# A Novel Maneuver-Based Driving Envelope Generation Approach for Driving Safety Assessment
## 1 Introduction
The extreme trajectory bound for obstacle avoidance is not generated, and the existence of collision avoidance trajectories is determined by checking the collision area of the obstacles and the reachable set of the ego vehicle. Inspired by their work, we propose a driving envelope for a human-in-the-loop vehicle considering the various constraints including human operation, vehicle motion limits, and collision avoidance with road boundaries and obstacles. The main contributions of our work are two-fold. First, the safe distance considering uncertainty for collision avoidance with obstacles is derived. The lateral motion and the longitudinal motion are considered. The extreme boundary trajectories for collision avoidance are obtained based on the derived safe distance. Second, a novel driving envelope is proposed. The driving envelope considers the constraints including steering input of the driver, vehicle motion limitation, the boundary of road, and the safe distance for collision avoidance. Using the proposed driving envelope, the safety and the intervention time of candidate driving maneuvers can be determined. Motion planning algorithm can be applied considering the proposed driving envelope. The safe distance in this paper is inspired by the MLSS [9], which is the safe distance to start a lane-change maneuver, the safe distance during the lane-change process is not derived. In this paper, the safe distances during the lane-change process and for the lane-change abortion are derived. The driving envelope in this paper is different from that in [27], where the sub-reachable-set generation method did not consider the collision avoidance behavior with obstacles on the road. In this paper, the collision avoidance maneuver is considered for the driving envelope generation method. The proposed driving envelope in this paper is also different from that in [16; 17; 18; 19; 20], where the environmental driving envelope is the unoccupied area at each prediction step. In the above papers, whether safe trajectories exist or not is identified by solving the optimization problem of trajectory generation. The driving envelope proposed in this paper is the non-collision area during the whole time domain of lane-change maneuver and lane-change abortion maneuver. The existence of non-collision trajectories can be identified based on the proposed driving envelope conveniently. In the future, with the help of V2X technology [28; 29], the uncertainty of perception and prediction will be reduced, and the driving envelope will be more reliable. Furthermore, the proposed driving envelope can be used for guiding the search of an underlying planning algorithm to find a solution and determining the time for intervention. The remainder of this paper is organized as follows. The motion constraints for human-in-the-loop vehicles are introduced in Section 2. The driving envelope for candidate maneuvers is described in Section 3. The applications of the proposed driving envelope are discussed in Section 4. The experiment results and the discussions are shown in Section 5. The conclusions are drawn in Section 6.