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arXiv · 1001.4494

Geometric Analysis of the Formation Problem for Autonomous Robots

Florian Dorfler·Bruce Francis
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Abstract

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. It is well known that there are various other undesired invariant sets of the robots' closed-loop dynamics. This paper addresses a global stability analysis by a differential geometric approach considering invariant manifolds and their local stability properties. The 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.

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Florian Dorfler, Bruce Francis. 2010-01-25. Geometric Analysis of the Formation Problem for Autonomous Robots. https://arxiv.org/abs/1001.4494

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