A Unified Analytical Look at Reynolds Flocking Rules

In this paper, we present a unified theoretical view of the so-called ``Flocking Rules of Reynolds'' introduced in 1987. No equations describing the rules or mathematical models of the mobile agents known as ``boids'' were presented in the original work by Reynolds. We show how to model a group of autonomous mobile agents by dynamic nets and achieve flocking by dissipation of the structural energy of the multi-agent system. As a by-product, we obtain a single protocol called the (alpha,alpha) protocol that encompasses all three flocking rules of Reynolds. We provide geometric interpretations of the advanced forms of some of these flocking rules. Simulation results are provided that demonstrate flocking of 100 agents towards a sink

Enhancing self-similar patterns by asymmetric artificial potential functions in partially connected swarms

The control of mobile robotic agents is required to be highly reliable. Artificial potential function (APF) methods have previously been assessed in the literature for providing stable and verifiable control, whilst maintaining a high degree of nonlinearity. Further, these methods can, in theory, be characterised by a full analytic treatment. Many examples are available in the literature of the employment of these methods for controlling large ensembles of agents that evolve into minimum energy configurations corresponding in many cases to regular lattices [1-2]. Although regular lattices can present naturally centric symmetry and self-similarity characteristics, more complex formations can also be achieved by several other means. In [3] the equilibrium configuration undergoes bifurcation by changing a parameter belonging to the part of artificial potential that couples the agents to the reference frame. In this work it is shown how the formation shape produced can be controlled in two further ways, resulting in more articulated patterns. Specifically the control applied is to alter the symmetry of interactions amongst agents, and/or by selectively rewiring interagent connections. In the first case, the network of connections remains the same, and may be fully connected

Internal agent states : experiments using the swarm leader concept

In recent years, an understanding of the operating principles and stability of natural swarms has proven to be a useful tool for the design and control of artificial robotic agents. Many robotic systems, whose design or control principals are inspired by behavioural aspects of real biological systems such as leader-follower relationship, have been developed. We introduced an algorithm which successfully enhances the navigation performance of a swarm of robots using the swarm leader concept. This paper presents some applications based on that work using the simulations and experimental implementation using a swarming behaviour test-bed at the University of Strathclyde. Experimental and simulation results match closely in a way that confirms the efficiency of the algorithm as well as its applicability

Swarm potential fields with internal agent states and collective behaviour

Swarm robotics is a new and promising approach to the design and control of multi-agent robotic systems. In this paper we use a model for a system of self-propelled agents interacting via pairwise attractive and repulsive potentials. We develop a new potential field method using dynamic agent internal states, allowing the swarm agents' internal states to manipulate the potential field. This new method successfully solves a reactive path planning problem that cannot be solved using static potential fields due to local minima formation. Simulation results demonstrate the ability of a swarm of agents that use the model to perform reactive problem solving effectively using the collective behaviour of the entire swarm in a way that matches studies based on real animal group behaviour

Characteristics of swarms on the edge of fragmentation

Fragmentation of particle swarms into isolated subgroups occurs when interaction forces are weak or restricted. In the restricted case, the swarm experiences the onset of bottlenecks in the graph of interactions that can lead to the fragmentation of the system into subgroups. This work investigates the characteristics of such bottlenecks when the number of particles in the swarm increases. It is shown, for the first time, that certain characteristics of the bottleneck can be captured by considering only the number of particles in the swarm. Considering the case of a connected communication graph constructed in the hypothesis that each particle is influenced by a fixed number of neighbouring particles, a limit case is determined for which a lower limit to the Cheeger constant can be derived analytically without the need for extensive algebraic calculations. Results show that as the number of particles increases the Cheeger constant decreases. Although ensuring a minimum number of interactions per particle is sufficient, in theory, to ensure cohesion, the swarm may face fragmentation as more particles are added to the swarm

Flocking with Obstacle Avoidance

In this paper, we provide a dynamic graph theoretical framework for flocking in presence of multiple obstacles. In particular, we give formal definitions of nets and flocks as spatially induced graphs. We provide models of nets and flocks and discuss the realization/embedding issues related to structural nets and flocks. This allows task representation and execution for a network of agents called alpha-agents. We also consider flocking in the presence of multiple obstacles. This task is achieved by introducing two other types of agents called beta-agents and gamma-agents. This framework enables us to address split/rejoin and squeezing maneuvers for nets/flocks of dynamic agents that communicate with each other. The problems arising from switching topology of these networks of mobile agents make the analysis and design of the decision-making protocols for such networks rather challenging. We provide simulation results that demonstrate the effectiveness of our theoretical and computational tools

Swarm robot social potential fields with internal agent dynamics

Swarm robotics is a new and promising approach to the design and control of multiagent robotic systems. In this paper we use a model for a second order non-linear system of self-propelled agents interacting via pair-wise attractive and repulsive potentials. We propose a new potential field method using dynamic agent internal states to successfully solve a reactive path-planning problem. The path planning problem cannot be solved using static potential fields due to local minima formation, but can be solved by allowing the agent internal states to manipulate the potential field. Simulation results demonstrate the ability of a single agent to perform reactive problem solving effectively, as well as the ability of a swarm of agents to perform problem solving using the collective behaviour of the entire swarm