Graph Laplacians and Stabilization of Vehicle Formations

By J. Alexander Fax, Richard M. Murray. 2002

290 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ea3f7dbab25be14398c8272822db327e6008c2a2

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In Computer Networks and Communications

In Geometry and Topology

Citations in the corpus

Agreement over random networks (2004, background): “In recent years, this area has attracted the attention of researchers in system theory, biology, and statistical physics; system theoretic references include [6], [9], [14], [15], [18], and [20].”
Consensus seeking in multiagent systems under dynamically changing interaction topologies (2005, unknown): “2:The discrete update scheme ( 1) achieves asymptotic consensus for A if and only if D[k − 1]D[k − 2] · · ·D[2]D[1]D[0] → 1c (5)”
Stability analysis for multi-agent systems using the incidence matrix: Quantized communication and formation control (2010, methodology): “We consider the agreement control laws in Fax and Murray (2002) and Olfati-Saber and Murray (2004), which were given by”
Coordination of groups of mobile autonomous agents using nearest neighbor rules (2002, unknown): “Each agent’s heading is updated using a local rule based on the average of its own heading plus the headings of its “neighbors.””
Information flow and cooperative control of vehicle formations (2004, background): “The Perron–Frobenius theory can be found in many texts; the presentation here is based on material in [29]–[31].”
Cooperative Minimum Time Surveillance With Multiple Ground Vehicles (2010, background): “In particular the so called art gallery problems [13], [23], [24], multiple traveling salesman problems [47] and [48] and the information graph [43], [48] will be discussed below.”
Decentralized overlapping control of a formation of unmanned aerial vehicles (2002, background): “Factors which make a UAV system a low cost alternative, such as rapid reconfigurability in the event of single point failures and dispensability of vehicles, also represents the main challenge from the control design perspective [4, 5 , 12, 14].”
Distributed Event-Triggered Control for Multi-Agent Systems (2012, unknown): “The agreement control laws in [9], [20] were given by”
Decentralized Cooperative Aerial Surveillance Using Fixed-Wing Miniature UAVs (2006, background): “[11] VV, BGraph Laplacians and stabilization of vehicle formations,[ in Proc.”
Event-triggered control for multi-agent systems (2009, unknown): “The agreement control laws in [8], [17] were given by and the closed-loop equations of the nominal system (without quantization) were ˙ x i = − j ∈ N i ( x i − x j , ) , i ∈ { 1 , . . . , N } , so that ˙ x = − Lx , where x = [ x 1 , . . . , x N ] T is the stack vector of agents’ states and L is the…”
Flocking in Fixed and Switching Networks (2007, background): “" Each such interaction is associated with a link in the sensing network of the group, which, being position dependent, is represented by the position graph defined as follows.”
Distributed Coordination Control of Multiagent Systems While Preserving Connectedness (2007, background): “It should be noted that these problems have already been solved if either connectedness is assumed [5], [7], [15], or connectedness is only required at distinct times [4], [3], [16], [26]–[28] in the sense that the agents sense their environment and then move in such a way that the network is…”
On the spectra of nonsymmetric Laplacian matrices (2005, unknown): “1 Studying the spectra of nonsymmetric Laplacian matrices is also needed for solving control problems that involve graphs [9].”