Maintaining limited-range connectivity among second-order agents

Abstract

Abstract. In this paper we consider ad-hoc networks of robotic agents with double integrator dynamics. For such networks, the connectivity maintenance problems are: (i) do there exist control inputs for each agent to maintain network connectivity, and (ii) given desired controls for each agent, can one compute the closest connectivity-maintaining controls in a distributed fashion? The proposed solution is based on three contributions. First, we define and characterize admissible sets for double integrators to remain inside disks. Second, we establish an existence theorem for the connectivity maintenance problem by introducing a novel state-dependent graph, called the double-integrator disk graph. Specifically, we show that one can always maintain connectivity by maintaining a spanning tree of this new graph, but one will not always maintain connectivity of a particular agent pair that happens to be connected at one instant of time. Finally, we design a distributed "flow-control" algorithm for distributed computation of connectivity-maintaining controls.1. Introduction. This work is a contribution to the emerging discipline of motion coordination for ad-hoc networks of mobile autonomous agents. This loose terminology refers to groups of robotic agents with limited mobility and communication capabilities. It is envisioned that such networks will perform a variety of useful tasks including surveillance, exploration and environmental monitoring. The interest in this topics arises from the potential advantages of employing arrays of agents rather than single agents in certain applications. For example, from a control viewpoint, a group of agents inherently provides robustness to failures of single agents or of communication links.The motion coordination problem for groups of autonomous agents is a control problem in the presence of communication constraints. Typically, each agent makes decisions based only on partial information about the state of the entire network that is obtained via communication with its immediate neighbors. One important difficulty is that the topology of the communication network depends on the agents' locations and, therefore, changes with the evolution of the network. In order to ensure a desired emergent behavior for a group of agents, it is necessary that the group does not disintegrate into subgroups that are unable to communicate with each other. In other words, some restrictions must be applied on the movement of the agents to ensure connectivity among the members of the group. In terms of design, it is required to constrain the control input such that the resulting topology maintains connectivity throughout its course of evolution. In [2], a connectivity constraint was developed for a group of agents modeled as first-order discrete time dynamic systems. In [2] and in the related references [3,4], this constraint is used to solve rendezvous problems. Connectivity constraints for line-of-sight communication are proposed in

Decentralized estimation and control of graph connectivity for mobile sensor networks

“…For discrete-time second-order agents, a feasible control space is computed in [14] for each agent to maintain all existing pairwise connections. In comparison, in [18] each agent tries to maintain its two-hop communication neighbors.…”

Bilateral Teleoperation of Groups of UAVs with Decentralized Connectivity Maintenance

“…In literature two classes of decentralized connectivity maintenance approaches are present: i) the conservative methods, which aim at preserving the initial graph topology during the task [1,5,10], and ii) the flexible approaches, which allow to switch anytime among any of the connected topologies. These usually produce local control actions aimed at keeping (a decentralized estimate of) λ 2 , the second smallest eigenvalue of the graph Laplacian, positive over time [16,17].…”

Connectivity preserving distributed swarm aggregation for multiple kinematic agents

“…In this way, if the communication graph, which is formed based on the initial displacement between the agents, is connected, then it remains connected for all time. Connectivity preserving algorithms for multi-agent systems with linear motion models were recently presented in [5], [7].…”