Robust environment mapping using flux skeletons

We consider how to directly extract a road map (also known as a topological representation) of an initially-unknown 2-dimensional environment via an on-line procedure which robustly computes a retraction of its boundaries. While such approaches are well known for their theoretical elegance, computing such representations in practice is complicated when the data is sparse and noisy. In this paper we present the online construction of a topological map and the implementation of a control law for guiding the robot to the nearest unexplored area. The proposed method operates by allowing the robot to localize itself on a partially constructed map, calculate a path to unexplored parts of the environment (frontiers), compute a robust terminating condition when the robot has fully explored the environment, and achieve loop closure detection. The proposed algorithm results in smooth safe paths for the robot's navigation needs. The presented approach is an any-time-algorithm which allows for the active creation of topological maps from laser-scan data, as it is being acquired. The resulting map is stable under variations to noise and the initial conditions. The key idea is the use of a flux-based skeletonization algorithm on the latest occupancy grid map. We also propose a navigation strategy based on a heuristic where the robot is directed towards nodes in the topological map that open to empty space. The method is evaluated on both synthetic data and in the context of active exploration using a Turtlebot 2. Our results demonstrate complete mapping of different environments with smooth topological abstraction without spurious edges.