Required Lateral Acceleration (\({a}_{\mathit{lat,req}}\))¶

Description¶

Similar to the required longitudinal acceleration, the \({a}_{\mathit{lat,req}}\) [Jansson2005] is defined as the minimal absolute lateral acceleration in either direction that is required for a steering maneuver to evade collision. For two actors \(A_1, A_2\) at time \(t\), \({a}_{\mathit{lat,req}}\) measures the minimum absolute lateral acceleration required, on average, by actor \(A_1\) to avoid a collision in the future:

\[{a}_{\mathit{lat,req}}(A_1, A_2, t) = \min \{ |a_{1,\mathit{lat}}| ~|~\forall \, \tilde{t} \ge 0: d(p_1(t+\tilde{t}),p_2(t+\tilde{t})) > 0 \}\,.\]

For actors \(A_1\) and \(A_2\) with constant acceleration where \(A_1\) is following \(A_2\), the formula concretizes to

\[{a}_{\mathit{lat,req}}(A_1, A_2, t) = \min \{ |a_{1,\mathit{lat,left}}(A_1,A_2,t)|, |a_{1,\mathit{lat,right}}(A_1,A_2,t)| \}\]

where

\[{a}_{1,\mathit{lat,k}}(A_1,A_2,t) = {a}_{2,\mathit{lat,k}} + \frac{2(v_{2,\mathit{lat}}(t) - v_{1,\mathit{lat}}(t))}{\mathit{TTC}(A_1,A_2,t)} + \frac{2}{\mathit{TTC}(A_1,A_2,t)^2} \cdot \left[ \pm \left( \frac{w_1+w_2}{2}\right) + p_{2,\mathit{lat}}(t) - p_{1,\mathit{lat}}(t)\right]\]

with \(w_i\) denoting the width of \(A_i\) and \(k \in \{\mathit{left}, \mathit{right}\}\) depends on the sign of \(\frac{w_1+w_2}{2}\).

Properties¶

Run-time capability¶

Yes

Target values¶

\([-7,-2.5]\) m/s² dependent on speed [Benmimoun2011] (incident detection)

Subject type¶

Road vehicles (automated and human)

Scenario type¶

Intersecting predicted paths for a significant time span in the scenario

Inputs¶

\(v_i, a_i, p_i\) for \(i \in \{1,2\}\) assuming the constant acceleration motion model

Output scale¶

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

Reliability¶

High, under the assumption that collisions can be reliably predicted in the prediction model

Validity¶

High, but only lateral evasion considered, knowledge on vehicle capabilities necessary for interpretation [Zheng2019]

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)