Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
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 …
A Note On Lattice Chains And Delannoy Numbers, John S. Caughman Iv, Clifford R. Haithcock, J. J. P. Veerman
A Note On Lattice Chains And Delannoy Numbers, John S. Caughman Iv, Clifford R. Haithcock, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
Fix nonnegative integers n1,…,nd and let L denote the lattice of integer points (a1,…,ad)∈Zd satisfying 0⩽ai⩽ni for 1⩽i⩽d. Let L be partially ordered by the usual dominance ordering. In this paper we offer combinatorial derivations of a number of results concerning chains in L. In particular, the results obtained are established without recourse to generating functions or recurrence relations. We begin with an elementary derivation of the number of chains in L of a given size, from which one can deduce the classical expression for the total number …
Flocks And Formations, J. J. P. Veerman, Gerardo Lafferriere, John S. Caughman Iv, A. Williams
Flocks And Formations, J. J. P. Veerman, Gerardo Lafferriere, John S. Caughman Iv, A. Williams
Mathematics and Statistics Faculty Publications and Presentations
Given a large number (the “flock”) of moving physical objects, we investigate physically reasonable mechanisms of influencing their orbits in such a way that they move along a prescribed course and in a prescribed and fixed configuration (or “in formation”). Each agent is programmed to see the position and velocity of a certain number of others. This flow of information from one agent to another defines a fixed directed (loopless) graph in which the agents are represented by the vertices. This graph is called the communication graph. To be able to fly in formation, an agent tries to match the …