Singularity-Free Guiding Vector Field for Robot Navigation

In robot navigation tasks, such as unmanned aerial vehicle (UAV) highway traffic monitoring, it is important for a mobile to follow specified desired path. However, most of the existing path-following algorithms cannot guarantee global convergence paths or enable following self-intersected due existence singular points where return unreliable even no solutions. One typical example arises in vector-field guided (VF-PF) algorithms. These are based on vector field, and exactly field diminishes. Conventional VF-PF generate same dimensions those space path lives. this article, we show that mathematically impossible conventional achieve just simple closed (precisely, homeomorphic unit circle). Motivated by new impossibility result, propose novel method transform nonself-intersected unbounded real line) counterparts higher dimensional space. Corresponding path, construct singularity-free guiding The integral curves thus exploited therefore projection lower subspace converge physical (lower dimensional) Rigorous theoretical analysis carried out results using dynamical systems theory. addition, both numerical simulations our proposed an extension combining trajectory tracking Finally, practical value approach complex engineering systems, conduct outdoor experiments with fixed-wing airplane windy environment 2-D 3-D paths.