We study a simple but compelling model of network of agents interacting via time-dependent communication links. The model finds application in a variety of fields including synchronization, swarming and distributed decision making. In the model, each agent updates his current state based upon the current information received from neighboring agents. Necessary and/or sufficient conditions for the convergence of the individual agents' states to a common value are presented, thereby extending recent results reported in the literature. The stability analysis is based upon a blend of graph-theoretic and system-theoretic tools with the notion of convexity playing a central role. The analysis is integrated within a formal framework of set-valued Lyapunov theory, which may be of independent interest. Among others, it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence, even for the simple models discussed in the present paper.

Stability of multiagent systems with time-dependent communication links

This paper reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles, and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations.

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An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination

This article reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, task assignment, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations.

An Overview of Recent Progress in the Study of Distributed Multi-agent Coordination

Brief paper: An internal model principle is necessary and sufficient for linear output synchronization

Brief paper: Synchronization in networks of identical linear systems

In this paper we address stabilization of a network of underactuated mechanical systems with unstable dynamics. The coordinating control law stabilizes the unstable dynamics with a term derived from the method of controlled Lagrangians and synchronizes the dynamics across the network with potential shaping designed to couple the mechanical systems. The coupled system is Lagrangian with symmetry, and energy methods are used to prove stability and coordinated behavior. Two cases of asymptotic stabilization are discussed; one yields convergence to synchronized motion staying on a constant momentum surface, and the other yields convergence to a relative equilibrium. We illustrate the results in the case of synchronization of $n$ carts, each balancing an inverted pendulum.

Stable Synchronization of Mechanical System Networks

We address stable synchronization of a network of rotating and translating rigid bodies in three-dimensional space. Motivated by applications that require coordinated spinning spacecraft or diving underwater vehicles, we prove control laws that stably couple and coordinate the dynamics of multiple rigid bodies. We design decentralized, energy shaping control laws for each individual rigid body that depend on the relative orientation and relative
position of its neighbors. Energy methods are used to prove stability of the coordinated multi-body dynamical system. To prove exponential stability, we break symmetry and consider a controlled dissipation term that requires
each individual to measure its own velocity. The control laws are illustrated in simulation for a network of spinning rigid bodies.

https://www.aimsciences.org/article/exportPdf?id=a06f531e-7980-40de-b337-280273723bcc

Stable synchronization of rigid body networks

We derive a nonlinear control law for stabilization of the Furuta pendulum system with the pendulum in the upright position and the rotating rigid link at rest at the origin. The control law is derived by first applying feedback that makes the Furuta pendulum look like a planar pendulum on a cart plus a gyroscopic force. The planar pendulum on a cart is an example of a class of mechanical systems which can be stabilized in full state space using the method of controlled Lagrangians. We consider this class of systems as our normal form and for the case of the Furuta pendulum, we add to the first transforming feedback law, the energy-shaping control law for the planar pendulum system. The resulting system looks like a mechanical system plus feedback-controlled dissipation and an external force that is quadratic in velocity. Using energy as the Lyapunov function we prove local exponential stability and demonstrate a large region of attraction.

A normal form for energy shaping: application to the Furuta pendulum

In this paper we present a stabilizing and coordinating control law for a network of spinning rigid bodies with unstable dynamics. The control law stabilizes each rigid body to spin about its unstable, intermediate axis while also aligning all of the spinning rigid bodies so that their orientations in inertial space are identical. The control law is derived using kinetic energy shaping for stabilization and potential shaping for coupling. The coupled system is Lagrangian with symmetry, and energy methods are used to prove stability and coordinated behavior.

Stabilization of a coordinated network of rotating rigid bodies

In this paper we present a coordinating control law for a network of mechanical systems with unstable dynamics. The control law is derived using the Method of Controlled Lagrangians together with potential shaping designed to couple the mechanical systems. The coupled system is Lagrangian with symmetry, and energy methods are used to prove stability and coordinated behavior. The class of mechanical systems we consider includes the planar inverted pendulum on a cart as well as the spherical inverted pendulum on a 2D cart. For these examples, the control law stabilizes each inverted pendulum and coordinates the relative motion of the carts.

Sujit Nair

Papers

Stable Synchronization of Mechanical System Networks

Stable synchronization of rigid body networks

A normal form for energy shaping: application to the Furuta pendulum

Stabilization of a coordinated network of rotating rigid bodies

Coordinated control of networked mechanical systems with unstable dynamics