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GRASP Seminar Series: Spring 2005
January 21, 11:00 AM, Levine Hall 315.
Calin Belta
Department of Mechanical Engineering, NYU
Abstractions of Robot Planning and Control
Abstract: Tasks for large groups of robots (swarms) evolving in 0complex environments are usually "qualitatively" specified. This notion has a dual meaning. First, a swarm is naturally described in terms of a small set of "features", such as shape, size, and position of the region in plane or space occupied by the robots, while the exact position or trajectory of each robot is not of interest. Second, robotic missions in complicated environments are usually specified in terms of regions to be reached or avoided. The accomplishment of such tasks do not require exact values for swarm features, but rather it is equivalent to guaranteeing their inclusion in given sets. For example, in the planar case, if the robots are constrained to stay inside an ellipse, there is a whole set of values for the pose and semiaxes of the ellipse which guarantees that the swarm will not collide with an obstacle of given geometry. Or, for the particular case of one pursuer robot playing a visibility based game, its winning strategy is based on inclusion in the same convex set as the evader, while its exact trajectory is not of interest. In this talk, I will present some recent results on reducing the dimension and complexity of such problems by defining abstractions. First, I will talk about continuous abstractions, in which we show how to extract a small set of essential features of a planar swarm that can be used for planning and control. Second, I will talk about discrete abstractions, in which we use partitions and tools from formal analysis of hybrid systems to capture the complexity of the environment. These two levels of abstraction, possibly combined into a hierarchical abstraction architecture, hold the promise of providing a framework in which swarming tasks can be specified in a high level language, such as temporal logic formulas, and automatically checked for feasibility and solved.
Biography: Calin Belta received B.S. and M.Sc. degrees in Control and Computer Science from the Technical University of Iasi, before earning an M.Sc. in Electrical Engineering from Louisiana State University and M.Sc. and Ph.D. in Mechanical Engineering from the University of Pennsylvania. He is currently an Assistant Professor in the Department of Mechanical Engineering at Drexel University. His research interests include planning and control for formations of robots, hybrid systems, and bio-molecular networks.
