Geometric Analysis of the Formation Problem for Autonomous Robots
| Autor: | Bruce A. Francis, Florian Dörfler |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Lyapunov function
Geometric analysis Mobile robot Autonomous robot Topology Computer Science Applications symbols.namesake Control and Systems Engineering Linearization Control theory symbols Electrical and Electronic Engineering Invariant (mathematics) Autonomous system (mathematics) Center manifold Mathematics |
| Zdroj: | IEEE Transactions on Automatic Control. 55:2379-2384 |
| ISSN: | 1558-2523 0018-9286 |
| DOI: | 10.1109/tac.2010.2053735 |
| Popis: | In the formation control problem for autonomous robots, a distributed control law steers the robots to the desired target formation. A local stability result of the target formation can be derived by methods of linearization and center manifold theory or via a Lyapunov-based approach. Besides the target formation, the closed-loop dynamics of the robots feature various other undesired invariant sets such as nonrigid formations. This note addresses a global stability analysis of the closed-loop formation control dynamics. We pursue a differential geometric approach and derive purely algebraic conditions for local stability of invariant embedded submanifolds. These theoretical results are then applied to the well-known example of a cyclic triangular formation and result in instability of all invariant sets other than the target formation. |
| Databáze: | OpenAIRE |
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