Flexible Distributed Flocking Control for Multi-agent Unicycle Systems

Currently, the general aim of flocking and formation control laws for multi-agent systems is to form and maintain a rigid configuration, such as, the alpha-lattices in flocking control methods, where the desired distance between each pair of connected agents is fixed. This introduces a scalability issue for large-scale deployment of agents due to unrealizable geometrical constraints and the constant need of centralized orchestrator to ensure the formation graph rigidity. This paper presents a flexible distributed flocking cohesion algorithm for nonholonomic multi-agent systems. The desired geometry configuration between each pair of agents is adaptive and flexible. The distributed flocking goal is achieved using limited information exchange (i.e., the local field gradient) between connected neighbor agents and it does not rely on any other motion variables measurements, such as (relative) position, velocity, or acceleration. Additionally, the flexible flocking scheme with safety is considered so that the agents with limited sensing capability are able to maintain the connectedness of communication topology at all time and avoid inter-agent collisions. The stability analysis of the proposed methods is presented along with numerical simulation results to show their effectiveness.Comment: 9 pages, 2 figure

Agent-based pedestrian modelling

When the focus of interest in geographical systems is at the very fine scale, at the level of streets and buildings for example, movement becomes central to simulations of how spatial activities are used and develop. Recent advances in computing power and the acquisition of fine scale digital data now mean that we are able to attempt to understand and predict such phenomena with the focus in spatial modelling changing to dynamic simulations of the individual and collective behaviour of individual decision-making at such scales. In this Chapter, we develop ideas about how such phenomena can be modelled showing first how randomness and geometry are all important to local movement and how ordered spatial structures emerge from such actions. We focus on developing these ideas for pedestrians showing how random walks constrained by geometry but aided by what agents can see, determine how individuals respond to locational patterns. We illustrate these ideas with three types of example: first for local scale street scenes where congestion and flocking is all important, second for coarser scale shopping centres such as malls where economic preference interferes much more with local geometry, and finally for semi-organised street festivals where management and control by police and related authorities is integral to the way crowds move

Declarative vs Rule-based Control for Flocking Dynamics

The popularity of rule-based flocking models, such as Reynolds' classic flocking model, raises the question of whether more declarative flocking models are possible. This question is motivated by the observation that declarative models are generally simpler and easier to design, understand, and analyze than operational models. We introduce a very simple control law for flocking based on a cost function capturing cohesion (agents want to stay together) and separation (agents do not want to get too close). We refer to it as {\textit declarative flocking} (DF). We use model-predictive control (MPC) to define controllers for DF in centralized and distributed settings. A thorough performance comparison of our declarative flocking with Reynolds' model, and with more recent flocking models that use MPC with a cost function based on lattice structures, demonstrate that DF-MPC yields the best cohesion and least fragmentation, and maintains a surprisingly good level of geometric regularity while still producing natural flock shapes similar to those produced by Reynolds' model. We also show that DF-MPC has high resilience to sensor noise.Comment: 7 Page

Topological Sound and Flocking on Curved Surfaces

Active systems on curved geometries are ubiquitous in the living world. In the presence of curvature orientationally ordered polar flocks are forced to be inhomogeneous, often requiring the presence of topological defects even in the steady state due to the constraints imposed by the topology of the underlying surface. In the presence of spontaneous flow the system additionally supports long-wavelength propagating sound modes which get gapped by the curvature of the underlying substrate. We analytically compute the steady state profile of an active polar flock on a two-sphere and a catenoid, and show that curvature and active flow together result in symmetry protected topological modes that get localized to special geodesics on the surface (the equator or the neck respectively). These modes are the analogue of edge states in electronic quantum Hall systems and provide unidirectional channels for information transport in the flock, robust against disorder and backscattering.Comment: 15 pages, 6 figure

Hydrodynamic Model for the System of Self Propelling Particles with Conservative Kinematic Constraints; Two dimensional stationary solutions

We consider a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we prove that the only types of the stationary planar solutions in the model are either of translational or axial symmetry of the flow. Within the proposed model we differentiate between finite and infinite flocking behavior by the finiteness of the kinetic energy functional.Comment: 12 pages, 1 figur