Distance-based undirected formations of single-integrator and double-integrator modeled agents in n -dimensional space

Abstract

SUMMARYWe study the local asymptotic stability of undirected formations of single‐integrator and double‐integrator modeled agents based on interagent distance control. First, we show that n‐dimensional undirected formations of single‐integrator modeled agents are locally asymptotically stable under a gradient control law. The stability analysis in this paper reveals that the local asymptotic stability does not require the infinitesimal rigidity of the formations. Second, on the basis of the topological equivalence of a dissipative Hamiltonian system and a gradient system, we show that the local asymptotic stability of undirected formations of double‐integrator modeled agents in n‐dimensional space is achieved under a gradient‐like control law. Simulation results support the validity of the stability analysis. Copyright © 2013 John Wiley & Sons, Ltd.

A survey of multi-agent formation control

“…There are a couple of works that have extended the analysis to three-or higher dimensional cases. Oh and Ahn (2014a) have designed a control law for distance-based undirected formations in n-dimension; but it has been focused on local stability properties. Park, Jeong, and Ahn (2013) have extended the existing result on distance-based formation control of three-agents in twodimension to four-agent tetrahedral formation with equilateral edges in three-dimension.…”

“…Further they have shown that the gradient control law is indeed the optimal control law with respect to a cost functional. Extending the result in Dörfler and Francis (2009) to n-dimension, Oh and Ahn (2014a) have shown that the infinitesimal rigidity of (G, p * ) is not crucial for local asymptotic stability of E p * . They have shown that if (G, p * ) is rigid in R n , E p * is locally asymptotically stable with respect to (32) by (1970).…”

“…In the case that G has a cycle, the global stability property is not valid any more as studied in Johansson (2009, 2010). While G has been assumed to be a tree for the investigation of global stability properties of E ′ p * in Johansson (2008, 2010), it can be shown that if (G, p * ) is rigid, E p * is locally asymptotically stable with respect to (32) under the gradient control law based on (34) by using the result in Oh and Ahn (2014a). Oh and Ahn (2011b,c,e) have proposed a distance-based formation control law for the agents (25), which is aimed to allow inter-agent distances to converge to desired values in some desired manner.…”

“…Distance-based control of double-integrator modeled agents has been studied in Oh and Ahn (2014a) and Olfati-Saber and Murray (2002). Consider the following N double-integrator modeled agents in n-dimensional space over a graph G:…”

Formation-scaling strategy for an acyclic triangular formation: Distance-based approach

“…Recently, there have been wide research interests on the formation control problems [1][2][3][4][5][6][7][8][9][10]. Basically, the for mation control problem arises when we deal with a group of agents that can move on in the plane or space.…”