Coordinate-free formation stabilization based on relative position measurements

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Summary This paper investigates the convergence of nonholonomic multiagent coordinate‐free formation control to a prescribed target formation subject to communication delays by means of Lyapunov‐Krasovskii approach and smooth state‐feedback control laws. As a result, an iterative algorithm based on linear matrix inequalities is provided to obtain the worst‐case point‐to‐point delay under which the multiagent system is guaranteed to be stable. It is worth mentioning that: (i) the given algorithm holds for any connected communication topology and (ii) the formation control is coordinate‐free, that is, a common frame is not required to be shared between agents. The effectiveness of the given method is illustrated through simulation results.

Section: Corollarymentioning

confidence: 99%

Section: Contributionsmentioning

confidence: 99%

Section: Corollarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stability analysis of nonholonomic multiagent coordinate‐free formation control subject to communication delays

González

Aragüés

López‐Nicolás

et al. 2018

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“…() Alternative control laws were proposed, for examples, designing control weights for the stabilization of affine formations, simultaneously aligning the agents' local coordinate frames and controlling the relative positions. () These strategies provide global convergence of the formation to the desired shape; however, there are also trade‐offs on these solutions. In affine formations, all agents are required to have the same coordinate systems.…”

Section: Introductionmentioning

confidence: 99%

Formation control of rigid graphs with flex edges

Pham

Trinh

Ahn

2018

Summary This paper studies a distance‐based formation control problem of multiagent systems, in which each agent uses only relative positions of its neighbors with respect to its own coordinate system. First, we provide an analysis for the properties of the undesired equilibria‐corresponding 2 specific formations, ie, a triangle group in 2‐dimensional space and a tetrahedron group in 3‐dimensional space. Then, we consider the formation of multiagent systems whose interaction graph consists of a rigid group and an extra node. Although the extra node may have an additional control input, the desired formation where all interagent distance constraints are satisfied is asymptotically stable. If the rigid group is a triangle in 2‐dimensional space or a tetrahedron in 3‐dimensional space, any undesired equilibrium is unstable. In these cases, the desired formations are almost globally asymptotically stable. Finally, we extend these results to a more general formation, which is a series of rigid groups connecting via flex edges.

Distance‐based control of formations with hybrid communication topology

Hou

2017

Summary In this paper, we focus on the control of multiagent formations with hybrid communication topology through a distance‐based approach. By saying hybrid topology, we mean that the communication topology contains both undirected and directed links, or the underlying graph of the formation contains both undirected and directed edges. A new type of graph, ie, hybrid graph, is introduced. We discuss the persistence of hybrid graphs and present the persistence verification strategy for hybrid graphs. It is proved that all the minimally persistent hybrid graphs can be obtained from persistent directed graphs by the operation of edge transformation. As the main result, it is shown that multiagent formations modeled by acyclic persistent hybrid graphs can be stabilized locally under distance‐based controllers.