Robot navigation in unknown terrains using learned visibility graphs. Part I: The disjoint convex obstacle case

TLDR: An algorithm is presented to navigate a robot in an unexplored terrain that is arbitrarily populated with disjoint convex polygonal obstacles in the plane and it is proven to yield a convergent solution to each path of traversal.

Abstract: The problem of navigating an autonomous mobile robot through unexplored terrain of obstacles is discussed. The case when the obstacles are "known" has been extensively studied in literature. Completely unexplored obstacle terrain is considered. In this case, the process of navigation involves both learning the information about the obstacle terrain and path planning. An algorithm is presented to navigate a robot in an unexplored terrain that is arbitrarily populated with disjoint convex polygonal obstacles in the plane. The navigation process is constituted by a number of traversals; each traversal is from an arbitrary source point to an arbitrary destination point. The proposed algorithm is proven to yield a convergent solution to each path of traversal. Initially, the terrain is explored using a rather primitive sensor, and the paths of traversal made may be suboptimal. The visibility graph that models the obstacle terrain is incrementally constructed by integrating the information about the paths traversed so far. At any stage of learning, the partially learned terrain model is represented as a learned visibility graph, and it is updated after each traversal. It is proven that the learned visibility graph converges to the visibility graph with probability one when the source and destination points are chosen randomly. Ultimately, the availability of the complete visibility graph enables the robot to plan globally optimal paths and also obviates the further usage of sensors.