Talk of Prof. M.-A. Belabbas

February 11, 2020

--- A Homotopy Method for Motion Planning

Time: February 11, 2020
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Prof. M.-A. Belabbas
Associate Professor
Electrical and Computer Engineering
Coordinated Science Laboratory
University of Illinois, Urbana-Champaign  


Tuesday 2020-02-11 16:00
IST-Seminar-Room V9.2.255 - Pfaffenwaldring 9 - Campus Stuttgart-Vaihingen


The motion planning problem is one of the oldest and most studied problems in control theory. It consists of determining control signals that drive a system from its initial state to a desired final state. The difficulty of the problem lies in the fact that the dynamics can be arbitrary nonlinear, and the trajectory of the system may be subject to additional holonomic, non-holonomic or obstacle constraints. We present in this talk a new point of view on motion planning and, as a result, provide a new method to solve this important problem. The method proceeds by deforming an arbitrary path joining the initial state of the system to a desired final state into an admissible path, that is a path that meets the various constraints of the problem. The method builds on relatively recent developments in geometric analysis. In a nutshell, it consists of encoding the various constraints of the problem in an appropriately-defined inner product which is then used to derive a parabolic partial differential equation whose solution provides the sought homotopy between an arbitrary path and a feasible trajectory for the system to follow. We will present the method in details and apply it to various motion planning examples, including wheeled vehicles control and robot gymnastics.  

Biographical Information

M.-A. Belabbas obtained his PhD degree in applied mathematics from Harvard University and his undergraduate degree from Ecole Centrale Paris, France, and Universite Catholique de Louvain, Belgium. He is currently an associate professor in the Electrical and Computer Engineering department at the University of Illinois, Urbana-Champaign and at the Coordinated Science Laboratory. His research interests are in geometric control theory, stochastic control and learning.  

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