Abstract
This paper addresses the n-vehicle formation shape maintenance problem in the plane. The objective is to design decentralized motion control laws for each vehicle to restore formation shape in the presence of small perturbations from the desired shape. Formation shape is restored by actively controlling a certain set of interagent distances, and we assign the task of controlling a particular interagent distance to only one of the involved agents. We restrict our attention to a class of directed information architectures called minimally persistent leader-remote-follower. The nonlinear closed-loop system has a manifold of equilibria, which implies that the linearized system is nonhyperbolic. We apply center manifold theory to show local exponential stability of the desired formation shape. Choosing stabilizing gains is possible if a certain submatrix of the rigidity matrix has all leading principal minors nonzero, and we show that this condition holds for all leader-remote-follower formations with generic agent positions. Simulations are provided.
| Original language | English |
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| Title of host publication | 2009 European Control Conference |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 2438-2443 |
| Number of pages | 6 |
| ISBN (Print) | 978-3-9524173-9-3 |
| DOIs | |
| Publication status | Published - 26 Mar 2014 |
| Event | 10th European Control Conference: ECC 2009 - Budapest, Hungary Duration: 23 Aug 2009 → 26 Aug 2009 Conference number: 10th http://ieeexplore.ieee.org/document/7074402/ http://ieeexplore.ieee.org/document/7074461/ |
Conference
| Conference | 10th European Control Conference: ECC 2009 |
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| Abbreviated title | ECC |
| Country/Territory | Hungary |
| City | Budapest |
| Period | 23/08/09 → 26/08/09 |
| Internet address |