Automated driving aids that will soon be fitted to cars will warn motorists of possible accidents. They may even help them actively to avoid crashes.

Driving fast along a road outside Turin, snow-capped mountains beckon in the far distance. A dog suddenly runs out into the road. A collision looks inevitable when the driver fails to respond. At the last moment, the car executes a smooth, mathematically precise swerve around the dog and then returns to its lane.