In a recent Physical Review Letters paper, Vicsek et. al. propose a simple but compelling discrete-time model of n autonomous agents fi.e., points or particlesg all moving in the plane with the same speed but with dierent headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its \neighbors." In their paper, Vicsek et. al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models.

In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no time-delays, ii) networks with fixed topology and communication time-delays, and iii) max-consensus problems (or leader determination) for groups of discrete-time agents. In each case, we introduce a linear/nonlinear consensus protocol and provide convergence analysis for the proposed distributed algorithm. Moreover, we establish a connection between the Fiedler eigenvalue of the information flow in a network (i.e. algebraic connectivity of the network) and the negotiation speed (or performance) of the corresponding agreement protocol. It turns out that balanced digraphs play an important role in addressing average-consensus problems. We introduce disagreement functions that play the role of Lyapunov functions in convergence analysis of consensus protocols. 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.

Submitted to the IEEE Transactions on Automatic Control Technical Report CIT-CDS 2004-005 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 α-lattices. We use a multi-species framework for construction of collective potentials that consist of flock-members, or α-agents, and virtual agents associated with α-agents called β- and γ-agents. We show that the tracking/migration problem for flocks can be solved using an algorithm with a peer-to-peer architecture. Each node (or macro-agent) of this peer-to-peer network is the aggregation of all three species of agents. The implication of this fact is that “flocks

We introduce a framework, called "physicomimetics," that provides distributed control of large collections of mobile physical agents in sensor networks. The agents sense and react to virtual forces, which are motivated by natural physics laws. Thus, physicomimetics is founded upon solid scientific principles. Furthermore, this framework provides an effective basis for self-organization, fault-tolerance, and self-repair. Three primary factors distinguish our framework from others that are related: an emphasis on minimality (e.g., cost effectiveness of large numbers of agents implies a need for expendable platforms with few sensors), ease of implementation, and run-time efficiency. Examples are shown of how this framework has been applied to construct various regular geometric lattice configurations (distributed sensing grids), as well as dynamic behavior for perimeter defense and surveillance. Analyses are provided that facilitate system understanding and predictability, including both qualitative and quantitative analyses of potential energy and a system phase transition. Physicomimetics has been implemented both in simulation and on a team of seven mobile robots. Specifics of the robotic embodiment are presented in the paper.

This is the second of a two-part paper, investigating the stability properties of a system of multiple mobile agents with double integrator dynamics. In this second part, we allow the topology of the control interconnections between the agents in the group to vary with time. Specifically, the control law of an agent depends on the state of a set of agents that are within a certain neighborhood around it. As the agents move around, this set changes giving rise to a dynamic control interconnection topology and a switching control law. This control law consists of a a combination of attractive/repulsive and alignment forces. The former ensure collision avoidance and cohesion of the group and the latter result to all agents attaining a common heading angle, exhibiting flocking motion. Despite the use of only local information and the time varying nature of agent interaction which affects the local controllers, flocking motion can still be established, as long as connectivity in the neighboring graph is maintained.

This research demonstrates how principles of self-organization and behavior simulation can be used to represent dynamic data evolutions by extending the concept of information flocking, originally introduced by Proctor & Winter [1], to time-varying datasets. A rule-based behavior system continuously controls and updates the dynamic actions of individual, three-dimensional elements that represent the changing data values of reoccurring data objects. As a result, different distinguishable motion types emerge that are driven by local interactions between the spatial elements as well as the evolution of time-varying data values. Notably, this representation technique focuses on the representation of dynamic data alteration characteristics, or how reoccurring data objects change over time, instead of depicting the exact data values themselves. In addition, it demonstrates the potential of motion as a useful information visualization cue. The original information flocking approach is extended to incorporate time-varying datasets, live database querying, continuous data streaming, real-time data similarity evaluation, automatic shape generation and more stable flocking algorithms. Different experiments prove that information flocking is capable of representing short-term events as well as long-term temporal data evolutions of both individual and groups of time-dependent data objects. An historical stock market quote price dataset is used to demonstrate the algorithms and principles of time-varying information flocking.

Summary. The motion of a group of nonholonomic mobile agents is synchronized using local control laws. This synchronization strategy is inspired by the early flocking model proposed by Reynolds [22] and following work [29, 8]. The control laws presented ensure that all agent headings and speeds converge asymptotically to the same value and collisions between the agents are avoided. The stability of this type of motion is closely related to the connectivity properties of the underlying interconnection graph. Proof techniques are based on LaSalle’s invariant principle and algebraic graph theory and the results are verified in numerical simulations. 1

Abstract- In prior work we established how artificial physics can be used to self-organize swarms of mobile robots into hexagonal formations. In this paper we extend the framework to moving formations, by providing additional theoretical analysis that facilitates the implementation of seven robots in a hexagonal formation moving towards a goal.

This paper in vestigates the aggregated stability properties of of a system of multiple mobileagen ts described by simpledynleS55 systems. Theagen ts are steered through local coordin2Sfi5 con trol laws that arise as a combin7 tion of attractive/repulsivean align2F t forces. These forces ences collision avoidan e a n cohesion of the groupan result to all agen ts attain[S a common headin anin exhibitin flockin motion Two cases are con197 ered: in the first, position in[]5 ation from all group members is available to each agen t; in the seconc each agen t has access to position i n ormation of on( the agen ts layin in ide its n ighborhood. It is then shown that regardless ofan y arbitrary chan[1 in thenS[9 bor set, the flockinmotion remain stable aslon as the graph that describes the n ighborin relation amon the agen ts in the group is always con9 cted. 1

In this paper, we provide a dynamic graph theoretical framework for ocking in presence of multiple obstacles. In particular, we give formal de nitions of nets and ocks as spatially induced graphs. We provide models of nets and ocks and discuss the realization/embedding issues related to structural nets and ocks. This allows task representation and execution for a network of agents called -agents. We also consider ocking in the presence of multiple obstacles.