Abstract-We describe a framework for cooperative control of a group of nonholonomic mobile robots that allows us to build complex systems from simple controllers and estimators. The resultant modular approach is attractive because of the potential for reusability. Our approach to composition also guarantees stability and convergence in a wide range of tasks. There are two key features in our approach: 1) a paradigm for switching between simple decentralized controllers that allows for changes in formation; 2) the use of information from a single type of sensor, an omnidirectional camera, for all our controllers. We describe estimators that abstract the sensory information at different levels, enabling both decentralized and centralized cooperative control. Our results include numerical simulations and experiments using a testbed consisting of three nonholonomic robots.

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. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. Modeling and Control of Formations of Nonholonomic Mobile RobotsJaydev P. Desai, James P. Ostrowski, and Vijay KumarAbstract-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, ( ), consisting of a group element that describes the gross position of the lead robot, a set of shape variables that describe the relative positions of robots, and a control graph 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.

This paper uses geometric methods to study basic problems in the mechanics and control of locomotion. We consider in detail the case of "undulatory locomotion" in which net motion is generated by coupling internal shape changes with external nonholonomic con straints. Such locomotion problems have a natural geometric inter pretation as a connection on a principal fiber bundle. The properties of connections lead to simplified results for studying both dynamics and issues of controllability for locomotion systems. We demonstrate the utility of this approach using a novel "snakeboard" and a mul tisegmented serpentine robot that is modeled after Hirose's active cord mechanism.

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