Myoung-Chul Park

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.

Stability analysis on four agent tetrahedral formations

We consider a four agent tetrahedral formation of mobile agents in 3-dimensional Euclidean space. Each agent is required to maintain prescribed inter-agent distances from its neighbors so that they collectively form a desired formation shape, a task which is now called distance-based formation control. Under a common gradient-based control law, there exists an incorrect equilibrium set in which the agents do not achieve the desired formation shape. By investigating the linearized dynamics of the system, we prove that all incorrect equilibria are unstable, which results in that desired formation shape is almost globally asymptotically stable. Numerical simulation results are also included.

Distance-based formation control with a single moving leader

This paper proposes distance-based adaptive formation control laws for the leader-follower system. The developed controller makes all the agents maintain the formation group and move with a constant reference velocity in a plane. It is assumed that there are one leading and two following agents. The leading agent knows the reference velocity whereas the follower does not know the velocity of other agents. Thus, to move in a group, the controller for the follower estimates the reference velocity. An adaptive method is used in the estimation process. The stability and boundedness of the formation are proved by using Lyapunov stability analysis and Barbalats lemma. Simulations results are included to illustrate the validity of the developed theories.

Distributed stabilization control of rigid formations with prescribed orientation

Most rigid formation controllers reported in the literature aim to only stabilize a rigid formation shape, while the formation orientation is not controlled. This paper studies the problem of controlling rigid formations with prescribed orientations in both 2-D and 3-D spaces. The proposed controllers involve the commonly-used gradient descent control for shape stabilization, and an additional term to control the directions of certain relative position vectors associated with certain chosen agents. In this control framework, we show the minimal number of agents which should have knowledge of a global coordinate system (2 agents for a 2-D rigid formation and 3 agents for a 3-D rigid formation), while all other agents do not require any global coordinate knowledge or any coordinate frame alignment to implement the proposed control. The exponential convergence to the desired rigid shape and formation orientation is also proved. Typical simulation examples are shown to support the analysis and performance of the proposed formation controllers.

Modified gradient control for acyclic minimally persistent formations to escape from collinear position

In this paper, we consider formation shape control of moving agents in the plane, which has been examined for several years. We use distance-based control approach to achieve desired formations by controlling the relative distances between agents. Although there are various control schemes in the literature to control the moving agents, gradient control shows us a quite systematic way. However, one of the main problems in the gradient control happens when the agents are in an invariant subset under the collinearity, namely the agents cannot escape from the invariant subset under the gradient control. We propose a modification of the gradient control to solve the problem faced in the preliminary literature. Using the proposed control laws, we examine the convergence of distance errors to confirm that we are able to achieve the desired formations. Simulations supporting our results are provided.

Finite-time convergence control for acyclic persistent formations

In this paper, we propose a distance-based control law for acyclic persistent formations of mobile agents. The proposed normalized gradient law, which can be implemented distributively by using local measurements, allows agents to achieve their desired formation shape specified by inter-agent distance constraints in finite time, with local but not global con-vergence. We show some local finite-time convergence properties including an upper bound for the convergence time. Further the existence of attractive incorrect equilibrium formations is demonstrated. Simulation results are provided for illustration.

Control of undirected four-agent formations in 3-dimensional space

We investigate a four-agent tetrahedral formation consisting of mobile autonomous agents in 3-dimensional space. The formation shape is required to be maintained only by the given inter-agent distance constraints. We use the gradient control to maneuver the agents to achieve the desired inter-agent distances. We provide analysis on the global behavior of the agents to explain whether or not the agents converge to the desired equilibrium set. Numerical simulation results are also included.

Distance-based control of formations with orientation control

In this paper, we deal with formation stabilization of a group of mobile agents with orientation control. The proposed method is to combine usual distance-based control with displacement-based control so that the shape of the formation is dominantly controlled by distance-based control, and the orientation of the whole formation is forced to converge to the desired orientation by the additional displacement control input. We assume that the network topology is represented by an undirected graph and that the motion of each agent is simplified to a single-integrator model. We provide stability analysis for the desired formation shape, and four-agent systems are explored to understand asymptotic convergence of the agents. Simulation results are also included to verify our results.

Control of inter-agent distances in cyclic polygon formations

This paper considers n-agent cyclic polygon formations of mobile autonomous agents in the plane. The aim of each agent is to maintain a desired distance from its neighbor. Since the formation graph is directed, only one agent is responsible for maintaining each distance. The control law for each agent is designed in distributive manner. Hence, it utilizes only local information. We use gradient-like control and Lyapunov-based stability analysis. Since there exist invariant subsets which include undesirable equilibrium state, the inter-agent distances are not globally stable under the given control law. However, once the initial locations of the agents are not inside the subsets, the agents do not approach them.

Distance-based Control of Kn Formations in General Space with Almost Global Convergence

In this paper, we propose a distance-based formation control strategy for a group of mobile agents to achieve almost global convergence to a target formation shape provided that the formation is represented by a complete graph, and each agent is governed by a single-integrator model. The fundamental idea of achieving almost global convergence is to use a virtual formation of which the dimension is augmented with some virtual coordinates. We define a cost function associated with the virtual formation and apply the gradient-descent algorithm to the cost function so that the function has a global minimum at the target formation shape. We show that all agents finally achieve the target formation shape for almost all initial conditions under the proposed control law.