This paper addresses the control of a team of nonholonomic mobile robots navigating in a terrain with obstacles while maintaining a desired formation and changing formations when required, using graph theory. We model the team as a triple, (g, r, H), consisting of a group element g that describes the gross position of the lead robot, a set of shape variables r that describe the relative positions of robots, and a control graph H that describes the behaviors of the robots in the formation. Our framework enables the representation and enumeration of possible control graphs and the coordination of transitions between any two formations.

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Modeling and control of formations of nonholonomic mobile robots

This paper presents a survey of recent research in cooperative control of multivehicle systems, using a common mathematical framework to allow different methods to be described in a unified way. The survey has three primary parts: an overview of current applications of cooperative control, a summary of some of the key technical approaches that have been explored, and a description of some possible future directions for research. Specific technical areas that are discussed include formation control, cooperative tasking, spatiotemporal planning, and consensus.

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Recent Research in Cooperative Control of Multivehicle Systems

In this paper, a new framework based on matrix theory is proposed to analyze and design cooperative controls for a group of individual dynamical systems whose outputs are sensed by or communicated to others in an intermittent, dynamically changing, and local manner. In the framework, sensing/communication is described mathematically by a time-varying matrix whose dimension is equal to the number of dynamical systems in the group and whose elements assume piecewise-constant and binary values. Dynamical systems are generally heterogeneous and can be transformed into a canonical form of different, arbitrary, but finite relative degrees. Utilizing a set of new results on augmentation of irreducible matrices and on lower triangulation of reducible matrices, the framework allows a designer to study how a general local-and-output-feedback cooperative control can determine group behaviors of the dynamical systems and to see how changes of sensing/communication would impact the group behaviors over time. A necessary and sufficient condition on convergence of a multiplicative sequence of reducible row-stochastic (diagonally positive) matrices is explicitly derived, and through simple choices of a gain matrix in the cooperative control law, the overall closed-loop system is shown to exhibit cooperative behaviors (such as single group behavior, multiple group behaviors, adaptive cooperative behavior for the group, and cooperative formation including individual behaviors). Examples, including formation control of nonholonomic systems in the chained form, are used to illustrate the proposed framework.

Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles

Intelligent vehicle cooperation based on reliable communication systems contributes not only to reducing traffic accidents but also to improving traffic flow. Adaptive cruise control (ACC) systems can gain enhanced performance by adding vehicle-vehicle wireless communication to provide additional information to augment range sensor data, leading to cooperative ACC (CACC). This paper presents the design, development, implementation, and testing of a CACC system. It consists of two controllers, one to manage the approaching maneuver to the leading vehicle and the other to regulate car-following once the vehicle joins the platoon. The system has been implemented on four production Infiniti M56s vehicles, and this paper details the results of experiments to validate the performance of the controller and its improvements with respect to the commercially available ACC system.

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Cooperative Adaptive Cruise Control in Real Traffic Situations

We propose a model independent coordination strategy for multi-agent formation control. The main theorem states that under a bounded tracking error assumption our method stabilizes the formation error. We illustrate the usefulness of the method by applying it to rigid body constrained motions, as well as to mobile manipulation.

Formation constrained multi-agent control

Introduces the notion of string stability of a countably infinite interconnection of a class of nonlinear systems. Intuitively, string stability implies uniform boundedness of all the states of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded. It is well known that the input output gain of all the subsystems less than unity guarantees that the interconnected system is input-output stable. The authors derive sufficient ("weak coupling") conditions which guarantee the asymptotic string stability of a class of interconnected systems. Under the same "weak coupling" conditions, string-stable interconnected systems remain string stable in the presence of small structural/singular perturbations. In the presence of parameter mismatch, these "weak coupling" conditions ensure that the states of all the subsystems are all uniformly bounded when a gradient-based parameter adaptation law is used and that the states of all the systems go to zero asymptotically.

String stability of interconnected systems

In this paper we introduce the notion of string stability of a countably infinite interconnection of a class of nonlinear systems. Intuitively, string stability implies uniform boundedness of all the states of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded. It is well known that the I/O gain of all the subsystems less than unity guarantees that the interconnected system is I/O stable. We derive sufficient ("weak coupling") conditions which guarantee asymptotic string stability of a class of interconnected systems. Under the same "weak coupling" conditions, string stable interconnected systems remain string stable in the presence of small structural/singular perturbations. In the presence of parameter mismatch, these "weak coupling" conditions ensure that the states of all the subsystems are all uniformly bounded when gradient based parameter adaptation law is used and that they go to zero asymptotically.

D. Swaroop

Papers

String stability of interconnected systems

String stability of interconnected systems