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Mathematics Colloquium


Date:  Friday, March 24, 2017

Title:  Sumner Myers lecture: Symmetric Hybrid Systems: Periodic Gait Design for Legged Robots

Abstract:  While wheeled vehicles are very efficient on even terrains, legged robots can outperform them on uneven terrains and where there is no continuous path of travel (such as stairs and ladders). This versatility of legged robots, however, brings challenges such as obtaining stable walking and running gaits. A type of walking gait, which is the focus of this talk, is a periodic one, which can be associated with a periodic orbit of the dynamic model that represents the legged robot. The common method for obtaining such periodic orbits is conducting a numerical search for fixed points of a Poincaré map. However, as the number of degrees of freedom of the system grows, such numerical search becomes computationally expensive because in each search trial the dynamic equations need to be integrated. Moreover, the numerical search for periodic orbits is in general sensitive to model errors. I will show that we can overcome these issues by using the �Symmetry Method for Limit Cycle Walking�, which relaxes the need to search for periodic orbits, and at the same time, gives rise to limit cycles that are robust to model errors. Mathematically, the symmetry method is described in the context of Symmetric Hybrid Systems. I will show that legged robots, due to the symmetries that they possess, are symmetric hybrid systems and hence, have an infinite number (indeed, a continuum) of periodic orbits that can be identified easily. I will present the experimental results of the symmetry method on the humanoid robot COMAN at the Biorobotics laboratory of EPFL.

Speaker:  Hamed Razavi
Institution:  ETH


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