Alex Goldstein

Harvey Mudd College Mathematics 2017

Thesis Proposal: Group Theory and Applications to Robotic Arms
Thesis Advisor: Prof. Michael Orrison
Second Reader: Prof. Christopher Clark

Group Theory and Applications to Robotic Arms

An important problem in robotics is, given a robotic arm with many linkages, what is the best way for its end effector to travel from point a to point b. Because a binary robotic arm with n actuators has 2^n degrees of freedom, this is a problem that even with a good heuristic is very difficult to brute force. One item that is helpful in robotic arm manipulation is having a probability distribution function of where the robotic arm can reach. This can be generated by taking a fourier transform of each small 'module' of a robotic arm's workspace, multiplying in the frequency doiman, and then applying an inverse fourier transform to return to the time domain. My thesis explores possible spaces over which to model these robots and fast algorithms for Discrete Fourier Transforms on those spaces.