Locally constrained connectivity control in mobile robot networks

Abstract

Abstract-In this paper, we consider the problem of controlling the connectivity of a network of mobile agents under local topology constraints and proximity-limited communication. The inverse iteration algorithm for spectral analysis is formulated in a distributed manner to allow each agent to estimate a component of global network connectivity, improving on the convergence rate issues of previous approaches. Potential-based controls drive the agents to maximize connectivity under local degree constraints, maintain established links to guarantee connectivity, and avoid collisions. To achieve constraint satisfaction we propose a switched model of interaction that regulates link addition through symmetric, repulsive potentials between constraint violators, enforcing discernment in communication through spatial organization. Simulations of connectivity estimation as well as agent aggregation and leader-following applications demonstrate the ability of our proposed methods to generate connectivity maximizing, constraint-aware self organization. I. INTRODUCTIONIntense interest has been focused recently on the analysis and control of networked systems, and particularly on distributed systems of mobile agents. Such systems provide significant gains in efficiency, scalability, and robustness when compared to classical centralized solutions. Applications of mobile agent networks are multi-disciplinary and highly varied; examples include formation control [1], adaptive sampling [2], and target tracking [3].In this work we are concerned with the connectivity property of networks under proximity-limited communication and the topological dynamics induced by mobile agents. Network topology has been shown to have a profound impact on the performance and robustness of networked algorithms, for example in the analysis of formation stability [4], consensus seeking [5], and swarming behaviors [6]. Considering for example the consensus problem, it is demonstrated in [5] that topology fundamentally impacts the convergence and robustness of consensus, yielding distinct tradeoffs in connectivity and network design. These conclusions are further reflected in works such as [7], with biological insight [8]. It is then natural to consider controlling network topology to yield performance gains in networked processes like consensus, or to otherwise shape network information flow [4]. Note that connectivity (topology) control differs sharply from works that seek enhancements to the consensus algorithm itself, e.g. [9], [10]; such algorithms continue to perform at the mercy of network topology.Connectivity control has been addressed in recent works by considering various connectivity measures together with both distributed and centralized control schemes. In [11] marketbased auctions and a local connectivity measure yield hybrid

Topology-constrained flocking in locally interacting mobile networks

“…In order to exercise the spatial discrimination of link additions and deletions simultaneously, together with varied and realistic topology constraints, we construct the following novel coordination scenario. Suppose we have a system of n = 10 agents operating in a bounded workspace over R 2 , with interaction model parameters (ρ 2 , ρ 1 , ρ 0 ) = (20,15,5). We assign 6 agents the flocking controller (7) together with an additional dispersive control…”

Collective control objective and connectivity preservation for multi-robot systems with bounded input

“…Lemma 1 Consider the dynamics of the system given in (5) and the condition given in (7). Assume the initial value of the algebraic connectivity to be λ 2 > .…”

“…Consequenly, several connectivity maintenance techniques have been developed based on the algebraic connectivity, as described in the recent survey paper [4]. Decentralized estimation procedures for the computation of the second-smallest eigenvalue of the Laplacian matrix were introduced in [5]- [7]. A gradient based control strategy was then introduced in [8], [9] that provably ensures connectivity maintenance.…”

Global connectivity control for spatially interacting multi-robot systems with unicycle kinematics

“…With such an algebraic modeling, briefly speaking, the key idea of continuous control frameworks is to design a control law which moves on the positive gradient of the algebraic connectivity when the adjacency matrix is weighted by some function of inter-robot distance. Originally proposed in [3], and successively extended for example in [4], [5], this control law can be implemented in a decentralized fashion once an estimate of the algebraic connectivity and of the related eigenvector is available to the robots, achievable by exploiting various estimation techniques such as [6], [7]. However, the primary shortcomings of continuous connectivity controllers are the very high cost of continuous estimation (due to embedded consensus filters), the inability to cope with repeated eigenvalues, and the notion that maximizing connectivity through gradient following necessarily improves connectivity.…”