Representing Lanes as Arc-length-based Parametric Curves to Facilitate Estimation in Vehicle Control

TL;DR

This paper introduces an arc-length-based parametric curve representation for lanes, improving vehicle control by enabling accurate lane estimation even with low perception update rates.

Contribution

It develops a transformation between function and arc-length parametric representations, enhancing lane estimation robustness in vehicle control systems.

Findings

Effective lane estimation at low perception update rates.

Transformation preserves form under coordinate changes.

Simulation confirms improved control performance.

Abstract

This paper revisits the fundamental mathematics of Taylor series to approximate curves with function representation and arc-length-based parametric representation. Parametric representation is shown to preserve its form in coordinate transformation and parameter shifting. These preservations can significantly facilitate lane estimation in vehicle control since lanes perceived by cameras are typically represented in vehicle body-fixed frames which are translating and rotating. Then we derived the transformation from function representation to arc-length-based parametric representation and its inverse. We applied the transformation to lane estimation in vehicle control problem, and derived the evolution of coefficients for parametric representation that can be used for prediction. We come up with a procedure to simulate the whole process with perception, lane estimation and control for the path-following problem. Simulations are performed to demonstrate the efficacy of the proposed lane estimation algorithm using parametric representation. The results indicate that the proposed technique ensures that vehicle control can achieve reasonably good performance at very low perception updating rate.