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This article discusses cooperative stabilization control of rigid formations via an event-based approach. We first design a centralized event-based formation control system, in which a central event controller determines the next triggering time and broadcasts the event signal to all the agents for control input update. We then build on this approach to propose a distributed event control strategy, in which each agent can use its local event trigger and local information to update the control input at its own event time. For both cases, the triggering condition, event function, and triggering behavior are discussed in detail, and the exponential convergence of the event-based formation system is guaranteed. [ABSTRACT FROM AUTHOR]

This paper proposes three different distributed event-triggered control algorithms to achieve leader–follower consensus for a network of Euler–Lagrange agents. We first propose two model-independent algorithms for a subclass of Euler–Lagrange agents without the vector of gravitational potential forces. By model-independent, we mean that each agent can execute its algorithm with no knowledge of the agent self-dynamics. A variable-gain algorithm is employed when the sensing graph is undirected; algorithm parameters are selected in a fully distributed manner with much greater flexibility compared to all previous work studying event-triggered consensus problems. When the sensing graph is directed, a constant-gain algorithm is employed. The control gains must be centrally designed to exceed several lower bounding inequalities, which require limited knowledge of bounds on the matrices describing the agent dynamics, bounds on network topology information, and bounds on the initial conditions. When the Euler–Lagrange agents have dynamics that include the vector of gravitational potential forces, an adaptive algorithm is proposed. This requires more information about the agent dynamics but allows for the estimation of uncertain parameters associated with the agent self-dynamics. For each algorithm, a trigger function is proposed to govern the event update times. The controller is only updated at each event, which ensures that the control input is piecewise constant and thus saves energy resources. We analyze each controller and trigger function to exclude Zeno behavior. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we focus on the control of multiagent formations with hybrid communication topology through a distance‐based approach. By saying hybrid topology, we mean that the communication topology contains both undirected and directed links, or the underlying graph of the formation contains both undirected and directed edges. A new type of graph, ie, hybrid graph, is introduced. We discuss the persistence of hybrid graphs and present the persistence verification strategy for hybrid graphs. It is proved that all the minimally persistent hybrid graphs can be obtained from persistent directed graphs by the operation of edge transformation. As the main result, it is shown that multiagent formations modeled by acyclic persistent hybrid graphs can be stabilized locally under distance‐based controllers. [ABSTRACT FROM AUTHOR]

Self-localization and formation control tasks are considered when each agent in a multiagent formation observes its neighbors but does not communicate. Each agent is restricted to a predefined motion type on a 2-D plane and collects bearing-only measurements over a time interval to localize neighboring agents. The localization process is used by a three agent formation to achieve velocity consensus combined with formation shape control. Simulations are provided and noisy bearing measurements are investigated. [ABSTRACT FROM PUBLISHER]

This paper investigates the group consensus phenomenon for multiple interacting clusters of double-integrator agents in the presence of both cooperative and competitive inter-cluster couplings under two different frameworks, viz., the framework that all agents share the same position and velocity interaction topology and the framework that the position and velocity topologies are modeled by totally independent graphs. Both the case without leaders and the leader-following (meaning there is a single leader for each cluster of agents) case are systematically investigated. Different systems models are systematically analyzed accordingly using various different techniques. Theoretical analysis shows that for most cases, there holds a consistent structural result that group consensus can be achieved if the underlying topology for each cluster of agents satisfies certain connectivity assumptions and further, the intra-cluster couplings are sufficiently strong. Some lower bounds for such strengths are explicitly specified as well. [ABSTRACT FROM AUTHOR]

Multi-agent formations have been recently the subject of many studies. An important operational challenge, largely unaddressed in the literature, is to ensure that functionality of the formation is retained should agents be lost through misadventure, mission reassignment, and so on. In the context of sensor networks, it is also important to allow for the loss of multiple sensors as the low quality of sensor hardware, common unattended implementations, and so on makes it a common issue. In this paper, we address these issues by proposing information structures that are tolerant to the loss of multiple agents. Using graph theory (and more specifically rigidity theory), we characterize several properties of such formations/networks in a unified framework: We characterize the k-vertex rigidity property of the underling graph of such formations. This is performed by deriving a set of useful conditions that can form a guideline for designing agent-loss-tolerant formations. We elaborate the study by characterizing robust formations with the optimal number of control links. We also propose a set of operations preserving the tolerance to multiple agent losses in such formations. These operations provide flexibility in designing the formations in terms of several designing parameters (e.g., geometry, diameter, and max degree). Especially in the case of formations, the ability to handle controller adjustments in a distributed way is important, and the paper addresses this issue for a number of the robustness problems considered. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates the semiglobal synchronization problem for a group of agents with input saturation under directed interaction topology, where each agent is modeled as a generic linear system rather than the single-integrator or double-integrator dynamics. The main result is the construction of a feedback coupling gain that achieves semiglobal synchronization if all the agents have identically saturated linear dynamics, which can be of any order. It is shown that the coupling gain obtained via parametric Lyapunov equations can semiglobally synchronize any directed network provided that the interaction topology has a directed spanning tree. Furthermore, due to the use of parametric Lyapunov equations, a convergence rate is analytically obtained. Finally, a simulation example is provided to demonstrate the effectiveness and advantages of our theoretical findings. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the consensus control of generic linear multi-agent systems (MASs) under directed dynamic topology. Nonnegative matrix theory, in particular the product properties of infinite row-stochastic matrices, which are widely used for multiple integrator agents, is explored to deal with the convergence analysis of generic linear MASs. It is finally shown that the exponential consensus can be reached under very relaxed conditions, i.e., the directed interaction topology is only required to be repeatedly jointly rooted and the exponentially unstable mode of each individual system is weak enough. Moreover, a least convergence rate and a bound for the unstable mode of the individual agent system, both of which are independent of the switching mode, can be explicitly specified. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the synchronization problem for a group of agents with identical linear dynamics subject to input saturation. Two classes of linear systems, asymptotically null controllable with bounded control (ANCBC) systems and double-integrator systems, are studied. For ANCBC systems, it is shown that a linear protocol with the control gain obtained via parametric Lyapunov equations can semiglobally synchronize the undirected topology provided that its augmented directed topology has a spanning tree. For a special case of ANCBC, the double-integrator systems, it is established that if the augmented directed topology has a spanning tree, then in the presence of input saturation, using linear protocols with positive control gains can achieve global synchronization. Two numerical examples are given to demonstrate the effectiveness of the theoretical results. [Copyright &y& Elsevier]

Abstract: This paper investigates the cluster consensus control for generic linear multi-agent systems (MASs) under directed interaction topology via distributed feedback controller. Focus of this paper is particularly on addressing the following problem which is of both theoretical and practical interests but have not been considered in the existing literature: under what kind of interaction among the clusters can the cluster consensus control be achieved regardless of the magnitudes of the coupling strengths among the agents? Directed acyclic interaction topology among the clusters is proved to have this property. As opposed to the algebraic conditions provided in the existing literature, conditions for guaranteeing the cluster consensus control in this paper are presented in terms of purely the graphic topology conditions and thus are very easy to be verified. [Copyright &y& Elsevier]

SUMMARY This paper considers a novel problem of how to choose an appropriate geometry for a group of agents with only shape constraints but with a flexible scale. Instead of assigning the formation system with a specific geometry, here, the desired geometry is only characterized by its shape without any location, rotation, and most importantly, scale constraints. Optimal rigid transformation between two different geometries is discussed with especial focus on the scaling operation, and the cooperative performance of the system is evaluated by what we call the geometries' degrees of similarity with respect to the desired shape during the entire convergence process. The design of the scale when measuring the degree of similarity is discussed from constant value and time-varying function perspectives, respectively. Fixed structured nonlinear control laws that are functions on the scale and the relative positions of agents are developed to guarantee the exponential convergence of the system to the assigned shape. Our research is originated from a three-agent formation system and is further extended to multiple ( n > 3) agents by defining a triangular complement graph. Simulations demonstrate that a formation system with the time-varying scale function outperforms the one with an arbitrary constant scale, and the relationship between underlying topology and the system performance is further discussed according to the simulation observations. Moveover, the control scheme is applied to bearing-only sensor-target localization to show its application potentials. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the asynchronous consensus problem of discrete-time second-order multi-agent system under dynamically changing communication topology, in which the asynchrony means that each agent detects the neighbors' state information to update its state information by its own clock. It is not assumed that the agents' clocks are synchronized. Nor is it assumed that the time sequence over which each agent update its state information is evenly spaced. By using tools from graph theory and nonnegative matrix theory, particularly the product properties of row-stochastic matrices from an infinite set, we finally show that essentially the same result as that for the synchronous discrete-time system holds in the face of asynchronous setting. This generalizes the existing result to a very general case. [ABSTRACT FROM PUBLISHER]

Abstract: This paper proposes algorithms to coordinate a formation of mobile agents when the agents are not able to measure the relative positions of their neighbors, but only the distances to their respective neighbors. In this sense, less information is available to agents than is normally assumed in formation stabilization or station keeping problems. To control the shape of the formation, the solution advanced in the paper involves subsets of non-neighbor agents cyclically localizing the relative positions of their respective neighbor agents while these are held stationary, and then moving to reduce the value of a cost function which is nonnegative and assumes the zero value precisely when the formation has correct distances. The movement schedule is obtained by a novel vertex-coloring algorithm whose computation time is linear in the number of agents when implemented on the graphs of minimally rigid formations. Since in some formations, it may be that an agent is never allowed to be stationary (e.g. it is a fixed-wing aircraft), or because formations may be required to move as a whole in a certain direction, the results are extended to allow for cyclic localization of agents in this case. The tool used is the Cayley–Menger determinant. [Copyright &y& Elsevier]

In this paper we discuss and discover several conservation and associated decay laws in distributed coordination control systems, in particular in formation shape control systems. Specifically, we reveal conservations of linear momentum and angular momentum for gradient-based multi-agent formation systems modelled by single integrators, and show several corresponding conservation/decay laws for double-integrator formation stabilization systems and double-integrator flocking systems, respectively. By exploiting translation and rotation symmetry properties and insights from Noether’s theorem, we further establish a multi-agent version of the relation between symmetry and conservation laws for gradient-based coordination systems derived from general potential functions, from which we generalize the conservation/decay laws to more general networked coordination control systems. The results hold in ambient spaces of any dimensions, and we focus on the 2-D and 3-D cases due to their natural interpretation as positions of agents. [ABSTRACT FROM AUTHOR]

This brief presents a new distributed scheme to solve the consensus problem for a group of agents if neither their absolute states nor inter-agent relative states are available. The new scheme considers a random partition of agents into two subgroups at each step and then uses the relative group representative state as feedback information for the consensus purpose. It is then shown that almost sure consensus can be achieved under the proposed scheme in both discrete time and continuous time. For the discrete time case, almost sure consensus is achieved if and only if the weighting parameter for state update is greater than one. For the continuous time case, almost sure consensus is realized when the weighting parameter is positive. Moreover, it is shown that if a uniform probability is considered for group selection, then the group of agents can reach average consensus in mean. [ABSTRACT FROM AUTHOR]