Autonomous Emergency Braking: Sensor Latency vs Stopping Distance

Scenario

Approach speed 80 km/h

System latency (perceive→brake) 300 ms

Sensor detection range 120 m

Road grip (braking decel.) 6.0 m/s²

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Live Readouts

Current speed

80.0 km/h

Gap to obstacle

— m

Reaction distance

0.0 m

Braking distance

0.0 m

Predicted stop dist.

0.0 m

Range margin

0.0 m

How it works

An automatic emergency braking system only starts slowing the car once three things have happened in sequence: the sensor detects the obstacle, the software decides to brake, and the actuator applies torque. That whole chain has a fixed system latency t_lat — during it the car keeps moving at its approach speed v. Only after that does braking deceleration a take over.

Reaction distance:  d_react  = v · t_lat
Braking distance:   d_brake  = v² / (2·a)
Total stop distance: d_total = d_react + d_brake

Safe if: d_total ≤ R_sensor  (detection range)

Speed — reaction distance grows linearly with v; braking distance grows with v², so speed dominates at highway range.
System latency — camera-only pipelines and heavier sensor-fusion stacks add tens to hundreds of milliseconds; every 100 ms at 100 km/h costs about 2.8 m of reaction distance with zero braking yet applied.
Sensor range — lidar/radar range sets how early the obstacle can be seen at all; a shorter range only gives the latency+braking budget less room before it runs out.
Road grip — wet or icy surfaces cut achievable deceleration roughly in half to a third versus dry asphalt, which more than doubles d_brake for the same speed.

This is the same arithmetic real AEB and forward-collision-warning systems use to pick a minimum detection range for a given target operating speed — it is why lidar's centimeter-level range accuracy and low latency matter as much as raw resolution for highway-speed autonomy.

Sensor detection ring Obstacle Skid marks (braking)

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