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.
- Search-based Path Planning with Homotopy Class Constraints (2010)
- Identity and Representation of Homotopy Classes of Trajectories for Search-based Path Planning in 3D (2011)
- Search-based Path Planning with Homotopy Class Constraints in 3D (2012)
- Hierarchical Motion Planning in Topological Representations (2012)
- Multiscale Topological Trajectory Classification with Persistent Homology (2014)
- Topological Trajectory Classification with Filtrations of Simplicial Complexes and Persistent Homology (2014)
- Data-Driven Topological Motion Planning with Persistent Cohomology (2015)
- Topological Motion Planning (2016 ICRA Workshop)
- Uses of Persistence for Interpreting Coarse Instructions (2016 ICRA Workshop)
- Persistence & Topological Data Analysis for Robotics (2016 ICRA Workshop)
- Search-based Motion Planning with Topology-based Heuristic Functions (2016 ICRA Workshop)
- High-Dimensional Winding-Augmented Motion Planning with 2D Topological Task Projections and Persistent Homology (2016)
- Topological Trajectory Clustering with Relative Persistent Homology (2016)
- Caging and Path Non-Existence: a Deterministic Sampling-Based Verification Algorithm (2017)
- Topology-Guided Path Integral Approach for Stochastic Optimal Control in Cluttered Environment (2018)
- Topological Signatures for Fast Mobility Analysis (2018)
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.