Kwang-Kyo Oh

A survey of multi-agent formation control

We present a survey of formation control of multi-agent systems. Focusing on the sensing capability and the interaction topology of agents, we categorize the existing results into position-, displacement-, and distance-based control. We then summarize problem formulations, discuss distinctions, and review recent results of the formation control schemes. Further we review some other results that do not fit into the categorization.

Formation control of mobile agents based on inter-agent distance dynamics

We propose a novel formation control strategy based on inter-agent distances for single-integrator modeled agents in the plane. Attempting to directly control the inter-agent distances, we derive a control law from the distance dynamics. The proposed control law achieves the local asymptotic stability of infinitesimally rigid formations. Triangular infinitesimally rigid formations are globally asymptotically stable under the proposed control law, with all squared distance errors exponentially and monotonically converging to zero. As an extension of existing results, the stability analysis in this paper reveals that any control laws related with the gradient law by multiplication of a positive matrix ensure the local asymptotic stability of infinitesimally rigid formations.

Formation Control and Network Localization via Orientation Alignment

We propose a formation control strategy based on inter-agent displacements for single-integrator modeled agents in the plane. Since the orientations of the local reference frames of the agents are not aligned with each other due to the absence of a common sense of orientation, the proposed strategy consists of an orientation alignment law and a formation control law. Under the proposed strategy, if the interaction graph is uniformly connected and all the initial orientation angles belong to an interval with length less than π, the orientations are exponentially aligned and the formation exponentially converges to the desired formation. We also show that the proposed strategy can be utilized for network localization as a dual problem.

Stability and Stabilization of Fractional-Order Linear Systems Subject to Input Saturation

In this technical note, we provide a method for the asymptotic stabilization of fractional-order linear systems subject to input saturation. Gronwall-Bellman lemma and sector bounded condition of the saturation function are exploited for stability analysis and stabilization of such systems. Based on the proposed stability condition, we provide a bilinear matrix inequality for stability test and an algorithm for estimation of the stable region. Further, we provide an algorithm for state-feedback controller design that maximizes the estimated stable region.

Formation Control of Mobile Agents Based on Distributed Position Estimation

We propose a formation control strategy based on distributed position estimation for single-integrator modeled agents by using relative position measurements. Under the proposed strategy, the estimated and the actual formations globally exponentially converge to the actual and the desired formations, respectively, up to translation, if and only if the interaction graph for the agents has a spanning tree. A sufficient condition is provided for the case that the edge weights of the interaction graph are time-varying. Further, the proposed strategy is applied to formation control of unicycle-like agents.

Distance-based control of cycle-free persistent formations

In this paper, we study distance-based control of cycle-free persistent formations of single-integrator modeled agents in the plane. First, we propose a sequential control law consisting of algebraic calculations and primitive motions for agent groups having cycle-free persistent formations. Second, we prove the local asymptotic stability of cycle-free persistent formations under the well-known gradient law, which can be interpreted as a simultaneous version of the proposed sequential law, based on input-to-state stability. Furthermore, we show that if the leader-agent of a cycle-free persistent formation moves sufficiently slowly, then the formation of the group remains in the neighborhood of the desired formation.

A survey of formation of mobile agents

This paper presents a survey of formation of mobile agents, considering the significant interest in the topic. It is shown that formation problems consist of two sub-problems, i.e. the assignment of the local goals derived from the overall goal to agents and the stabilization of agents to achieve the local goals. Displacement-based and distance-based approaches are summarized and how two sub-problems are addressed in each approach is discussed. Future works in distance-based approach are given.

Disturbance Attenuation in a Consensus Network of Identical Linear Systems: An

We consider two problems related to disturbance attenuation in undirected consensus networks of identical linear systems subject to exogenous disturbances: 1) network interconnection design and 2) design of distributed and decentralized controllers. We use the H∞ norm of the transfer function from the disturbance vector to the disagreement vector of the network as the performance metric for disturbance attenuation. We show that the disturbance attenuation performance is enhanced by maximizing the second smallest eigenvalue of the graph Laplacian under a certain condition, which can be checked using a linear matrix inequality. For the case of a consensus network with fixed interconnection weights, e.g., as the result of physical constraints, we provide algorithms for the design of both decentralized and distributed controllers that ensure a prescribed disturbance attenuation performance.

{\cal H}_{\infty }

In this paper, we propose a triangular formation control law based on inter-agent distance information for a group of three single-integrator modeled agents on the plane. Although most of existing distance-based formation control laws have been designed by using the gradient of artificial potential functions, the proposed control law is derived from the time derivative of the Euclidean distance matrix associated with the realization of the agent group. Consequently, if the initial and desired formations are not collinear and the information graph of the group is complete, then the desired formation of the group is globally asymptotically stable with all squared inter-agent distance errors exponentially converging to zero. Furthermore, the proposed control law has a coordination property in the sense that the dynamics of all inter-agent distances are fully decoupled. Simulation results support the effectiveness of the proposed control law, demonstrating the coordination property.

Approach

This paper addresses possible benefits and potential utilities of Euclidean distance matrix (EDM) in multi-agent formation systems. Using interval concept, this paper considers range variation, measurement uncertainties, and possible disturbances in the distances; and then using this result, we address a realization problem of partial interval matrices, a rigidity problem of corresponding graph, and a unique realization of partial interval distance matrices. This paper also outlines some specific applications of Euclidean distance matrix in command coordination. The central contribution of this paper is to propose of using Euclidean distance matrix in generating a command for multi-agent coordination.