Vision-based Distributed Coordination and Flocking of Multi-agent Systems

Abstract

Abstract-We propose a biologically inspired, distributed coordination scheme based on nearest-neighbor interactions for a set of mobile kinematic agents equipped with vision sensors. It is assumed that each agent is only capable of measuring the following three quantities relative to each of its nearest neighbors (as defined by a proximity graph): time-to-collision, a single optical flow vector and relative bearing. We prove that the proposed distributed control law results in alignment of headings and flocking, even when the topology of the proximity graph representing the interconnection changes with time. It is shown that when the proximity graph is "jointly connected" over time, flocking and velocity alignment will occur. Furthermore, the distributed control law can be extended to the case where the agents follow a leader. Under similar connectivity assumptions, we prove that the headings converge to that of the leader.Simulations are presented to demonstrate the effectiveness of this approach.

On Recurrence of Graph Connectivity in Vicsek's Model of Motion Coordination for Mobile Autonomous Agents

“…The theorem provides a sufficient condition for a sequence of real-valued r-dimensional vectors to be equidistributed 4 mod 1. Roughly speaking, the theorem states conditions under which the fraction of the fractional parts of the sequence terms which fall into a subset of the unit hypercube [0,1] r is equal to the Lebesgue measure of that subset.…”

“…by setting z i (k) → tan θ i (k), the above iteration becomes exactly identical to Vicsek's update scheme (1). In other words, Vicsek's update is nothing but a distributed weighted averaging scheme or implementation of a splitting algorithm for finding the fixed point of the Kuramoto model.…”

“…From flocking, velocity alignment [1]- [3] and consensus [4]- [9] to distributed locational optimization and rendezvous problems [10], researchers have been trying to analyze and design distributed protocols for motion coordination that use local information and result in a global desired behavior.…”

Optimal Agent Cooperation with Local Information

“…We find many examples in map building [66,69,73,75] and search problems [65]. In [52], the authors use a scheme whereby each agent observes the state of the agents located within a certain radius R, and prove stability in the sense that all agents reach a consensus on the heading to adopt. Little to no effort goes in determining the relevance of the observations in the different observation directions.…”

Beat-Based Synchronization and Steering for Groups of Fixed-Wing Flying Robots

“…Work on formation path following for unicycle-type vehicles has so far concentrated on mathematical models and simulations built upon the assumption that robots know the precise relative position of neighbors (range and bearing) and sometimes their heading and speed [2,3,8,10]. Using this knowledge, robots continuously align their position to that of their neighbors and to the trajectory they need to follow.…”