Higher Education Topological Complexity

Published on September 15th, 2016 | by editor

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Topological Complexity

Ricky Salgado and Emiliano Velasquez, students from Hellen Colman’s Mathematics class, did a research on Topological Complexity for Driverless Vehicles that was published electronically on August 11, 2016.

Topological complexity sounds complicated, but it relates to the way commands are given to the autonomous robots so that they can operate and move in a given space. For a driverless car, that means the space is the road being shared by other cars.

These ideas were introduced to the students during an undergrad project led by Professor Hellen Colman. To explain these concepts, Ricky and Emiliano walked through the various algebraic definitions and provided physical examples along the way. They calculated the topological complexity for various scenarios, starting with a single robot moving on a simple space, they added on to this scenario towards a final case including more robots and more complicated spaces where they move. Finally, they provided an example where two driverless vehicles move in a track joining seven colleges throughout Chicago. They determined the number of constructions as well as their content for their case study.

We are really thrilled and proud of Ricky, Emiliano, and Professor Colman for their accomplishment.

For the mathematically inclined, or just the generally curious, please see the whole publication on Topological Complexity for Driverless Vehicles.




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