A computer-implemented method comprises: initiating, by an assisted-driving system that is controlling motion of a vehicle, a lane change of the vehicle from an ego lane to a target lane, the lane change to be performed based only on local information of the vehicle; defining, by the assisted-driving system, a parametric representation of the target lane, the parametric representation based on first waypoints of the target lane; receiving, by the assisted-driving system and during the lane change, a first output of a perception component of the vehicle, the first output being the local information and reflecting second waypoints of the target lane; performing, by the assisted-driving system, a comparison based on the first output and the parametric representation; and providing, by the assisted-driving system, references of a first global path to controllers of the vehicle for actuating the lane change, the references selected based on the comparison.