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.
This controllability result is based on a topological tool known as the Nerve Lemma, which may also be seen as a statement about relations and bipartite graphs. Thinking about uncertainty in robotics therefore leads to thoughts about privacy. One discovery is that homology in relations provides lower bounds on how long an individual can defer de-anonymization. Coupled with the earlier controllability result, one sees how a fully controllable system might obfuscate its strategies and goals.