Efficient Re-planning for Robotic Cars

We consider the problem of the reactive re-planning of an optimal trajectory for autonomous vehicles subject to geometric and dynamic constraints. Reactive replanning is used when a vehicle following a planned trajectory encounters an unforeseen obstacle. In such a case, a new local trajectory that avoids the obstacle has to be generated, without violating any constraint and preserving optimality. The solution presented in the paper guarantees that the new trajectory rejoins the previously planned one shortly after the obstacle. Moreover, the transition between old and new trajectory is smooth up to second derivative (curvature), which makes it easy to track an emergency manoeuvre. Finally, our solution is efficient and can be implemented in real-time on lean hardware. In order to validate the approach, we show how the re-planning can be executed in a few milliseconds (on a standard machine) for the realistic example of a racing car.