# A Novel Maneuver-Based Driving Envelope Generation Approach for Driving Safety Assessment
## 1 Introduction  
The advanced driver assistance systems (ADAS) are expected to reduce the risk of accidents and enhance driving comfort. The driving states can be classified into five types: normal driving state, warning state, collision avoidable state, collision inevitable state, and post-collision state. With a human-in-the-loop, it is necessary to establish safety indicators for situation assessment to determine whether the vehicle is in a safe state and whether the driver can avoid potential collisions. Generally, the driving situation assessment modular estimates the current driving state, predicts the future driving state, and evaluates the collision risk. The single threat metric includes time-related metrics, acceleration-related metrics, and distance-related metrics, etc. Given the current speed of the host vehicle, the Inter-Vehicle-Time (IVT) indicates the time required for the host vehicle to travel the relative distance to the obstacle [1]. The time-to-collision (TTC) denotes the collision time under the assumption that the vehicle will follow a specific trajectory in the future time-domain [2]. Time-to Maneuver (TTM) is the remaining time to avoid a collision by a specific driving maneuver, such as Time-to-Brake (TTB), Time-to-Steer (TTS), and Time-to-Kickdown (TTK) [3, 4]. The Brake Threat Number (BTN) and the Steering Threat Number (STN) are acceleration-related metrics introduced in [5, 6]. The STN is used to evaluate the risk of the steering maneuver to avoid a collision. The BTN is an indicator for evaluating the risk of braking to avoid a collision. The minimum safe distance in [7] is calculated under the assumption that the leading vehicle will maintain a constant deceleration until it comes to a stop, and the host vehicle starts to brake at a constant deceleration after reaction time. The minimal safe distance (MSD) is the safe distance required for two vehicles to keep minimal safety [8]. The Minimum Longitudinal Safety Spacing (MLSS) represents the safe distance to start a lane-change maneuver [9]. However, the above methods have not considered the current input of thedriver. Due to the driving limits and driving comfort, the curvature of the evasive path should have an upper bound. In some works, path planning methods are used to determine whether there is a safe obstacle avoidance trajectory. In [10; 11; 12; 13; 14; 15], the motion planner generates a bundle of candidate trajectories, and the safety of each trajectory is determined by collision detection. In [16; 17; 18; 19; 20], the handling envelope and the environmental envelope at each time step are taken into account. Whether a safe trajectory exists or not is identified by solving the optimization problem of trajectory generation. However, these methods consume massive computing resources. For a human-in-the-loop system, the human and the machine are complicatedly coupled. The driver's input and the vehicle's driving safety need to be considered at the same time. The Inevitable Collision State (ICS) is defined as a state that ultimately ends in a collision, regardless of what the input is selected [21; 22; 23]. In [24], the reachable occupancy without collision utilizing the concept of ICS is calculated at discrete time steps. However, determining the set of ICS is computationally expensive. Owing to the consumption of computing resources, it is difficult to apply ICS in real-time, and the time horizon is often very short. In [25; 26; 27], a kind of reachable set is mentioned, where the current input of the driver can be considered. The data-driven reachable set is built to represent the probability distribution of the future trajectories considering individual driver steering behavior. The probability distribution of future position is highly related to the curvature of the road. The data-driven method needs to learn the distribution on roads with different curvatures.