Multi-Vehicle Flocking: Scalability of Cooperative Control Algorithms using Pairwise Potentials

Abstract

In this paper, we study cooperative control algorithms using pairwise interactions, for the purpose of controlling flocks of unmanned vehicles. An important issue is the role the potential plays in the stability and possible collapse of the group as agent number increases. We model a set of interacting Dubins vehicles with fixed turning angle and speed. We perform simulations for a large number of agents and we show experimental realizations of the model on a testbed with a small number of vehicles. In both cases, critical thresholds exist between coherent, stable, and scalable flocking and dispersed or collapsing motion of the group.

Motility versus fluctuations in mixtures of self-motile and passive agents

“…Previous studies showed that an active suspension can be stabilized into a large-scale circulating state through appropriate confinement [29,30]. Further, the vortical phase in our simulations appears to resemble "milling" patterns observed in investigations of "pure" systems of self-motile particles [20][21][22][23][24][25] with the flocking term (1). Most remarkably, in our simulations the large-scale vortical patterns are found without the inclusion of stabilizing attractive forces or confining boundaries.…”

“…Working with reduced units and using the standard parameter values [19] for a passive DPD fluid, we set k B T = 1.0, r c = 1.0, A = 25.0, γ = 4.5, and ρ 2D = N L 2 = 2.5 (two-dimensional (2D) analog of ρ 3D = 4.0), where L is the dimensionless edge length of the square computational domain. Apart from standard DPD forces, we incorporate selfpropulsion through a flocking termwith α ≥ 0 the constant self-propulsion force parameter and β ≥ 0 the constant Rayleigh friction parameter [20][21][22][23][24][25]. To model the features of a mixture, we apply f i F only on the fraction φ of active agents and the random contribution of the DPD interactions f ij R only between pairs of the fraction 1 − φ of passive agents.…”

“…with α ≥ 0 the constant self-propulsion force parameter and β ≥ 0 the constant Rayleigh friction parameter [20][21][22][23][24][25]. To model the features of a mixture, we apply f i F only on the fraction φ of active agents and the random contribution of the DPD interactions f ij R only between pairs of the fraction 1 − φ of passive agents.…”

Solving the potential field local minimum problem using internal agent states

“…Recently, swarm stabilization or collapse with increasing constituent number has been predicted along with complex behaviour such as phase transitions and emergent patterns [7,8]. Virtual leaders [9] and structural potential functions [10] have also been introduced to provide provable group behaviour to ensure agents can avoid obstacles and form desired patterns. The actual realization of selfpropelled agents interacting according to virtual potentials has also been investigated [11].…”

Swarming in viscous fluids: Three-dimensional patterns in swimmer- and force-induced flows

“…DOI: 10.1103/PhysRevE.93.043112 The collective behavior of self-propelled agents in natural and artificial systems has been extensively studied . Many of the lessons learned from experimental and theoretical work conducted on organisms as diverse as bacteria, ants, locusts, and birds [23][24][25][26][27][28][29][30][31][32][33][34][35][36] have been successfully applied to engineered robotic systems to help frame decentralized control strategies through ad hoc algorithms [37][38][39][40][41][42][43][44]. In most mathematical "swarming" models, particles are assumed to be self-driven by internal mechanisms that impart a characteristic speed.…”