in the stability of vehicle formations , 2004, Proceedings of the 2004 American Control Conference.

[19]  Chris D. Godsil,et al.  ALGEBRAIC COMBINATORICS , 2013 .

[20]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.