Flocking is a coordinated collective behavior that results from local sensing between individual agents that have a tendency to orient towards each other. Flocking is common among animal groups and might also be useful in robotic swarms. In the interest of learning how to control flocking behavior, recent work in the multiagent systems literature has explored the use of influencing agents for guiding flocking agents to face a target direction. The existing work in this domain has focused on simulation settings of small areas with toroidal shapes. In such settings, agent density is high, so interactions are common, and flock formation occurs easily. In our work, we study new environments with lower agent density, wherein interactions are more rare. We study the efficacy of placement strategies and influencing agent behaviors drawn from the literature, and find that the behaviors that have been shown to work well in high-density conditions tend to be much less effective in lower density environments. The source of this ineffectiveness is that the influencing agents explored in prior work tended to face directions optimized for maximal influence, but which actually separate the influencing agents from the flock. We find that in low-density conditions maintaining a connection to the flock is more important than rushing to orient towards the desired direction. We use these insights to propose new influencing agent behaviors, which we dub "follow-then-influence"; agents act like normal members of the flock to achieve positions that allow for control and then exert their influence. This strategy overcomes the difficulties posed by low density environments.
@cite_32 studied Reynolds-Vicsek agents from an analytical perspective. Two strong results from this work were that a group of Reynolds-Vicsek agents in a toroidal setting will eventually converge regardless of initial conditions, and that in the presence of a single agent with fixed orientation (analogous to a single influencing agent), all the agents will converge to that fixed agent's orientation. This theory provides important context for Genter and Stone's work and the work that we present here: when the setting is toroidal, convergence is guaranteed, so the interesting question is how fast we can reach convergence.
@cite_32
2165744313 2159499856 1493636406 2158401151
In a recent Physical Review Letters article, propose a simple but compelling discrete-time model of n autonomous agents (i.e., points or particles) all moving in the plane with the same speed but with different 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, 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. The Vicsek model proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function. This paper uses recently established properties of compositions of directed graphs together with results from the theory of nonhomogeneous Markov chains to derive worst case convergence rates for the headings of a group of mobile autonomous agents which arise in connection with the widely studied Vicsek consensus problem. The paper also uses graph-theoretic constructions to solve modified versions of the Vicsek problem in which there are measurement delays, asynchronous events, or a group leader. In all three cases the conditions under which consensus is achieved prove to be almost the same as the conditions under which consensus is achieved in the synchronous, delay-free, leaderless case. Two anonymous mobile agents (robots) moving in an asynchronous manner have to meet in an infinite grid of dimension δ > 0, starting from two arbitrary positions at distance at most d. Since the problem is clearly infeasible in such general setting, we assume that the grid is embedded in a δ-dimensional Euclidean space and that each agent knows the Cartesian coordinates of its own initial position (but not the one of the other agent). We design an algorithm permitting the agents to meet after traversing a trajectory of length O(dδ polylog d). This bound for the case of 2D-grids subsumes the main result of [12]. The algorithm is almost optimal, since the Ω(dδ) lower bound is straightforward. Further, we apply our rendezvous method to the following network design problem. The ports of the δ-dimensional grid have to be set such that two anonymous agents starting at distance at most d from each other will always meet, moving in an asynchronous manner, after traversing a O(dδ polylog d) length trajectory. We can also apply our method to a version of the geometric rendezvous problem. Two anonymous agents move asynchronously in the δ-dimensional Euclidean space. The agents have the radii of visibility of r1 and r2, respectively. Each agent knows only its own initial position and its own radius of visibility. The agents meet when one agent is visible to the other one. We propose an algorithm designing the trajectory of each agent, so that they always meet after traveling a total distance of O((d r)δ polylog(d r)), where r = min(r1, r2) and for r ≥ 1. This paper is concerned with the convergence of a class of continuous-time nonlinear consensus algorithms for single integrator agents. In the consensus algorithms studied here, the control input of each agent is assumed to be a state-dependent combination of the relative positions of its neighbors in the information flow graph. Using a novel approach based on the smallest order of the nonzero derivative, it is shown that under some mild conditions the convex hull of the agents has a contracting property. A set-valued LaSalle-like approach is subsequently employed to show the convergence of the agents to a common point. The results are shown to be more general than the ones reported in the literature in some cases. An illustrative example demonstrates how the proposed convergence conditions can be verified.