Traffic is a reality of modern life. With the recent innovations in autonomous vehicles, we might be able to make navigating traffic faster, easier, and safer than ever before!

By formulating and solving this complex problem as a fixed-horizon ILQ game, we can find a safe, efficient solution!

The image to the left depicts a sequence of four key snapshots in the evolution of this three-car system. We see in the left-most snapshot that the cars start at the same place, displaying their intended path. in the second snapshot, P1 has sped up to pass the other cars and P3 has slowed down to merge behind P2. In the third snapshot, they enter a potentially hazardous point where their paths could intersect if they aren't careful. And finally, in the fourth snapshot, they have all arrived in their desired lane and can continue along their way.