Event Details

Speaker: Dan Zelazo (Technion)

Title: Formation Control through Group Symmetries

Abstract:

Formation control concerns the problem of steering a collection of interacting agents to a prescribed geometric configuration using only local interactions. Classical approaches formulate the desired formation through collections of distance, bearing, or angle constraints, leading naturally to rigidity-theoretic questions. In this talk, we present an alternative geometric framework in which the desired formation is specified directly through symmetry.

The central idea is to encode the action of finite point groups on graphs and Euclidean frameworks, replacing metric constraints by prescribed rotational and reflection symmetries between neighboring agents. These symmetry constraints give rise to matrix-weighted Laplacians whose null spaces coincide with the desired symmetric formations. The resulting gradient dynamics converge exponentially to these null spaces while requiring only minimally connected interaction graphs.

In the talk, we first develop the construction for cyclic point groups, where rotational symmetries alone determine the formation, and then extend the framework to dihedral groups, incorporating reflections to realize a broader class of symmetric configurations. Throughout the talk we will emphasize the underlying mathematical structures—including group actions, graph automorphisms, symmetric frameworks, and matrix-weighted Laplacians—and illustrate how they provide a unified perspective on distributed coordination problems.

Bio: Daniel Zelazo is a Professor in the Stephen B. Klein Faculty of Aerospace Engineering at the Technion–Israel Institute of Technology, Haifa, Israel. He received the B.Sc. and M.Eng. degrees in Electrical Engineering and Computer Science from the Massachusetts Institute of Technology (MIT) in 1999 and 2001, respectively, and the Ph.D. degree in Aeronautics and Astronautics from the University of Washington in 2009. Following postdoctoral appointments at the University of Stuttgart, Germany, he joined the Technion in 2012. His research interests lie at the intersection of systems and control theory, network science, and nonlinear dynamical systems, with current work spanning multi-agent systems, geometric control, synchronization, and network resilience. He currently serves as an Associate Editor of the IEEE Transactions on Control of Network Systems.