Automatic Emergency Braking

This is actually a more important problem and hard problem than it seems.

If you draw your confusion matrix, you have two bad scenarios:

• Too loose threshold: You don’t need to break, but AEB is toggled anyways $\to$ False Positives
• Too strict threshold: REALLY BAD. You have to break, but your AEB doesn’t toggle (you kill a pedestrian) $\to$ False Negatives

Good AEB systems are really tuned well to find the perfect balance. https://docs.google.com/presentation/d/1HQSLPLE-fZ3EN-9PyqMd7-ti7JSLKL7qlrouGFEprU0/edit#slide=id.p11

Nowadays, AEB systems in cars are mandatory to promote safety.

Simple AEB using TTC

The simplest way to do AEB is calculating TTC (Time-to-Collision), where $TT{C}_i(t)=\frac{r_i(t)}{[-{\dot{r}}_i(t){]}_{+}}$

where $r_i$ is the instantaneous range measurements and $\dot{r}$ is the current range rates. The operator $[x{]}_{+}$ is defined as $\max (x,0)$.

We obtain:

• $r_i$ by using the current measurements from the LaserScan message
• ${\dot{r}}_i$ by mapping the vehicle’s current longitudinal velocity onto each scan beam’s angle by using $v_x\cos ({\theta }_i)$, where $v_x$ is the forward speed in the vehicle’s frame of reference (obtained from Odometry message), and ${\theta }_i$ is the beam angle obtained from LaserScan messages