In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.

/pdf/consensus-problems-in-networks-of-agents-with-switching-25c3hqvtd8.pdf

Consensus problems in networks of agents with switching topology and time-delays

In this paper, we intend to formulate a new meta-heuristic algorithm, called Cuckoo Search (CS), for solving optimization problems. This algorithm is based on the obligate brood parasitic behaviour of some cuckoo species in combination with the Levy flight behaviour of some birds and fruit flies. We validate the proposed algorithm against test functions and then compare its performance with those of genetic algorithms and particle swarm optimization. Finally, we discuss the implication of the results and suggestion for further research.

Cuckoo Search via Lévy flights

http://masou-keshtkar.persiangig.com/document/sdarticle.pdf

GSA: A Gravitational Search Algorithm

In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in free-space and presence of multiple obstacles are considered. We present three flocking algorithms: two for free-flocking and one for constrained flocking. A comprehensive analysis of the first two algorithms is provided. We demonstrate the first algorithm embodies all three rules of Reynolds. This is a formal approach to extraction of interaction rules that lead to the emergence of collective behavior. We show that the first algorithm generically leads to regular fragmentation, whereas the second and third algorithms both lead to flocking. A systematic method is provided for construction of cost functions (or collective potentials) for flocking. These collective potentials penalize deviation from a class of lattice-shape objects called /spl alpha/-lattices. We use a multi-species framework for construction of collective potentials that consist of flock-members, or /spl alpha/-agents, and virtual agents associated with /spl alpha/-agents called /spl beta/- and /spl gamma/-agents. We show that migration of flocks can be performed using a peer-to-peer network of agents, i.e., "flocks need no leaders." A "universal" definition of flocking for particle systems with similarities to Lyapunov stability is given. Several simulation results are provided that demonstrate performing 2-D and 3-D flocking, split/rejoin maneuver, and squeezing maneuver for hundreds of agents using the proposed algorithms.

/pdf/flocking-for-multi-agent-dynamic-systems-algorithms-and-5efqu9aidp.pdf

Flocking for multi-agent dynamic systems: algorithms and theory

From the Publisher: 
The accessible presentation of this book gives both a general view of the entire computer vision enterprise and also offers sufficient detail to be able to build useful applications. Users learn techniques that have proven to be useful by first-hand experience and a wide range of mathematical methods. A CD-ROM with every copy of the text contains source code for programming practice, color images, and illustrative movies. Comprehensive and up-to-date, this book includes essential topics that either reflect practical significance or are of theoretical importance. Topics are discussed in substantial and increasing depth. Application surveys describe numerous important application areas such as image based rendering and digital libraries. Many important algorithms broken down and illustrated in pseudo code. Appropriate for use by engineers as a comprehensive reference to the computer vision enterprise.

Computer vision : a modern approach = 计算机视觉 : 一种现代的方法

In this chapter, we consider a swarm composed of N agents whose dynamics have velocity constraints and evolve based on the equations 

$$ \begin{array}{rcl} \dot{p}_{xi} & = & v_i\cos(\theta_i), \\ \dot{p}_{yi} & = & v_i\sin(\theta_i), \\ \dot{\theta}_i & = & w_i, \\ \dot{v}_i & = & \frac{1}{m_i}\left[u_{i1}+f_{v_i}\right], \\ \dot{w}_i & = & \frac{1}{I_i}\left[u_{i2}+f_{w_i}\right], \end{array} \label{eqn:unicycle_dynamics} $$

where $x_i(t)=[p_{xi}(t), p_{yi}(t)]^{\top}$ denotes the position of agent i at time instant t in cartesian coordinates, θ i is the steering angle, v i is the linear speed, and w i is the angular speed of agent i. The quantities m i and I i are positive constants and represent the mass and the moment of inertia of agent i, respectively. The control inputs for agent i are the force input ui1 = F i and the torque input ui2 = τ i .

Swarms of Non-holonomic Unicycle Agents with Model Uncertainty

This paper presents a methodology to generate proper state trajectories of a swarm of agents, described as a single integrator model. The main goal of the proposed methodology is to route the agents into planar polygons like areas, so that to accomplish for cooperative perimeter surveillance or target capturing tasks. In particular, the agents are driven into a polygonal strip defined by a given containment external convex polygonal region and an internal forbidden convex polygonal region around a prescribed target. The control law is designed looking at a circular strip, then a conversion from circular to polygonal areas is applied to achieve the prescribed goal. Steady-state conditions are analyzed and sufficient conditions derived in terms of the control law parameters. Simulation results put in light the main properties of the resulting kinematic state description.

A Swarm Model for Target Capturing in a Polygonal Strip

In this paper we focus on the target capturing problem for a swarm of agents modelled as double integrators in any finite space dimension. Each agent knows the relative position of the target and has only an estimation of its velocity and acceleration. Given that the estimation errors are bounded by some known values, it is possible to design a control law that ensures that agents enter a user-defined ellipsoidal ring around the moving target. Agents know the relative position of the other members whose distance is smaller than a common detection radius. Finally, in the case of no uncertainty about target data and homogeneous agents, we show how the swarm can reach a static configuration around the moving target. Some simulations are reported to show the effectiveness of the proposed strategy.

Target Capturing in an Ellipsoidal Region for a Swarm of Double Integrator Agents

The National Institute of Standards and Technology (NIST) has been developing the "Real-Time Control Systems (RCS)" software for more than two decades and using it for the design and implementation of complex intelligent control systems. Present applications of RCS include mining, manufacturing, robotics, and autonomous vehicles. In this paper we summarize the efforts at Ohio State University to develop an educational program for the NIST RCS that includes classroom instruction, a strong laboratory component (complete with small-scale RCS implementations), and a software handbook.

Real-Time Control System software for intelligent system development: experiments and an educational program

This work describes a methodology to generate trajectories for a swarm of agents, modeled as single integrators, for achieving target capturing/enclosing and containment. The discussed method proposes a robust solution which relaxes the strong assumptions about the exact knowledge of the target information. In particular, each agent requires a rough estimation of the reference, with an a-priori known bounded error both on the position and the velocity. It is shown that the swarm can be properly guided to enter a given capturing region while remaining outside a defined distancing region around the target. Steady-state analysis for velocity consensus is also provided for the case in which the reference information is exactly known by the agents. 

Veysel Gazi

Papers

Swarms of Non-holonomic Unicycle Agents with Model Uncertainty

A Swarm Model for Target Capturing in a Polygonal Strip

Target Capturing in an Ellipsoidal Region for a Swarm of Double Integrator Agents

Real-Time Control System software for intelligent system development: experiments and an educational program

Swarm Trajectories Generation for Target Capturing With Uncertain Information