Graph Matching-Based Formation Reconfiguration of Networked Agents With Connectivity Maintenance

Abstract

Various applications require networked agents to cooperatively achieve specified formations. In this paper, formation reconfiguration for a group of identical agents with limited communication capabilities is considered. Since the agents considered are identical, their roles are interchangeable, and each position in the desired formation can be taken by any agent. To reduce the total amount of node movement required for formation reconfiguration, a weighted graph matching based node mapping strategy is developed to specify the node correspondence between an arbitrary initial graph and the desired graph. After the node mapping is determined, agents are required to move physically to form the desired formation. Since agents are only able to communicate within a certain range, formation reconfiguration must be accomplished with network connectivity constraints (i.e., specified nodes remain within specified sensing and communication ranges). A decentralized control scheme is developed to guarantee network connectivity by maintaining a desired neighborhood determined by the node mapping algorithm, and to ensure convergence of all agents to the desired configuration with collision avoidance among agents. The developed strategy is demonstrated through simulation results.

Connectivity-Preserving Synchronization of Time-Delay Euler–Lagrange Networks With Bounded Actuation

“…Assumption 2 is widely used in gradient-based connectivity-preserving consensus control [6]- [15] to ensure that the potential function providing the controller is strictly smaller than its maximum intially. Assumption 2 is equivalent to assumption q ij (0) < r in [10]- [15] if the controller design does not require ǫ, like for example in kinematic MAS strategies based on the generalized potential in Section III. However, the potential in [10]- [15] requires sophisticated parameter selections, as shown in [19].…”

“…(15) Equation (15) indicates that V decreases monotonically along the system trajectories, in particular V (t) ≤ V (0) ∀t ≥ 0. Assumption 2 and Proposition 1 lead to V (0) < Ψ max and further Ψ(q) ≤ V (0) < Ψ max .…”

Multi-Robot Persistent Surveillance With Connectivity Constraints

“…Then a tree T a is selected from G a [41], and a matching between T a and T f is calculated [42] (line 14). The labels for the vertices that could not be matched are determined (line 15).…”

“…(Ta, La) ← calc_graph_matching(Ga, T f , L f ) (see [41], [42]) 15: La ← complete_labels_trie(Ta, La) (see [40]) 16: (Ve, Vm) ← calc_extra_missing(La, L f ) (see [40]) 17: for i ∈ Ve, j ∈ Vm do 18: D(i, j) ← distT a (i, closest parent of j also in Ta) 19: M ← calc_matching(D) 20: for i ∈ Ve do sp(i) ← shortest_pathT a (i, M (i)) 21: while true do 22: p ← pt 23: for i ∈ R do 24: if i ∈ Ve then 25: p (i) ← first step in GM along sp(i) 26: if p (i) = M (i) then 27: La ← update_labels(La) 28: Ve ← Ve \ {i} 29: Ga ← GC {p (i) : i ∈ R} ∪ {b} 30: if compare_graphs(Ga, La, T f , L f ) then 31: w ← v ∈ VS with L f (v) = La(i) 32: p (i) ← first step on shortest_pathG M (p (i), w) 33: pt+1 ← p , t ← t + 1 34: if all v1 to vκ have been reached then break locations, it is beneficial that the tour visits sensing location first that are farther away from the base station and that the relaying robots maintain an equal distance between each other on the chain. Two possible tours are depicted in Figure 8.…”

Connectivity-Preserving Swarm Teleoperation With A Tree Network

“…In particular, decentralized algebraic connectivity estimation [12]- [14] helps maintain global connectivity. For kinematic MRS-s, gradient-based controllers derived from unbounded [15]- [18] or bounded [19]- [21] potentials preserve the local connectivity and account for disturbances [22], Lipschitz nonlinearities [23] and obstacles [24], [25]. Topics of recent interest include intermittent connectivity [26], [27], strong connectivity in directed graphs [28], robustness and invariance of connectivity maintenance with additional control terms [29], and the tradeoffs among bounded controls, connectivity maintenance and additional control objectives [30].…”