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.

A Very Large Scale Robotic (VLSR) system may consist of from hundreds to perhaps tens of thousands or more autonomous robots. The costs of robots are going down, and the robots are getting more compact, more capable, and more flexible. Hence, in the near future, we expect to see many industrial and military applications of VLSR systems in tasks such as assembling, transporting, hazardous inspection, patrolling, guarding and attacking. In this paper, we propose a new approach for distributed autonomous control of VLSR systems. We define simple artificial force laws between pairs of robots or robot groups. The force laws are inverse-power force laws, incorporating both attraction and repulsion. The force laws can be distinct and to some degree they reflect the 'social relations' among robots. Therefore we call our method social potential fields. An individual robot's motion is controlled by the resultant artificial force imposed by other robots and other components of the system. The approach is distributed in that the force calculations and motion control can be done in an asynchronous and distributed manner. We also extend the social potential fields model to use spring laws as force laws. This paper presents the first and a preliminary study on applying potential fields to distributed autonomous multi-robot control. We describe the generic framework of our social potential fields method. We show with computer simulations that the method can yield interesting and useful behaviors among robots, and we give examples of possible industrial and military applications. We also identify theoretical problems for future studies. 1999 Published by Elsevier Science B.V. All rights reserved.

Abstract — In this brief article we specify an “individual-based ” continuous time model for swarm aggregation in n-dimensional space and study its stability properties. We show that the individuals (autonomous agents or biological creatures) will form a cohesive swarm in a finite time. Moreover, we obtain an explicit bound on the swarm size, which depends only on the parameters of the swarm model. I.

This is the first of a two-part paper that investigates the stability properties of a system of multiple mobile agents with double integrator dynamics. In this first part we generate stable flocking motion for the group using a coordination control scheme which gives rise to smooth control laws for the agents. These control laws are a combination of attractive/repulsive and alignment forces, ensuring collision avoidance and cohesion of the group and an aggregate motion along a common heading direction. In this control scheme the topology of the control interconnections is fixed and time invariant. The control policy ensures that all agents eventually align with each other and have a common heading direction while at the same time avoid collisions and group into a tight formation.

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—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.

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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

We analyze the coordinated motion of a group of nonholonomic vehicles that are controlled in a distributed fashion to exhibit flocking behavior. This behavior emerges from aggregating the control actions of all group members; it is not imposed by some centralized control scheme. Each vehicle is locally controlled by a combination of a potential field force and an alignment force. The former control component ensures collision avoidance and attraction towards the group, while the latter steers each vehicle to the average heading of its `neighbors'. Eventually all vehicles attain a common heading and move in tight formation while avoiding collisions.

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