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

Description#

Similar to the required longitudinal acceleration, the \({a}_{\mathit{lat,req}}\) [jansson_collision_2005] 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)