Using Conformal Navigation Transformations for Robot Navigation in Complex Polygonal Workspaces

This brief proposes a novel method for collision-free robot navigation in arbitrary polygonal workspaces by introducing a new transformation called the conformal navigation transformation. The properties of the proposed transformation in a polygonal workspace and its ability to provide solutions to path and motion planning subproblems are investigated. The original definition of the navigation function is extended to the workspace with corners. Using the extended navigation function and the proposed transformation, a provably correct feedback control law is developed to ensure convergence to the target and obstacle avoidance. Furthermore, a rapid method to compute conformal navigation transformations is presented, which is valid for arbitrary polygonal workspaces. Finally, numerical simulations demonstrate the efficacy and applicability of the proposed methodology.