Robust and Efficient Curvilinear Coordinate Transformation with Guaranteed Map Coverage for Motion Planning

Curvilinear coordinate frames are a widespread representation for motion planners of automated vehicles. In structured environments, the required reference path is often extracted from map data, e.g., by linearly interpolating the center points of lanes. Often, these reference paths are not directly suited for curvilinear frames, as the representation of points is not guaranteed to be unique for relevant parts of the road. Artifacts arising from faulty coordinate conversions can impede the robustness of downstream planning tasks and may result in safety-critical situations. We present an iterative procedure to adapt a reference path, ensuring a unique representation of all points within a provided subset of a map. Our numerical experiments demonstrate the efficacy of our method when combined with two motion planning tasks: Computing the reachable set of the ego vehicle and planning trajectories using a sampling-based approach.