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This monograph presents new algorithms for formation control of multi-agent systems (MAS) based on principles of continuum mechanics. Beginning with an overview of traditional methods, the author then introduces an innovative new approach whereby agents of an MAS are considered as particles in a continuum evolving in ℝn whose desired configuration is required to satisfy an admissible deformation function. The necessary theory and its validation on a mobile-agent-based swarm test bed are considered for two primary tasks: homogeneous transformation of the MAS and deployment of a random distribution of agents on a desired configuration. The framework for this model is based on homogeneous transformations for the evolution of an MAS under no inter-agent communication, local inter-agent communication, and intelligent perception by agents. Different communication protocols for MAS evolution, the robustness of tracking of a desired motion by an MAS evolving in ℝn, and the effect of communication delays in an MAS evolving under consensus algorithms or homogeneous maps are also explored.
Featuring appendices which introduce the requisite concepts from continuum kinematics and graph theory, this monograph will provide advanced graduate students and researchers with the necessary background to understand and apply the methods presented.

Inhaltsverzeichnis

Chapter 1. Introduction

Abstract
Formation control has received considerable attentions during the past two decades. Some applications like formation flight, transportation engineering, air traffic control, gaming, maneuvering in a hazardous environment, and environmental sampling have been listed in literature for formation control. Formation control in a multi-agent system (MAS) has many advantages [91]. For example, keeping formation increases robustness and efficiency of a system reduces the cost of a system, and results in better fault tolerance and capability of reconfiguration [6, 8, 9, 19, 140].
Hossein Rastgoftar

Chapter 2. Homogeneous Deformation without Interagent Communication

Abstract
In this chapter, basics of MAS evolution as continuum deformation are presented, where an MAS is treated as particles of a continuum deforming under a homogeneous transformation. It is shown how a homogeneous deformation is acquired by the agents via no interagent communication. In this regard, agents’ desired positions, defined by a homogeneous deformation in $$\mathbb{R}^{n}$$, are uniquely specified by the trajectories chosen by n + 1 leaders. Followers acquire the desired homogeneous mapping only by knowing leaders’ positions. Evolution of the followers with nonlinear constrained dynamics under a homogeneous transformation is investigated in this chapter. Homogeneous transformation of an MAS containing agents with linear dynamics is also studied.
Hossein Rastgoftar

Chapter 3. Homogeneous Deformation of Multi-Agent Systems Communication

Abstract
In this chapter, it is shown how a multi-agent system (MAS) can acquire a desired homogeneous deformation in $$\mathbb{R}^{n}$$ (prescribed by n + 1 leaders) through local communication. For this purpose, two communication protocols are developed. The first protocol, that is called minimum communication, allows each follower to communicate only with n + 1 local agents. Under this protocol, communication weights
Hossein Rastgoftar

Chapter 4. Higher Order Dynamics for MAS Evolution as Continuum Deformation

Abstract
In this chapter, it is demonstrated how followers can apply higher order dynamics to acquire a desired homogeneous deformation under local communication. First, evolution of followers using a second order dynamics with a nonlinear control gain g is considered. Then, asymptotic tracking of desired position issued by a homogeneous deformation is demonstrated, while followers applying higher order dynamics only communicate with their in-neighbor agents for updating their positions. Finally, evolution of followers in presence of heterogeneous communication delay is considered and upper bounds for followers’ allowable communication delays are determined by using eigen-analysis.
Hossein Rastgoftar

Chapter 5. Alignment as Biological Inspiration for Control of Multi-Agent Systems

Abstract
In this chapter, a framework for the evolution of an MAS under alignment strategy is developed. This novel idea comes from the hypothesis that natural biological swarms do not perform peer-to-peer communication to sustain the group behavior as a collective. The group evolution is more likely based on what each individual agent perceives of its nearby agent’s behavior to control its own action. Most available engineering swarms rely on local interaction, where an individual agent requires precise state information of its neighboring agents to evolve. Here, agents of an MAS are considered as particles of a continuum (deformable Body) transforming under a homogeneous mapping. Using the key property of homogeneous transformation that two crossing straight lines in an initial configuration translate as two different crossing straight lines, agents can evolve collectively without peer-to-peer communication.
Hossein Rastgoftar

Chapter 6. Deployment of a Multi-Agent System on a Desired Formation

Abstract
In this chapter, a decentralized control approach for deployment of an arbitrary distribution of a multi-agent system (MAS) on a desired formation in $$\mathbb{R}^{n}$$ (n = 1, 2, 3) is proposed, where avoidance of interagent collision is addressed. For this purpose, the motion of an MAS in $$\mathbb{R}^{n}$$ is decoupled into n separate 1-D motion problems. For evolution of the q th (q = 1, 2, 3) components of the agents’ positions, two q-leaders are considered, where they guide the q th components of the MAS evolution. The remaining agents are considered as q-followers, where they update the q th components of their positions through local communication with the communication weights that are consistent with the q th components of the agents’ positions in the final configuration.
Hossein Rastgoftar

Chapter 7. Continuum Deformation of a Multi-Agent System over Nonlinear Surfaces

Abstract
In this chapter, it is shown how a multi-agent system (MAS) consisting of N agents can move collectively on a nonlinear surface through local communication. Collective motion of the MAS is treated as continuum deformation, therefore, interagent distances can be largely expanded or contracted. For collective motion on a p-D (p ≤ 3) nonlinear surface, leader-follower approach is applied and continuum deformation is prescribed by p + 1 leaders that move independently. Each follower uses a first-order discrete-time dynamics and communicate with p + 1 in-neighbor agents to acquire desired position specified by the continuum deformation. Similar to collective motion on linear surfaces, followers’ communication weights are consistent with agents’ initial positions. Examples of collective motion on an arbitrary curve as well as a 2-D nonlinear surface in a 3-D motion space are also provided.
Hossein Rastgoftar

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