A Universal Formulation for Path-Parametric Planning and Control: A Unified Framework, from Path following to Contouring Control and Progress Maximization

We present a unified framework for path-parametric planning and control. This formulation is universal, as it standardizes the entire spectrum of path-parametric techniques, from traditional path following to more recent contouring or progress-maximizing model predictive control (MPC) and reinforcement learning (RL), under a single framework. The ingredients underlying this universality are twofold. First, we present a compact and efficient technique capable of computing singularity-free, smooth, and differentiable moving frames. Second, we derive a spatial path parameterization of the Cartesian coordinates for any arbitrary curve, without prior assumptions on its parametric speed or moving frame, and that perfectly interplays with the aforementioned path parameterization method. The combination of these two ingredients leads to a planning and control framework that unites existing path-parametric techniques in the literature. Aiming to unify all these approaches, we open source a software library that implements the presented content, thereby providing a self-contained toolkit for the formulation of path-parametric planning and control methods.