Achieving a desired collective centroid by a formation of agents moving in a controllable force field

Circular Formation Control of Multiple Unicycle-Type Agents With Nonidentical Constant Speeds

Abstract: This paper discusses the problem of controlling formation shapes for a group of nonholonomic unicycle-type agents with constant speeds. The control input is designed to steer their orientations and the aim is to achieve a desired formation configuration for all the agents subject to constant-speed constraints. The circular motion center is adopted as a virtual position for each agent to define the desired formation shape. We consider several different formation design approaches based on different formation specifications under different interaction graphs. In particular, two different formation design approaches, namely, a displacement-based approach and a distance-based approach, are discussed in detail to coordinate constant-speed agents in achieving a desired formation shape with stable circular motions via limited interactions. The communication and measurement requirements for each approach are also discussed. Furthermore, we propose a combined controller to stabilize a formation shape and synchronize the heading of each agent simultaneously. The effectiveness of the proposed formation control schemes is validated by both numerical simulations and real experiments with actual unmanned fixed-wing aircraft.

Control of Many Agents Using Few Instructions

Abstract: This paper considers the problem of controlling a group of agents under the constraint that every agent must be given the same control input This problem is relevant for the control of mobile micro-robots that all receive the same power and control signals through an underlying substrate Despite this restriction, several examples in simulation demonstrate that it is possible to get a group of micro-robots to perform useful tasks All of these tasks are derived by thinking about the relationships between robots, rather than about their individual states

Moving Agents in Formation in Congested Environments

Abstract: In this paper, we formalize and study the Moving Agents in Formation (MAiF) problem, that combines the tasks of finding short collision-free paths for multiple agents and keeping them in close adherence to a desired formation Previous work includes controller-based algorithms, swarm-based algorithms, and potential-field-based algorithms They usually focus on only one or the other of these tasks, solve the problem greedily without systematic search, and thus generate costly solutions or even fail to find solutions in congested environment In this paper, we develop a two-phase search algorithm, called SWARM-MAPF, whose first phase is inspired by swarm-based algorithms (in open regions) and whose second phase is inspired by multi-agent path-finding (MAPF) algorithms (in congested regions) In the first phase, SWARM-MAPF selects a leader among the agents and finds a path for it that is sufficiently far away from the obstacles so that the other agents can preserve the desired formation around it It also identifies the critical segments of the leader's path where the other agents cannot preserve the desired formation and the refinement of which has thus to be delegated to the second phase In the second phase, SWARM-MAPF refines these segments Theoretically, we prove that SWARM-MAPF is complete Empirically, we show that SWARM-MAPF scales well and is able to find close-to-optimal solutions

Robust stabilization of balanced and splay formations with heterogeneous controller gains

Abstract: This paper analyses collective motion of multi-vehicle systems in balanced or splay formation when the vehicles are equipped with heterogeneous controller gains. Balancing refers to a situation in which the positional centroid of the vehicles is stationary. The splay formation is a special case of balancing in which the vehicles are spatially distributed with equal angular separation between them. The paper proposes strategies to achieve such balanced and splay formations about a desired centroid location while allowing the vehicles to move either along straight line paths or on individual circular orbits. Feedback control laws that can tolerate heterogeneity in the controller gains, which may be caused by imperfect implementation, are derived and analyzed. It is shown that drastic failures leading to controller gains becoming zero for almost half of the vehicles in the group can be tolerated and balanced formation can still be achieved. On the other hand, splay formation can still be achieved if the controller gain is zero for at most one vehicle. Simulation examples are given to illustrate the theoretical findings.

A heterogeneous control gain approach to achieve a desired collective centroid by a formation of agents

Abstract: This paper proposes a heterogeneous gains based controller design methodology to stabilize a particular type of collective motion in a multi-agent system where the heading angles of the agents are in balanced formation. Balancing refers to the situation in which the movement of agents causes the position of their centroid to become stationary. Our interest, in this paper, is to achieve balanced formation about a desired location of the centroid while allowing the agents to move either along straight line paths or around individual circular orbits. For this purpose, we derive feedback control laws that operate with heterogeneous control gains, and are more practical compared to the homogeneous gains based controls existing in the literature. We also show that if the heterogeneous control gains are zero for almost half of the agents of the group, it is possible to achieve balanced formation at an additional advantage of reduced computational complexity of the proposed control law. Simulations are given to illustrate the theoretical findings.

From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators

Abstract: The Kuramoto model describes a large population of coupled limit-cycle oscillators whose natural frequencies are drawn from some prescribed distribution. If the coupling strength exceeds a certain threshold, the system exhibits a phase transition: some of the oscillators spontaneously synchronize, while others remain incoherent. The mathematical analysis of this bifurcation has proved both problematic and fascinating. We review 25 years of research on the Kuramoto model, highlighting the false turns as well as the successes, but mainly following the trail leading from Kuramoto’s work to Crawford’s recent contributions. It is a lovely winding road, with excursions through mathematical biology, statistical physics, kinetic theory, bifurcation theory, and plasma physics. © 2000 Elsevier Science B.V. All rights reserved.

Distributed Consensus in Multi-vehicle Cooperative Control

Abstract: The coordinated use of autonomous vehicles has an abundance of potential applications from the domestic to the hazardously toxic. Frequently the communications necessary for the productive interplay of such vehicles may be subject to limitations in range, bandwidth, noise and other causes of unreliability. Information consensus guarantees that vehicles sharing information over a network topology have a consistent view of information critical to the coordination task. Assuming only neighbor-neighbor interaction between vehicles, Distributed Consensus in Multi-vehicle Cooperative Control develops distributed consensus strategies designed to ensure that the information states of all vehicles in a network converge to a common value. This approach strengthens the team, minimizing power consumption and the deleterious effects of range and other restrictions. The monograph is divided into six parts covering introductory, theoretical and experimental material and featuring: an overview of the use of consensus algorithms in cooperative control; consensus algorithms in single- and double-integrator dynamical systems; consensus algorithms for rigid-body attitude dynamics; rendezvous and axial alignment, formation control, deep-space formation flying, fire monitoring and surveillance. Notation drawn from graph and matrix theory and background material on linear and nonlinear system theory are enumerated in six appendices. The authors maintain a website at which can be found a sample simulation and experimental video material associated with experiments in several chapters of this book. Academic control systems researchers and their counterparts in government laboratories and robotics- and aerospace-related industries will find the ideas presented in Distributed Consensus in Multi-vehicle Cooperative Control of great interest. This text will also serve as a valuable support and reference for graduate courses in robotics, and linear and nonlinear control systems.

Collective Motion, Sensor Networks, and Ocean Sampling

Abstract: This paper addresses the design of mobile sensor networks for optimal data collection. The development is strongly motivated by the application to adaptive ocean sampling for an autonomous ocean observing and prediction system. A performance metric, used to derive optimal paths for the network of mobile sensors, defines the optimal data set as one which minimizes error in a model estimate of the sampled field. Feedback control laws are presented that stably coordinate sensors on structured tracks that have been optimized over a minimal set of parameters. Optimal, closed-loop solutions are computed in a number of low-dimensional cases to illustrate the methodology. Robustness of the performance to the influence of a steady flow field on relatively slow-moving mobile sensors is also explored

Elementary linear algebra

Abstract: The hallmark of this text has been the authors' clear, careful, and concise presentation of linear algebra so that students can fully understand how the mathematics works. The text balances theory with examples, applications, and geometric intuition.Learning Tools CD-ROM will be automatically packaged free with every new text purchased from Houghton Mifflin.Section 3.4, now named Introduction to Eigenvalues, has been broken into two separate sections to provide more emphasis on the early introduction of eigenvalues. The new Section 3.5, Applications of Determinants, covers the Adjoint of a Matrix; Cramer' s Rule; and the Area, Volume, and Equations of Lines and Planes.All real data in exercises and examples have been updated to reflect current statistics and information.This edition features more Writing Exercises to reinforce critical-thinking skills and additional multi-part True/False Questions in the end-of-section and chapter review exercise sets to encourage students to think about mathematics from different perspectives.Additional exercises involving larger matrices have been added to the exercise sets where appropriate. These exercises will be linked to the data sets found on the web site and the Learning Tools CD-ROM.Eduspace is Houghton Mifflin' s online learning tool. Powered by Blackboard, Eduspace is a customizable, powerful and interactive platform that provides instructors with text-specific online courses and content. The Larson Elementary Linear Algebra course features algorithmic exercises and test bank content in question pools.