IRIM Seminar Series

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Now showing 1 - 2 of 2
  • Item
    Mixed-Integer Convex Formulations for Planning Nonlinear Dynamics in Complex Environments
    (Georgia Institute of Technology, 2016-10-19) Tedrake, Russ
    Humanoid robots walking across intermittent terrain, robotic arms grasping multifaceted objects, or UAVs darting left or right around a tree — many of the dynamics and control problems we face today have an inherently combinatorial structure. In this talk, I’ll review some recent work on planning and control methods that address this combinatorial structure without sacrificing the rich underlying nonlinear dynamics. I’ll present some details of our explorations with mixed-integer convex- and SDP-relaxations applied to hard problems in legged locomotion over rough terrain, grasp optimization, and UAVs flying through highly cluttered environments.
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    Algebraic Methods for Nonlinear Dynamics and Control
    (Georgia Institute of Technology, 2013-10-23) Tedrake, Russ
    Some years ago, experiments with passive dynamic walking convinced me that finding efficient algorithms to reason about the nonlinear dynamics of our machines would be the key to turning a lumbering humanoid into a graceful ballerina. For linear systems (and nearly linear systems), these algorithms already exist—many problems of interest for design and analysis can be solved very efficiently using convex optimization. In this talk, I'll describe a set of relatively recent advances using polynomial optimization that are enabling a similar convex-optimization-based approach to nonlinear systems. I will give an overview of the theory and algorithms, and demonstrate their application to hard control problems in robotics, including dynamic legged locomotion, humanoids and robotic birds. Surprisingly, this polynomial (aka algebraic) view of rigid body dynamics also extends naturally to systems with frictional contact—a problem which intuitively feels very discontinuous.