论文概况

摘要

Cooperative vehicle collision warning system is made possi- ble by recent progress in advanced positioning systems and wireless com- munication technology. In this paper we report our work in developing a cooperative intersection collision warning system that is not limited by the requirement of line-of-sight. The novel elements of the system include the use of a dynamic ad hoc wireless network for peer-to-peer data sharing, a new intersection collision warning algorithm, and a flexible and extensible software architecture and system design. The very same system is also ca- pable of collision warning for other scenarios such as frontal and rear-end. Further, the tunable parameters in the algorithm make it possible for the system to adapt to the preference and capability of each individual driver.

背景讨论

intersection collisions 不如 forward collision 受重视,因为更复杂,以及雷达的硬件水平限制。

雷达有 line-of-sight 的限制,在大部分 intersection collisions 事故中,基本都是由于 line-of-sight 看不到对方车,看到的时候已经来不及躲避了。

作者提出了基于 GPS 的车车交互,解决 line-of-sight。(这部分,我不关心,笔记不整理)

intersection collisions 碰撞模型

top-down 的设计了 specification

Top-Level ICWS Specification

ICWS 是 Intersection Collision Warning System 的缩写

有 4 条:

  1. At most one warning is given at one intersection.
  2. No warning if there is no route contention.
  3. No warning if the driver has already taken appropriate action.
  4. Nowarningifthetime-to-collision(TTC)ismuch greater than time-to-avoidance(TTA).

第 4 条,特别有趣。作者解释:With all of the uncertainties on the road, a warning issued too early is more likely to be a false alarm, which is not desirable. 简单来说,路况的不确定性太高了,提前太久的 warning 基本都是 false alarm。

Top Level CWS Algorithm

两车相碰的数学描述

the expected path intersection $ (x_+, y_+) $ 计算方法如下:

\begin{align}
x_+ &= \frac {(y_2 −y_1)−(x_2 \tan \theta_2 −x_1 \tan \theta_1) } {\tan \theta_1 - \tan \theta_2} \\
y_+ &= \frac {(x_2 − x_1)−(y_2 \cot\theta_2 −y_1 \cot\theta_1)} {\cot\theta_1 − \cot\theta_2}
\end{align}

根据交点,计算 2 车的 TTX(time-to-intersection):

\begin{align}
\text{TTX}_1 &= \frac {| \vec r_+ - \vec r_1 | } { | \vec v_1 | } \mathrm{sign} ((\vec r_+ - \vec r_1) \cdot \vec v_1) \\
\text{TTX}_2 &= \frac {| \vec r_+ - \vec r_2 | } { | \vec v_2 | } \mathrm{sign} ((\vec r_+ - \vec r_2) \cdot \vec v_2)
\end{align}

其中,$ \vec r_n $ 向量表示位置点 $(x_n, y_n)$,$\text{sign}()$ 是符号函数,如果为负,表示不会经过交点。

如果 $ TTX_1 = TTX_2 $ 且大于 0, 则相碰。得到 time-to-collision(TTC) 公式:

$$
\text{TTC}_i =
\begin{cases}
\text{TTX}_i \quad & \text{if there is a route contention}\\
\text{Undefined} \quad & \text{otherwise}
\end{cases}
$$

考虑到 2 车的尺寸等,可以引入 $ \alpha $ 参数,把相碰的条件从相等改为:

$$ | TTX_1 - TTX_2 | < \alpha $$

time to avoidance(TTA)

在已检测到碰撞的前提下,2 种情况不用告警:

  1. 车辆已采取规避措施
  2. 距离 TTC 时间还远(见前面 ICWS specification 第 4 条)

规避时间,是考虑了人的反应时间 + 采取规避措施的时间。

其中,采取规避措施的时间,可能因为规避措施不同而不同。比如,刹车、加速、变向。

也可以简化为,用同一个常量。

总结

  1. ICWS Specification 和 CWS Algorithm 是非常有意义的工作。
  2. 这是一篇比较有实操意义的作弊神器,insight 一般。
  3. 文章有一半篇幅讨论用 GPS 作为车车通信,解决 line of sight 问题。不是我关注的内容,未整理到笔记里。
  4. 虽然笔记给出了详细公式和推导过程,但仅供参考,落地的时候,照着原文抄更安全。