Criticality Metrics for Automated Vehicles#

Introduction#

This page is supplementary material to the publication [Westhofen2021] and provides descriptions and evaluations of criticality metrics for automated vehicles.

The descriptions and assessments arose from a systematic suitability analysis, which is described in detail in the reference. It considers multiple properties that were deemed relevant for a broad albeit abstract set of applications the authors have observed criticality metrics being used in. Among others, we consider the metrics’ target values, scenario types, specificities, and sensitivities. Definitions of the properties are given in the reference.

Note

Please note that when applying one or multiple of the described metrics in a practical, concrete setting, a detailed analysis of the specific application at hand is mandatory.

Abbreviations#

For describing the criticality metrics, we use several abbreviations:

Abbreviation

Meaning

AV

Automated Vehicle

VRU

Vulnerable Road User

ODD

Operational Design Domain

ACC

Adaptive Cruise Control

AEB

Automated Emergency Braking

LKAS

Lane Keeping Assistance System

DMM

Dynamic Motion Model

MM

Maneuver Model

CA

Conflict Area

TT

Two Track

OT

One Track

Symbols#

Within formulae, we use the following symbols:

Symbol

Meaning

\(A_i\)

actor \(i\)

\(\mathcal{A}\)

set of all actors in a scene or scenario

\(t_0\)

starting time of a scenario

\(t_e\)

ending time of a scenario

\(t\)

a point in time

\(t_H\)

a time horizon

\(p_O(t)\)

position of object \(O\) at time \(t\)

\(p_i(t)\)

position of actor \(i\) at time \(t\)

\(p_{i,m}(t)\)

position of actor \(i\) at time \(t\) when conducting maneuver \(m\)

\(d(p_1(t),p_2(t))\)

euclidean distance of \(p_1(t)\) and \(p_2(t)\)

\(\dot{d}(p_1(t),p_2(t))\)

derivative of euclidean distance \(d\)

\(v_i(t)\)

velocity of actor \(i\) at time \(t\)

\(a_i(t)\)

acceleration of actor \(i\) at time \(t\)

\(a_{i,\mathit{min}}(t)\)

minimal available acceleration of actor \(i\) at time \(t\)

\(a_{i,\mathit{max}}(t)\)

maximal available acceleration of actor \(i\) at time \(t\)

\(j_i(t)\)

jerk of actor \(i\) at time \(t\)

\(\nu_\mathit{long}\)

longitudinal component of a vector \(\nu\)

\(\nu_\mathit{lat}\)

lateral component of a vector \(\nu\)

\(u_i(t)\)

control inputs of actor \(i\) at time \(t\)

\(\beta_i(t)\)

sideslip angle of actor \(i\) at time \(t\)

\(\psi_i(t)\)

yaw angle of actor \(i\) at time \(t\)

\(\omega_i(t)\)

yaw rate of actor \(i\) at time \(t\)

\(F_{idxy}\)

tire forces of actor \(i\) with direction \(d\) for tire \((x,y)\)

\(c_{i\alpha f}\)

front tire cornering stiffness of actor \(i\)

\(c_{i\alpha r}\)

rear tire cornering stiffness of actor \(i\)

\(l_{if}\)

distance from front axle to center of gravity of actor \(i\)

\(l_{ir}\)

distance from rear axle to center of gravity of actor \(i\)

\(L\)

distance from front to rear axle

\(m_i\)

mass of actor \(i\)

\(I_{iz}\)

moment of inertia of actor \(i\)

\(\delta_{if}\)

front steering angle at the tires of actor \(i\)

\(\tau\)

target value

\(\|\cdot\|_2\)

the euclidean norm

\(\nu_{\mathit{long}}\)

longitudinal component of a vector \(\nu\)

\(\nu_{\mathit{lat}}\)

lateral component of a vector \(\nu\)

Metrics#

Each criticality metric is described textually, accompanied by a formula. Furthermore, its properties are described concisely.