I am interested in making robots act purposefully and successfully in a world in which most everything is uncertain. Sensors are noisy, actions are imprecise, and models are faulty. I wish to understand how these uncertainties interact and how to overcome them. My research draws on tools from geometry, mechanics, planning, probability, and topology. Most recently I have explored topological methods for planning and control. Topology allows a system to abstract connectivity properties, filtering out the imprecision caused by uncertainty. For instance, one recent novel topological result is a graph controllability theorem:
A system can reach any state in a graph with control uncertainty if and only if the graph's strategy complex is homotopic to a sphere of dimension two less than the number of states in the graph.