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.

I. Introduction

Curvilinear coordinate frames (often referred to as Frenet frames) are commonly applied in motion planning [1], prediction [2] and control [3] for automated road vehicles. Because curvilinear coordinate systems can be aligned with the road geometry (see Fig. 1), they exhibit several desireable properties for motion planning in structured environments: We can formulate the nonlinear collision avoidance constraints from the road boundaries as linear constraints. Also, the nonlinear vehicle dynamics can be linearized around the reference path of the curvilinear frame [4].