References for Topology and Robotics

Topology is at the core of the most successful algorithms in Robotics. To understand how these methods work, you need a basic grasp of topological ideas (see Chapter 4 of LaValle’s book for example). But as computational topology has advanced and computers have gotten faster, there has been an increase in interest in the application of more sophisticated methods (particularly homotopy and homology) to problems in Robotics. I think these methods are going to get more important, so I’ve started collecting references to papers on the subject so I can better understand the field. This is an evolving list, so if you have recommendations, please let me know.

Topology for Planning

The connection between topology and robotics is most apparent through motion planning. Configuration spaces (see LaValle’s book above) are manifolds, and the papers in this list show that robot trajectories can be analyzed in terms of homotopy and homology.

Topology for Tracking

The following papers consider the problem of tracking a target using sensors. They organize the plausible paths of the target using homotopy classes.