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

The work of this paper is inspired by the flocking phenomenon observed in Reynolds (1987). We introduce a class of local control laws for a group of mobile agents that result in: (i) global alignment of their velocity vectors, (ii) convergence of their speeds to a common one, (iii) collision avoidance, and (iv) minimization of the agents artificial potential energy. These are made possible through local control action by exploiting the algebraic graph theoretic properties of the underlying interconnection graph. Algebraic connectivity a#ects the performance and robustness properties of the overall closed loop system. We show how the stability of the flocking motion of the group is directly associated with the connectivity properties of the interconnection network and is robust to arbitrary switching of the network topology.

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.

Abstract—Inspired by the so-called “bugs ” problem from mathematics, we study the geometric formations of multivehicle systems under cyclic pursuit. First, we introduce the notion of cyclic pursuit by examining a system of identical linear agents in the plane. This idea is then extended to a system of wheeled vehicles, each subject to a single nonholonomic constraint (i.e., unicycles), which is the principal focus of this paper. The pursuit framework is particularly simple in that the identical vehicles are ordered such that vehicle pursues vehicle CImodulo. In this paper, we assume each vehicle has the same constant forward speed. We show that the system’s equilibrium formations are generalized regular polygons and it is exposed how the multivehicle system’s global behavior can be shaped through appropriate controller gain assignments. We then study the local stability of these equilibrium polygons, revealing which formations are stable and which are not. Index Terms—Circulant matrices, cooperative control, multiagent systems, pursuit problems. I.

We study the stability properties of linear time-varying systems in continuous time whose system matrix is Metzler with zero row sums. This class of systems arises naturally in the context of distributed decision problems, coordination and rendezvous tasks and synchronization problems. The equilibrium set contains all states with identical state components. We present sufficient conditions guaranteeing uniform exponential stability of this equilibrium set, implying that all state components converge to a common value as time grows unbounded. Furthermore it is shown that this convergence result is robust with respect to an arbitrary delay, provided that the delay affects only the off-diagonal terms in the differential equation.

Abstract—In this article we specify an-member “individual-based” continuous time swarm model with individuals that move in an-dimensional space according to an attractant/repellent or a nutrient profile. The motion of each individual is determined by three factors: i) attraction to the other individuals on long distances; ii) repulsion from the other individuals on short distances; and iii) attraction to the more favorable regions (or repulsion from the unfavorable regions) of the attractant/repellent profile. The emergent behavior of the swarm motion is the result of a balance between inter-individual interactions and the simultaneous interactions of the swarm members with their environment. We study the stability properties of the collective behavior of the swarm for different profiles and provide conditions for collective convergence to more favorable regions of the profile. Index Terms—Aggregations, attraction, continuous time swarm, gradient climbing, individual-based, inter-individual interactions, multi-agent systems,-dimensional space, repulsion, stability analysis, swarms. I.

interaction kernels

Abstract—Bacteria, bees, and birds often work together in groups to find food. A group of robots can be designed to coordinate their activities to search for and collect objects. Networked cooperative uninhabited autonomous vehicles are being developed for commercial and military applications. Suppose that we refer to all such groups of entities as “social foraging swarms. ” In order for such multiagent systems to succeed it is often critical that they can both maintain cohesive behaviors and appropriately respond to environmental stimuli (e.g., by optimizing the acquisition of nutrients in foraging for food). In this paper, we characterize swarm cohesiveness as a stability property and use a Lyapunov approach to develop conditions under which local agent actions will lead to cohesive foraging even in the presence of “noise ” characterized by uncertainty on sensing other agent’s position and velocity, and in sensing nutrients that each agent is foraging for. The results quantify earlier claims that social foraging is in a certain sense superior to individual foraging when noise is present, and provide clear connections between local agent-agent interactions and emergent group behavior. Moreover, the simulations show that very complicated but orderly group behaviors, reminiscent of those seen in biology, emerge in the presence of noise. Index Terms—Biological systems, foraging, multiagent systems, stability analysis, swarming.

In this article we build on our earlier results in [1, 2] on swarm stability. In [1, 2] we had considered aggregating swarm model in n-dimensional space based on artificial potential functions for inter-individual interactions and motion along the negative gradient of the combined potential. Here we consider a general model for vehicle dynamics of each agent (swarm member) and use sliding mode control theory to force their motion to obey the dynamics of the swarm considered in [1, 2]. In this context, the results in [1, 2] serve as a ”proof of concept ” for swarm aggregation, whereas the present results serve as possible implementation method for engineering swarms with given vehicle dynamics. 1

We describe how a virtual node abstraction layer can be used to coordinate the motion of real mobile nodes in a region of 2-space. In particular, we consider how nodes in a mobile ad hoc network can arrange themselves along a predetermined curve in the plane, and can maintain themselves in such a configuration in the presence of changes in the underlying mobile ad hoc network, specifically, when nodes may join or leave the system or may fail. Our strategy is to allow the mobile nodes to implement a virtual layer consisting of mobile client nodes, stationary Virtual Nodes (VNs) at predetermined locations in the plane, and local broadcast communication. The VNs coordinate among themselves to distribute the client nodes relatively evenly among the VNs’ regions, and each VN directs its local client nodes to form themselves into the local portion of the target curve.