I use robotics in teaching the introductory calculus sequence for science and engineering students. The first-semester calculus course is centered on a robot which throws a ball into a cup. Computing when to release the ball in order to land on target requires most of the content of first-semester calculus. The second semester calculus course uses a Bluetooth controlled toy car with an accelerometer and gyro to study integration and error.
My research is in differential geometry. Currently, I’m working on understanding the geometry of the space of polygons (or robot arms) using a symplectic structure on the space in order to prove theorems about random curves and loops in space. This line of research answers some old questions in the statistical physics of polymers.