Trajectory Planning for Automated Vehicles in Overtaking Scenarios

Overtaking is a challenging task in the field of autonomous driving, especially on roads with an opposite lane and oncoming vehicles. Since trajectory planning is repeated cyclic it is highly important to trigger the maneuver only if it is guaranteed that collision-free trajectories that satisfy kinematic constraints exist at each planning step. The goal of this paper is to present an algorithm for planning overtaking trajectories on large temporal horizons in real-time. The main idea is as follows: once overtaking is desired by the behavior module an initial trajectory is simulated using a path tracking control algorithm for lane changing combined with a classical PI-controller for approaching the target speed. The controllers are parametrized in a way that the simulated trajectory will satisfy kinematic constraints. If no collisions are detected a corridor containing the simulated trajectory is created to state constraints for a subsequent optimal control problem to relax the trajectory and smooth it to be comfortable to the vehicle passengers.