Unscented Transform-based Pure Pursuit Path-Tracking Algorithm under Uncertainty

TL;DR

A modified geometric pure pursuit path-tracking algorithm is proposed, taking into consideration such uncertainties using the unscented transform, and tested through simulations for typical road geometries, such as straight and circular lines.

Abstract

Automated driving has become more and more popular due to its potential to eliminate road accidents by taking over driving tasks from humans. One of the remaining challenges is to follow a planned path autonomously, especially when uncertainties in self-localizing or understanding the surroundings can influence the decisions made by autonomous vehicles, such as calculating how much they need to steer to minimize tracking errors. In this paper, a modified geometric pure pursuit path-tracking algorithm is proposed, taking into consideration such uncertainties using the unscented transform. The algorithm is tested through simulations for typical road geometries, such as straight and circular lines.

Figures (10)

• Figure 1: In the path-tracking problem, two types of uncertainty can arise: 1) Localization uncertainty: Represented by a red confidence ellipse, this uncertainty leads to variations in the vehicle’s pose (position and orientation), depicted by dark blue and green lines. 2) Detection uncertainty: Shown in yellow, this arises from inaccurate identification of lane boundaries, increasing uncertainty in calculating the reference path, illustrated by green and blue lines.
• Figure 2: The general workflow of the proposed unscented transform-based pure pursuit algorithm under uncertainty is as follows.
• Figure 3: The calculation under uncertainty is simplified by consolidating the various types of uncertainty—specifically, the vehicle's uncertainty ($\pmb{\Sigma_V}$) and the road's uncertainty ($\pmb{\Sigma_R}$) - into a single representation centered around the vehicle, denoted as $\pmb{\Sigma_{V^*}}$.
• Figure 4: Tracking algorithm under uncertainty: (a) Different poses result in different tracking errors, denoted as $y_e^{V}$ and $y_e^{V'}$, along with corresponding steering angles, $\delta$ and $\delta'$. (b) Unscented Transform: (b1) Different sigma points $\pmb{\mathcal{X}_i}$ undergo a nonlinear transformation $g_i$, resulting in steering angles $\delta_i$. (b2) These angles are then weighted by $\mathcal{W}_i$ to produce the weighted steering angle $\delta$.
• Figure 5: Transforming a point from the global coordinates, denoted by $\pmb{p^G}$, into the vehicle's coordinates, denoted by $\pmb{p^V}$ and vice versa.