Collective Circular Motion Research Articles

A Survey on Techniques in the Circular Formation of Multi-Agent Systems

Distributed control solutions to the multi-agent systems in terms of coordination, formation, and consensus problems are extensively studied in the literature. The circular formation control of multi-agent systems becomes one of the most challenging and active research topics in distributed cooperative control. The research potential of circular formation control has grown especially in satellite formation and control. The circular formation control aims to drive a group of agents to move on a circular trajectory around a center with spacing adjustment to avoid the collision. This paper covers the fundamental research in consensus and formation control and the latest developments in the applications of formation control especially in circular formation control and stability analysis. Literature related to various control streams to achieve circular formation is discussed. Algebraic graph theory is used as a building block in problem definition, problem formulation, and solutions. A review of bearing, range, and received signal strength measurements with respect to circular formation control is presented. Leader following, behavior-based, artificial potential function, virtual structure, and cyclic pursuit are the methods discussed most in this context. The stabilization of the collective circular motion with the unicycles approach is also discussed. Further results on circular formation, several applications, and future research directions are presented.

Circular Formation Algorithms for Multiple Nonholonomic Mobile Robots: An Optimization-Based Approach

This paper revisits the circular formation control problem proposed in [G. S. Seyboth, J. Wu, J. Qin, C. Yu, and F. Allgower, “Collective circular motion of unicycle type vehicles with nonidentical constant velocities,” IEEE Transactions on Control of Network Systems , vol. 1, no. 2, pp. 167–176, Jun. 2014.] for multiple nonholonomic mobile robots with nonidentical constant forward speeds. Specifically, we study two types of circular formations: First, a circular motion with synchronized/balanced phase configuration; and second, a concentric circular formation with both circular orbits control and phase synchronization/balancing. Existing works on the above problems utilize a fixed-gain control input, which increases the workload of the engineers for selecting favorable algorithm parameters. To reduce this workload, we study the above problems from a new perspective by utilizing optimization methods, based on which two variable-gain control algorithms are proposed such that much greater flexibility on the selection of algorithm parameters is acquired. The global convergence properties of the proposed algorithms are analyzed under some mild assumptions. Both simulations and field experiments are presented to validate the effectiveness of the proposed formation algorithms.

Milling-induction and milling-destruction in a Vicsek-like binary-mixture model

Milling is a collective circular motion often observed in nature (e.g., in fish schools) and in many theoretical models of collective motion. In these models particles are considered to be identical. However, this is not the case in nature, where even individuals of the same species differ from each other in one or more traits. In order to get insights into the mechanisms of milling formation in heterogeneous systems (i.e., with non-identical particles), the emergence of milling in a binary mixture of particles that differ in one trait is investigated for the first time. Depending on parameter values, particles that in single-type systems do not mill can either be induced to mill or destroy the milling of other particles. Milling-induction and milling-destruction are studied varying the speed, the field of view, and the relative amount of the two types of particles.

Intermittence and connectivity of interactions in pigeon flock flights

Collective circular motion is a common yet spectacular behavior of pigeon flocks. Efficient and robust inter-individual communication is required for flock coordination during this widely-spreaded movement pattern. When a flock hovers near the home loft, the rotational direction undergoes regular spontaneous variations. Based on intensive analyses of high spatial-temporal resolution GPS data, we quantified the intensity of velocity alignment among different individuals in terms of their velocity fluctuations. It is found that pigeon flocks employ an intermittent interaction (alignment) mechanism, where intra-group information transmission is not required at every instant. However, the union of the topologies of several consecutive interaction networks always keeps connected. This biological observation strongly suggests the presence of a jointly connected topology in pigeon flocks, which helps substantially reduce the communication and/or information processing requirements while retaining the agility and stability of the group. Finally, we conducted extensive investigation on the interaction mechanism as well as the spontaneous changes in rotational direction of pigeon flocks. These results shed some light onto the coordination mechanism exploration of bird flocks’ collective motions.

Collective circular motion in synchronized and balanced formations with second-order rotational dynamics

This paper considers collective circular motion of multi-agent systems in which all the agents are required to traverse different circles or a common circle at a prescribed angular velocity. It is required to achieve these collective motions with the heading angles of the agents synchronized or balanced. In synchronization, the agents and their centroid have a common velocity direction, while in balancing, the movement of agents causes the location of the centroid to become stationary. The agents are initially considered to move at unit speed around individual circles at different angular velocities. It is assumed that the agents are subjected to limited communication constraints, and exchange relative information according to a time-invariant undirected graph. We present suitable feedback control laws for each of these motion coordination tasks by considering a second-order rotational dynamics of the agent. Simulations are given to illustrate the theoretical findings.

Collective Circular Motion of Unicycle Type Vehicles With Nonidentical Constant Velocities

This paper addresses formation control problems for heterogeneous groups of unicycle type mobile agents with fixed cruising speed. The heterogeneity in the group is caused by the cruising speeds being nonidentical, which complicates the motion coordination problem but is of practical relevance, for example, in unmanned aerial vehicle applications. We show that two different types of collective circular motion are possible in such groups: 1) a circular motion with common angular frequency and different radius for each agent; or 2) a circular motion with common radius but different angular frequency for each agent. For the first motion type, the orientation of all vehicles can additionally be coordinated such that an agreement or a balanced configuration is achieved. We present suitable control laws for each of these motion coordination tasks. These control laws explicitly take into account the nonidentical velocities and guarantee convergence to the desired configurations. Numerical examples illustrate all results.

Bacterial Cell Division: A Swirling Ring to Rule Them All?

FtsZ, a tubulin homologue and the major constituent of the bacterial Z ring, hasbeen shown to assemble into curved filament bundles, which exhibit GTP-hydrolysis-dependent turnover. Surprisingly, the presence of its membrane adaptor FtsA renders this turnover directional, inducing treadmilling and collective circular motion of filaments invitro.

Applications of Collective Circular Motion Control to Multirobot Systems

Collective circular motion is common in both natural systems and engineering applications. Recent theoretical research has intensively studied the fundamental control mechanism. This brief aims to pave the way from theoretical design to practical implementation by addressing a set of issues encountered in real applications. As a result, a practically effective control algorithm is successfully implemented and examined for a multirobot system to achieve a desired circular formation.

A remark on collective circular motion of heterogeneous multi-agents

The study on collective circular motion has attracted researchers over the past years. Many control algorithms have been successfully developed for achieving various circular motion patterns. However, the existing algorithms rely on more or less global information including a reference beacon, a common reference frame, agent labels, or agent homogeneity. In this paper, an improved algorithm is proposed for a group of heterogeneous agents, not relying on any of the aforementioned global information. The algorithm is supported by analytical analysis and verified in both simulation and experiments.

No-beacon collective circular motion of jointly connected multi-agents

In this paper, a decentralized control algorithm is proposed for a group of nonholonomic vehicles to form a class of collective circular motion behavior. Without the guidance of a global beacon, the desired collective behavior occurs provided that the multi-agent system is jointly connected. Moreover, a repulsion mechanism is considered to improve the distribution evenness of the agents’ circular motion phases and hence to avoid collision. The effectiveness of the approach is verified through both theoretical analysis and numerical simulation. Moreover, some interesting variations of the circular motion model are investigated to enrich the collective behaviors.

Experimental validation of collective circular motion for nonholonomic multi-vehicle systems

This paper presents the experimental validation of a recently proposed decentralized control law, for the collective circular motion of a team of nonholonomic vehicles about a virtual reference beacon. The considered control strategy ensures global asymptotic stability in the single-vehicle case and local asymptotic stability in the multi-vehicle scenario. The main contribution of this work is to evaluate the performance of the proposed algorithm in the presence of a number of uncertainty sources naturally arising in a real-world environment. Both static and moving reference beacons are considered, in a low-cost experimental framework based on the LEGO MINDSTORMS technology. The adopted setup features good scalability and is versatile enough to be adopted for the evaluation of different control strategies. At the same time, it represents a challenging testbed, exhibiting several issues that have to be faced in real-world applications.

Collective circular motion of multi-vehicle systems

This paper addresses a collective motion problem for a multi-agent system composed of nonholonomic vehicles. The aim of the vehicles is to achieve circular motion around a virtual reference beacon. A control law is proposed, which guarantees global asymptotic stability of the circular motion with a prescribed direction of rotation, in the case of a single vehicle. Equilibrium configurations of the multi-vehicle system are studied and sufficient conditions for their local stability are given, in terms of the control law design parameters. Practical issues related to sensory limitations are taken into account. The transient behavior of the multi-vehicle system is analyzed via numerical simulations.

EXPERIMENTAL ANALYSIS OF COLLECTIVE CIRCULAR MOTION FOR MULTI-VEHICLE SYSTEMS

This paper presents an experimental analysis of a recently proposed decentralized control strategy, for collective circular motion of a team of non-holonomic vehicles. Theoretical results ensuring global asymptotic stability in the single-vehicle case and local asymptotic stability in the multi-vehicle scenario, are validated on an experimental setup including the mobile robots Pioneer 3AT and Nomad XR4000. In addition, the role of the control law parameters is discussed and a design procedure is proposed.