Mohammad Mehdi Asadi

Distributed consensus control of unicycle agents in the presence of external disturbances

Abstract In this paper, a distributed consensus control strategy is presented for a team of unicycle agents subject to external disturbances. Bounded disturbances with unknown dynamics on both translational and angular velocities are applied to the system. The key idea is to design the control inputs of each agent in such a way that, after a finite time, agents move with an acute angle with respect to a reference vector typically used for the consensus control of disturbance-free single-integrator agents. Convergence to consensus is then proved using Lyapunov theory. Simulation results confirm the efficacy of the proposed controller.

Global network connectivity assessment via local data exchange for underwater acoustic sensor networks

This paper studies the problem of distributed connectivity assessment for a network of underwater sensors in a data aggregation mission. Motivated by a sufficient condition for asymptotic almost sure consensus in a network defined over a random digraph, vertex connectivity of the expected communication graph is used as a measure for the connectivity of the underwater sensor network. A distributed update scheme is proposed in which the sensors update their perception of the expected communication graph. The expected communication graph can be characterized by its associated probability matrix. A learning algorithm is employed by each sensor to update its belief on the probabilities using the broadcast messages it receives. Each sensor uses a polynomial-time algorithm to estimate the degree of vertex connectivity of the expected graph based on its perception of the network graph. The proposed algorithms can also handle changes in the topology of the network such as node addition, node deletion, and time-varying probabilities. The performance of the proposed algorithms is validated in simulation.

A consensus control strategy for unicycles in the presence of disturbances

In this paper, a distributed consensus control strategy for a team of unicycle agents subject to disturbance is presented. Disturbances on both the translational and angular velocities are considered. It is assumed that disturbance dynamics are known a priori while their initial conditions are unknown. The norm and the angle of a typical control vector for the consensus of disturbance-free single-integrator agents is used to design the proposed controllers. The control input for each agent consists of two parts. One part which leads to consensus in disturbance-free case, and a second term which compensates for the disturbances. The simulation results confirm the efficacy of the proposed controllers.

Connectivity measures for random directed graphs with applications to underwater sensor networks

In this paper, the problem of connectivity assessment for an underwater random sensor network is investigated. The weighted vertex connectivity is introduced as a metric to evaluate the connectivity of the weighted expected graph of a random sensor network where the elements of the weight matrix represent the operational probability of their corresponding communication links. The proposed weighted vertex connectivity measure extends the notion of vertex connectivity to random graphs by taking into account the joint effects of the path reliability and the network robustness to node failure. The approximate weighted vertex connectivity measure is defined subsequently as a lower bound on the introduced connectivity metric which can be computed by applying a polynomial-time shortest path algorithm. The performance of the proposed algorithms is validated by simulation.

Cooperative control of multi-agent systems with limited angular field of view

This paper is concerned with the problems of consensus and containment in a network of directed single-integrator agents with some practical constraints in sensing other agents. Limitations in field of view (FOV), which are considered in this work, are very common in vision-based sensing/communication devices (such as cameras or directed antennas). The set of neighbors for each agent depends on its angular position, which varies by time. This poses new challenges to the cooperative control of agents, where it is desired to achieve objectives such as consensus and containment. The problem is formulated in the context of impulsive switched systems, and a controller is proposed with a switching law which ensures the connectivity of the network at all times, except for some limited time instants. A controller is subsequently designed to achieve consensus using the concept of Laplacian-based control. Finally, two subgroups of agents are defined as static leaders and moving followers, and the controller is modified properly to achieve containment in this case asymptotically.

Distributed control of a network of single integrators with limited angular fields of view

The consensus and containment problems in a multi-agent system consisting of single integrators with angular field of view (FOV) constraints in their sensing capabilities are investigated in this paper. First, it is assumed that all FOVs are half-planes and an impulsive switching strategy is developed such that the underlying sensing graph of the network remains uniformly quasi-strongly connected (UQSC) throughout the system evolution. The control schemes are designed in the framework of switched interconnected systems in such a way that the objectives of consensus and containment are achieved over the entire network. Then, the problem is extended to address a network of single-integrator agents with limited heterogeneous angular FOVs. The FOV of all sensing devices are assumed to rotate with sufficiently large angular velocities, which are controlled independently along with the translational motion of all agents. The velocity vector and the lower bound on the magnitude of the angular velocity of the FOVs are designed such that the agents converge to an arbitrarily small ball, and reach consensus. The convergence of the moving followers to the convex hull of static leaders is addressed for the containment problem as well. Simulation results verify the effectiveness of the proposed control strategies.

Joint power optimization and connectivity control problem over underwater random sensor networks

In this paper, the problem of power optimization and connectivity control for an underwater random sensor network is investigated. The weighted edge connectivity is proposed as a metric to evaluate the connectivity of the weighted expected graph of a random sensor network where the elements of the weight matrix represent the operational probability of their corresponding communication links. The introduced connectivity measure is described as an explicit function of the transmission power of the sensors and the statistical parameters of the communication channels. An optimization problem is then presented to minimize the total power consumption of the network while a lower bound on the global weighted edge connectivity of the network is satisfied. An analytical solution to the optimization problem is obtained by considering a directed cycle topology for the expected communication graph. The efficacy of the obtained results is confirmed for log-normal distribution of the power gain of acoustic communication channels.

Potential-based flocking in multi-agent systems with limited angular fields of view

In this paper, the flocking problem in a network of double-integrator agents with angularly limited fields of view (FOV) is investigated. The conic-shaped angular FOVs impose sensing limitations on every agent in the network. To increase the sensing capability of agents and preserve network connectivity, the FOV of every agent rotates with a sufficiently fast angular velocity. The problem is formulated in the framework of distributed switched nonlinear systems to address the switching topology of the network. Potential-based control inputs are subsequently designed as a combination of alignment and attractive/repulsive forces, such that the velocity vector of each agent exponentially reaches a certain neighborhood of a given desired velocity vector and the inter-agent collision is avoided. The efficacy of the proposed control strategy is confirmed by the simulation results.

Expected Convergence Rate to Consensus in Asymmetric Networks: Analysis and Distributed Estimation

This paper investigates the expected rate of convergence to consensus in an asymmetric network represented by a weighted directed graph. The initial state of the network is represented by a random vector and the expectation is taken with respect to the random initial condition of the network. The proposed convergence rate is described in terms of the eigenvalues of the Laplacian matrix of the network graph. The generalized power iteration algorithm is then introduced based on the Krylov subspace method to compute the proposed expected convergence rate in a centralized fashion. To this end, the Laplacian matrix of the network is transformed to a new matrix such that existing techniques can be used to find the eigenvalue representing the expected convergence rate of the network. The convergence analysis of the centralized algorithm is performed with a prescribed upper bound on the approximation error of the algorithm. A distributed version of the centralized algorithm is then developed using the notion of consensus observer. The efficiency of the algorithms is subsequently demonstrated by simulations.

Generalized algebraic connectivity for asymmetric networks

The problem of connectivity assessment of an asymmetric network represented by a weighted directed graph is investigated in this paper. The notion of generalized algebraic connectivity is introduced for this type of network as an extension of conventional algebraic connectivity measure for symmetric networks. This new notion represents the expected asymptotic convergence rate of a cooperative algorithm used to control the network. The proposed connectivity measure is then described in terms of the eigenvalues of the Laplacian matrix of the graph representing the network. The effectiveness of this measure in describing the connectivity of asymmetric networks is demonstrated by some intuitive and counter-intuitive examples. A variation of the power iteration algorithm is then developed to compute the proposed connectivity measure. To this end, the Laplacian matrix of the network is properly transformed to a new matrix such that existing techniques can be used to find the eigenvalue representing network connectivity. The effectiveness of the proposed notion in describing network connectivity and also the efficiency of the developed algorithm are subsequently verified by simulations.