Required Acceleration (\({a}_{\mathit{req}}\))#

Description#

Based on \({a}_{\mathit{long,req}}\) and \({a}_{\mathit{lat,req}}\), the aggregate metric \({a}_{\mathit{req}}\) can be defined in various ways [Jansson2005], e.g. by taking the norm of the required acceleration of both directions, i.e.

\[{a}_{\mathit{req}}(A_1, A_2, t) = \sqrt{{a}_{\mathit{long,req}}(A_1, A_2, t)^2 + {a}_{\mathit{lat,req}}(A_1, A_2, t)^2}\,.\]

More complex aggregates might also take into account the maximally available acceleration in each direction by incorporating the coefficient of friction \(\mu\). Also, let us mention the \({a}_{\mathit{req,cond}}\) [neurohr2021criticality] which combines \({a}_{\mathit{req}}\) and SPrET for the analysis of urban intersection scenarios:

\[\begin{split}{a}_{\mathit{req,cond}}(A_1,A_2,t) = \begin{cases} {a}_{\mathit{req}}(A_1,A_2,t), \text{ if } \mathit{SPrET}(A_1,A_2,t) < 3s^2,\\ 0, \text{ otherwise.} \end{cases}\end{split}\]

The \({a}_{\mathit{req,cond}}\) demonstrates by example how new criticality metrics can be created by combination of existing metrics and target values. In particular, the conditionality of the \({a}_{\mathit{req,cond}}\) encodes that the dynamical aspects of criticality only become relevant when a certain temporal criticality is present. This construction, of course, can be generalized as it is not specific to the \({a}_{\mathit{req}}\) and SPrET. Generally, addressing the different aspects of criticality through combination of metrics could lead to vastly improved validity.

Properties#

Run-time capability#

Yes

Target values#

-3.4 m/s² (scenario classification) [Huber2020], other values for lateral and longitudinal required acceleration may apply

Subject type#

Road vehicles (automated and human)

Scenario type#

Intersecting predicted paths for a significant time span in the scenario

Inputs#

\({a}_{\mathit{lat,req}}\), \({a}_{\mathit{long,req}}\)

Output scale#

\((-\infty, \infty)\), acceleration (m/s²), ratio scale

Reliability#

High, under the assumption that the non-collision condition can be reliably predicted

Validity#

High, found to be lower than TTC and PET for large thresholds [Zheng2019], but comparable to CPI [Guido2011]

Sensitivity#

High, as most critical situations between two actors impose a high required acceleration at some point

Specificity#

Medium, as there exists situations with intersecting paths of actors, but planned trajectory is deviating (e.g. turning maneuvers)