Topology and robot motion planning

Michael Farber, Queen Mary University of London

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I will start by pointing out that the motion planning problem of robotics is equivalent to the task of finding a section of a specific fibration. The notion of Schwartz genus allows to quantify the complexity of this problem. The main part of the talk will be based on a recent joint work with Dan Cohen and Shmuel Weinberger which deals with parametrised motion planning, i.e. with motion planning algorithms which are in some sense universal, they are applicable to a variety external conditions (such as positions of obstacles etc) which are viewed as parameters.