基于弧长的参数曲线车道线表示方法及其在车辆控制中的应用
Representing Lanes as Arc-length-based Parametric Curves to Facilitate Estimation in Vehicle Control
摘要：
本文回顾了泰勒级数的基本数学，用函数表示和基于弧长的参数表示来逼近曲线。参数表示在坐标变换和参数移动中保持其形式。这些简化可以显著地促进车辆控制中的车道估计，因为由摄像机感知的车道通常表示在平移和旋转的车身固定框架中。然后推导了从函数表示到基于弧长的参数表示及其逆表示的变换。我们将这种变换应用于车辆控制问题中的车道线估计，并推导出可用于预测的参数表示系数的演化。我们提出了一个程序来模拟整个过程的感知，车道估计和控制的路径跟踪问题。仿真结果表明，所提出的车道估计算法，使用参数表示的有效性。结果表明，所提出的技术，确保车辆控制可以实现相当好的性能在非常低的感知更新率。
英文摘要：
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.
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