Methods for planning a trajectory for an autonomous vehicle are disclosed. A vehicle motion planning system will determine a reference curve that represents a path via which the vehicle may travel. The system will detect an actor that is moving in the environment. The system will segment the reference curve according to time intervals. For each of the time intervals, the system will identify a bounding geometry for the actor, predict a lateral offset distance between the reference curve and the actor, and use the predicted lateral offset distance to determine whether to alter a planned trajectory for the autonomous vehicle.