Second-Order Agents on Ring Digraphs

The paper addresses the problem of consensus seeking among second-order linear agents interconnected in a specific ring topology. Unlike the existing results in the field dealing with one-directional digraphs arising in various cyclic pursuit algorithms or two-directional graphs, we focus on the case where some arcs in a two-directional ring graph are dropped in a regular fashion. The derived condition for achieving consensus turns out to be independent of the number of agents in a network.Comment: 6 pages, 10 figure

Vehicle platoons through ring coupling

In this paper, a novel strategy for the control of a string of vehicles is designed. The vehicles are coupled in a unidirectional ring at the interaction level: each vehicle is influenced by the position of its immediate forward neighbor; the first vehicle in the platoon is influenced by the position of the last vehicle. Through these interactions a cooperative behavior emerges and a platoon of vehicles moving at a constant velocity with constant inter-vehicle spacings is formed. This contrasts with more traditional control schemes where an independent leader vehicle is followed by the remaining vehicles. For this control structure, stability properties are established. The concept of string stability of a platoon is discussed and applied to the ring interconnection. Design rules are presented, showing how an appropriate choice of parameter values leads to a constant spacing or constant time headway policy. Furthermore, the scheme has a characteristic property: it maintains the platoon structure when subject to malfunctioning vehicles

Station Keeping through Beacon-referenced Cyclic Pursuit

This paper investigates a modification of cyclic constant bearing (CB) pursuit in a multi-agent system in which each agent pays attention to a neighbor and a beacon. The problem admits shape equilibria with collective circling about the beacon, with the circling radius and angular separation of agents determined by choice of parameters in the feedback law. Stability of circling shape equilibria is shown for a 2-agent system, and the results are demonstrated on a collective of mobile robots tracked by a motion capture system

Curve Shortening and the Rendezvous Problem for Mobile Autonomous Robots

If a smooth, closed, and embedded curve is deformed along its normal vector field at a rate proportional to its curvature, it shrinks to a circular point. This curve evolution is called Euclidean curve shortening and the result is known as the Gage-Hamilton-Grayson Theorem. Motivated by the rendezvous problem for mobile autonomous robots, we address the problem of creating a polygon shortening flow. A linear scheme is proposed that exhibits several analogues to Euclidean curve shortening: The polygon shrinks to an elliptical point, convex polygons remain convex, and the perimeter of the polygon is monotonically decreasing.Comment: 15 pages, 18 figure

A Cyclic Pursuit Framework for Networked Mobile Agents Based on Vector Field Approach

This paper proposes a pursuit formation control scheme for a network of double-integrator mobile agents based on a vector field approach. In a leaderless architecture, each agent pursues another one via a cyclic topology to achieve a regular polygon formation. On the other hand, the agents are exposed to a rotational vector field such that they rotate around the vector field centroid, while they keep the regular polygon formation. The main problem of existing approaches in the literature for cyclic pursuit of double-integrator multiagent systems is that under those approaches, the swarm angular velocity and centroid are not controllable based on missions and agents capabilities. However, by employing the proposed vector field approach in this paper, while keeping a regular polygon formation, the swarm angular velocity and centroid can be determined arbitrary. The obtained results can be extended to achieve elliptical formations with cyclic pursuit as well. Simulation results for a team of eight mobile agents verify the accuracy of the proposed control scheme

COOPERATIVE TARGET TRACKING IN CONCENTRIC FORMATIONS

This paper considers the problem of coordinating multiple unmanned aerial vehicles (UAVs) in a circular formation around a moving target. The main contribution is allowing for versatile formation patterns on the basis of the following components. Firstly, new uniform spacing control laws are proposed that spread the agents not necessarily over a full circle, but over a circular arc. Uniform spacing formation controllers are proposed, regulating either the separation distances or the separation angles between agents. Secondly, the use of virtual agents is proposed to allow for different radii in agents’ orbits. Thirdly, a hierarchical combination of formation patterns is described. A Lyapunov analysis is conducted to study the stability characteristics. This paper also addresses the practical issue of collision avoidance that arises while UAVs are developing formations. An additional control component is added that repels agents to steer away from each other once they get too close. All UAVs have constant linear velocities. Control of the UAV is via its yaw rate. The proposed extensions to formation on a portion of a circle, circling on different radii for different agents, formation in local geometric shapes, and inter-vehicle collision avoidance, provide more complete solution to cooperative target tracking in concentric formations