I am extending this work, by reformulating it in terms of a 1D dynamical map ("map" as in logistic map). We can analyze the ergodicity and coverage of the map in different classes of polygons. To make a bouncing robot explore a space, you want a bouncing law that covers the polygon well. To make a bouncing robot localize, you want the robot to become "trapped" in a small region of phase space (the "attractor"). Work is ongoing here.
This project explores what can be reconstructed about the motion and environment of a rolling robot with an IMU fixed to the inside of its spherical surface. Projects like Sphero use IMUs fixed to an internal platform, whereas we're tracking the rotation of the robot, essentially creating a "3D wheel encoder".
Documentation on my github includes a general guide to setting up a small, battery-powered IMU that logs to an SD card.
Results from this project indicated that it is possible to get decent estimates of the distance and direction traveled by a rolling robot between collisions.
"Predicted Information Gain" is an exploratory learning algorithm developed by the Redwood Center for Computational Neuroscience. While working with Jim Crutchfield's group at UC Davis, I adapted this algorithm for small robots and analyzed their learned representations of the environment. I also worked on developing ways to include more memory in the algorithm to adapt to hidden environments. My paper on the project is here. From summer 2014.
Recent discoveries have indicated that some photosynthetic structures are able to use vibrational modes in proteins to encourage semi-coherent transport of energy. This means that excitons are not collapsed down into one state, but remain in a superposition of states during transport, which is a faster and more efficient way to transport energy. My project involved modelling this process using the Hierarchical Equations of Motion, a reformulated approximation to the solution of the Schrodinger Equation. Using these models, my group and myself identified several physical characteristics for highly coherent systems. This was a senior design project, and research has been passed on to a new group and is ongoing. My poster that I presented on my work can be found here, and a more detailed overview that I wrote with my two research partners is here. From academic year 2013-2014.