G. Lafferriere was supported in part by NSF grant DMS-0408334 and by a Career Support grant from Portland State University
Control theory -- Mathematical models, Multiagent systems -- Stability, Feedback control systems, Laplacian matrices
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.
Williams, Anca; Lafferriere, Gerardo; and Veerman, J. J. P., "Stable Motions of Vehicle Formations" (2005). Mathematics and Statistics Faculty Publications and Presentations. 132.