Robot navigation on star worlds using a single-step Navigation Transformation

This work presents a single-step diffeomorphic transformation from a known star world to a trivial domain called the point world, where the navigation task is reduced to connecting the images of the initial and destination configurations by a straight line. Obstacle potential functions - derived using Zenkin's formulas - are used to define a transformation activation region around each obstacle. Configurations in this region are radially mapped with respect to the center of the corresponding obstacle. The proposed transformation guarantees almost global navigation. The provided theoretical results are backed by analytical proofs, while the effectiveness of the method is demonstrated by a series of simulation studies.