Geometry, optimization and control in robot coordination

Motion coordination is a remarkable phenomenon in biological systems such as schools of fish and serves as a remarkable tool for man-made groups of robotic vehicles and active sensors. Although each individual agent has no global knowledge about the group as a whole or about the surrounding environment, complex coordinated behaviors emerge from local interactions. From a scientific point of view, the study of motion coordination poses novel challenges in systems theory: a comprehensive understanding of this phenomenon requires the joint ambitious study of mobility, communication, computation, and sensing aspects. This brief abstract and the presentation at the NE{S|T}COC symposium is a summary of some recent work on models and algorithms for coordinating the motion of multi-agent networks. In the companion papers (Mart́ınez, Bullo, Cortés, and Frazzoli, 2007), we propose a tractable and meaningful model for a network of robotic agents that move and communicate. Building on concepts from distributed computation, robotics and control theory, we define notions of robotic network, control and communication law, coordination task, and time and communication com-plexity. We illustrate our model and compute the proposed complexity measures in the prototyp-ical example of a network of locally connected agents on a circle that agree upon a direction o