Formations of multi-agent systems, such as satellites and aircraft, require that individual agents satisfy their kinematic equations while constantly maintaining inter-agent constraints. In this paper, we develop a systematic framework for studying formations of multiagent systems. In particular, we consider undirected formations for centralized formations and directed formations for decentralized formations. In each case, we determine differential geometric conditions that guarantee formation feasibility given the individual agent kinematics. Our framework also enables us to ex- tract a smaller control system that describes the formation kinematics while maintaining all formation con- straints.

Abstract—The paper investigates the stability properties of mobile agent formations which are based on leader-following. We derive nonlinear gain estimates that capture how leader behavior affects the interconnection errors observed in the formation. Leader to formation stability (LFS) gains quantify error ampli£cation, relate interconnection topology to stability and performance and offer safety bounds for different formation topologies. Analysis based on the LFS gains provides insight to error propagation and suggests ways to improve the safety, robustness and performance characteristics of a formation. I.

This paper presents the coupled dynamics approach to executing Elementary Formation Maneuvers (EFM) for Hilare-type mobile robots. The concept of an EFM is presented. It is then shown that each of these EFMs posses a common mathematical structure and thus may be executed by the same type of robot control. We present three different EFM controls in this paper. The first puts feedback on the relative motion and the global motion of each robot. The second control adds inter-robot damping. And the third control uses saturated inputs on the relative motion and the global motion of each robot. We present simulation and hardware results for each of these controls. I. Introduction Cooperative robots can often be used to perform tasks that are too difficult for a single robot to perform alone. For example a group of robots can be used for moving large awkward objects [1], [2] or for moving a large number of objects [3]. In addition groups of robots can be used for terrain model acquisition [3]...

Keywords: We describe a framework for controlling and coordinating a group of nonholonomic mobile robots equipped with range sensors, with applications ranging from scouting and reconnaissance, to search and rescue and manipulation tasks. We derive control algorithms that allow the robots to control their position and orientation with respect to neighboring robots or obstacles in the environment. We then outline a coordination protocol that automatically switches between the control laws to maintain a specified formation. Two simple trajectory generators are derived from potential field theory. The first allows each robot to plan its reference trajectory based on the information available to it. The second scheme requires sharing of information and enables a rigid group formation. Numerical simulations illustrate the application of these ideas and demonstrate the scalability of the proposed framework for a large group of robots.

Formation stability is now analyzed under a new prism using input-to-state stability. Formation ISS relates leader input to internal state of the formation and characterizes the way this input affects stability performance. Compared to other notions of stability for interconnected systems, formation ISS does not require attenuation of errors as they propagate, but instead quantifies the amplification and provides worst case bounds. The control interconnections that give rise to the formation are represented by a graph. The formation graphs considered are built from a small number of primitive graphs, the stability properties of which are used to reason about the composite. For the case of linear dynamics, a recursive expression allows the calculation of the bounds using the graph theoretic representation of the formation via the adjacency matrix. Illustrative examples demonstrate how formation ISS can be used as an analysis and a design tool. 1

Abstract — The coordinated consensus problem can be seen as one of the simplest instance of coordinated control. This problem has been widely investigated in the recent years. It is clear that the information exchange must have an important influence on the performance of the control strategy. In this contribution the information flow is modelled by a graph representing the information transmission from one vehicle to another one. In this graph there are two kinds of edges. One kind of edges represents exact data transmission. This is very expensive with respect to communication rate required. A second kind of edges represents transmission logarithmic quantized data. On the contrary this is very cheap with respect to communication rate required. The final goal of the present paper is to determine how the degree of connection of this graph influences the performance of the coordinated control system. I.

We present a decentralized, behavior-based approach to assembling and maintaining robot formations. Our approach dynamically grows formations from single robots into line segments and ultimately larger and more complex formations. Formation growth

A new type of stability of leader follower formations is defined, based on input-to-state stability (ISS) properties of cascade interconnections. Formation ISS links leader input to internal state of the formation and characterizes the way this input affects performance. The effect of feedforward and feedback inter-agent communication is then investigated in this framework and it is indicated how the structure of interconnections and the amount of available information can affect stability performance.

In this paper, we presented a review on the current control issues and strategies on a group of unmanned autonomous vehicles/robots formation. Formation control has broad applications and becomes an active research topic in the recent years. In this paper, we attempt to review the key issues in formation control with a focus on the main control strategies for formation control under different kinds of scenarios. Then, we point out some important open questions and the possible future research directions on formation control. This paper contributes with a new and interesting consideration on formation control and its application in distributed parameter systems. We pointed out that formation control should be classified as formation regulation control and formation tracking control, similar to regulator and tracker in conventional control.

In this paper, we propose a novel control scheme that enables a group of multiple spacecraft to maneuver according to a desired trajectory while the internal shape of the group is ensured to converge to a prescribed formation structure. The main innovation of this paper lies in the design of a special decomposition that decomposes the dynamics of the group into two parts: dynamics of the overall group motion (average system) and the dynamics of the group internal formation (shape system). In addition, the decomposition has the property that the energies of the average and shape systems preserve that of the original system. Thus, the maneuver of the group can be achieved by controlling the average system, while the formation control can be achieved by controlling the shape system. The proposed control scheme also can be extended hierarchically for multiple groups. Simulation is performed to show the efficacy of the proposed control. 1