Topological robotics is a subfield of applied algebraic topology that concerns itself with motion planning algorithms. It seeks to pin down a value known as the topological complexity for any given space. Loosely, this corresponds to the least number of rules needed to perform continuous motion planning on the space.

While the name ``topological complexityA'A' is recent, the ideas making the loose statement precise have been around for decades. Using techniques driven by work from the 1960s, along with more recent principles, it is possible to calculate the topological complexity exactly for many spaces.

In this talk, we will focus primarily on the work of Michael Farber in his book "Invitation to Topological Robotics" as well as the recent work of Don Davis studying the topological complexity of polygon spaces. In the process, we will examine some of the tools for finding upper and lower bounds for topological complexity, and see the application of them in some nice examples.