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Full-Text Articles in Non-linear Dynamics
Symmetry And Stability Of Homogeneous Flocks, J. J. P. Veerman
Symmetry And Stability Of Homogeneous Flocks, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
The study of the movement of flocks, whether biological or technological, is motivated by the desire to understand the capability of coherent motion of a large number of agents that only receive very limited information. In a biological flock a large group of animals seek their course while moving in a more or less fixed formation. It seems reasonable that the immediate course is determined by leaders at the boundary of the flock. The others follow: what is their algorithm? The most popular technological application consists of cars on a one-lane road. The light turns green and the lead car …
Stable Motions Of Vehicle Formations, Anca Williams, Gerardo Lafferriere, J. J. P. Veerman
Stable Motions Of Vehicle Formations, Anca Williams, Gerardo Lafferriere, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
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 …