In this talk we provide a rigorous analysis of a simple but plausible model, developed independently in the statistical physics and computer graphics literature, of a set of mobile autonomous agents also known as `boids'. The model has been inspired by flocking behavior of birds, schooling of fish andother similar aggregation behavior among other animal species.
We provide two flocking models: a kinematic model and a dynamic one. In the kinematic model, each agent is assumed to move with a constant speed in the plane with its heading direction chosen as the average of the heading of the agent itself and that of its nearest neighbors. In the dynamic model, each agent is modelled as a point-mass system whose acceleration is chosen to be the aggregate of cohesion, repulsion, and alignment forces among each agent and its nearest neighbors.
Both of these models have been studied extensively via simulation, in statistical physcis as well as computer graphics literature. Simulations (under various conditions) have indicated that the above simple local rule will result in the alignment of all agents with each other (in both cases), hence resulting in `emergence of ordered behavior' starting from arbitrary initial conditions. The above model has been extensively studied in the computer graphics literature as well as the biological physics literature as a landmark result in `artificial life' and as an example of `emergence of complex behavior', and has been featured as cover stories in the journals Nature and Scientific American. However, no system theoretic explanation or proof of the convergence result has been provided so far.
We will show that the above phenomenon can be analytically explained and proven, using tools from control and dynamical systems, graph theory, and theory of non-negative matrices. It is shown that when the graph induced by the neighboring relation is `connected in time', all headings will converge to the same value, resulting in the agents moving in a formation. Furthermore, we show that when one of the agents does not change its heading and acts as a group leader, all headings converge to that of the leader, under similar connectivity assumptions. We will also provide a connection between this problem and that of nonlinear coupled oscillators.
Brief bio of speaker: Ali Jadbabaie got his BS degree with (high honors) from Sharif University of Technology in Tehran, Iran in 1995. He received a Masters degree in Elecrical Engineering from the University of New Mexico, Albuquerque in 1997, and a PhD degree in Control and Dynamical Systems from California Institute of Technology (Caltech) in October 2000. From October of 2000 to July 2001 He was a postdoctoral scholar at the CDS department at Caltech. From July 2001 To August 2002, he was a post doctoral scholar at the Electrical Engineering Department at Yale University. Since August 2002, he has been an assistant professor in the department of Electrical and Systems Engineering at the University of Pennsylvania in Philadelphia, PA.
Dr. Jadbabaie's research interests are: real-time optimization based control with applications to Unmanned Aerial Vehicles, distributed coordination of multiple agents, and robust & optimal control.
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