Optimization of AEBS for Heavy Goods Vehicles Incorporating Driver’s Control and 3D Visibility of Vulnerable Road Users

Featured Application

Improving traffic safety of heavy goods vehicles.

Abstract

While an advanced emergency braking system (AEBS) significantly improves the safety of a heavy goods vehicle (HGV), current implementations face limitations including inadequate scenario coverage for vulnerable road users (VRUs), overriding driver control and limited human–machine collaboration mechanisms, and an insufficient consideration of blind spot challenges in HGVs. To improve the adaptability of the AEBS for HGVs, this study proposes and validates a novel 2D AEBS control algorithm incorporating driver’s control and 3D visibility of VRUs. The proposed algorithm is designed to firstly identify the motion state scenarios based on the spatial relationship between the HGV and VRU. Then, based on the scenario classification result, the proposed algorithm determines whether the HGV needs to brake in the current scenario according to the 2D time to collision for both entities to reach the potential collision area while maintaining their current speeds. Finally, for situations requiring braking, it evaluates whether safety can be ensured under three conditions: the ego vehicle in free driving, the ego vehicle under driver-controlled braking (considering the 3D visibility of the VRU), and the ego vehicle under 2D AEBS-controlled braking. According to the test results, the proposed algorithm can deal with the VRU crossing scenario and leverage the driver’s control capabilities while utilizing AEBS as a safety net function.

1. Introduction

According to the World Health Organization, road traffic accident is the leading cause of fatal injuries in the world [1], which is primarily influenced by roadways, drivers, as well as vehicles [2]. Moreover, the HGV is the primary vehicle type involved in traffic accidents. For HGVs, the cabin significantly restricts the driver’s field of view and blind spots are particularly significant, which pose serious driving risks to VRUs [3]. According to a study conducted by the Federal Motor Carrier Safety Administration and the National Highway Traffic Safety Administration, approximately 35% of HGV-related fatalities involve blind spots limitations [4]. As an important measure to improve the safety of HGVs, an AEBS combined with radar-based pedestrian and vehicle detection and identification can assist drivers in detecting objects within blind spots and braking in case of an emergency [5]. The data analysis demonstrates that AEBS is effective in reducing car–pedestrian collisions [6]. The European Commission, United States, and others have issued laws and regulations requiring the installation of AEBS in new trucks [7].

An AEBS includes three main subsystems: environment sensing, a triggering algorithm, and an execution layer [8]. The sensing layer obtains the parameters including the relative motion parameters of the targets and the ego vehicle, the load parameters of the ego vehicle, and the road parameters [9]. The execution layer performs braking control. Triggering algorithms are the core of an AEBS. Currently, the triggering algorithms of an AEBS mainly include two types: safe distance algorithms and time-related trigger algorithms (such as time to collision, TTC). Compared with typical safe distance algorithms like the Mazda model [10] and Honda model [11], the TTC algorithm delivers optimal collision avoidance performance [12]. The TTC algorithm uses the estimated collision time between the vehicle and the obstacle ahead as a risk assessment metric. By comparing it with a predefined value (usually between 0.5 s and 1.5 s), the system determines when to activate AEBS for emergency braking and collision avoidance. The TTC value represents a reliable parameter for classifying the traffic conflict between a vehicle and an object as an inevitable or avoidable event [13]. Some manufacturers such as Audi and Volvo combine FCW with multi-stage partial and fully autonomous braking. In addition, the constant time to collision has now been used for vehicle separation in vehicle platoons to ensure safety [14].

Extensive research has been performed on AEBS and TTC algorithms. Hirst and Graham pointed out that vehicle speed and relative speed were the main factors of driving, thus, the study proposed a TTC algorithm that incorporated speed compensation [15]. A novel metric termed driver risk response time for hazard perception assessment was proposed, which integrates both time to collision parameters and drivers’ braking behaviors under imminent collision scenarios [16]. A dual-indicator system was developed comprising emergency reaction time as a direct measure of perceptual sensitivity and vehicle operational parameters as an indirect proxy for braking urgency [17]. They subsequently implemented percentile regression to stratify drivers’ hazard perception capabilities. Murphy and Morris established a conflict-oriented safety evaluation paradigm that leverages TTC thresholds for conflict detection, complemented by a time-integrated TTC severity index for graded risk classification [18]. A real-time rear-end AEBS capable of effectively preventing collisions while increasing the final headway distance was proposed [19]. An AEBS incorporating sensor fusion technology was developed, which autonomously detects potential forward collisions and automatically engages the braking system to avoid or mitigate collisions [20].

Although existing studies conduct specific applications of AEBS and TTC algorithms, current research has several limitations:

The first point is the limited scenario coverage for VRUs: Current algorithms primarily focus on longitudinal car-following scenarios to avoid collisions between vehicles, with insufficient research on collision avoidance between HGVs and VRUs. HGVs often collide with VRUs not from the front but by crossing laterally from the side. The dynamics of vehicle collisions inherently involve coupled two-dimensional motion in both longitudinal and lateral directions. Some studies attempt to improve avoidance rates by expanding the lateral detection range of AEBS [21,22], but this fails to adapt to VRUs with various crossing speeds, increasing false triggers. For instance, in some scenarios, VRUs may have sufficient time to cross safely before the HGV reaches the predicted collision point.

The second point is that AEBS overrides driver control and its human–machine collaboration mechanism in critical scenarios remains limited [23]: Current AEBS algorithms neglect the driver’s ability to actively mitigate risks, excessively substituting manual braking. Compared with manual braking by the driver, AEBS-triggered braking is an unexpected and passive emergency intervention, compromising driving comfort. A collaborative approach integrating driver intent and AEBS is needed for braking decisions [24].

The third point is the 3D blind spot challenge in HGVs: HGVs feature large blind spot zones, especially on each side. The visibility of VRUs directly determines whether drivers can take proactive measures. The fusion of AEBS and driver braking capabilities must account for the impact of VRU visibility. Several approaches have been developed to measure blind spots and these approaches can be classified into two categories: manual and computer-aided methods [25]. Most of these approaches focus on measuring the blind area on the ground plane [26]. However, it may lead to erroneous conclusions when assessing the visibility of VRUs of a certain height. As stated elsewhere, the identification and definition of blind spots are inherently dependent on the presence and characteristics of the surrounding objects.

This paper addresses the above issues through the following steps:

(1)

Blind spots in any plane for HGVs: Develop a method to quantify driver blind spots and establish a 3D visibility evaluation function for external VRUs.

(2)

Scenario modeling and 2D TTC: Analyze accident scenarios between HGVs and VRUs to summarize kinematic patterns, formalized as a scenario function. A novel 2D time to collision segmentation model is proposed based on the time difference for HGVs and VRUs to reach trajectory intersection points, serving as the braking trigger criterion (braking scenario function). Three braking modes are then introduced, incorporating VRU 3D visibility’s influence on driver response.

(3)

Integrated Driver-2D AEBS collision avoidance algorithm: Combine the visibility function, scenario function, braking scenario function, and braking modes into a unified algorithm that fuses driver intent and AEBS for VRU collision avoidance.

(4)

Model validation: Evaluate the proposed model under typical traffic conditions.

2. The Evaluation Function of 3D Visibility of VRUs

Blind spots refer to areas around the vehicle that are invisible to the driver while seated in a normal driving posture due to obstructions caused by the vehicle structure. Blind spots can be categorized into the following: left-side blind spot, left mirror obstruction blind spot, left A-pillar blind spot, front blind spot, right mirror obstruction blind spot, right A-pillar blind spot, right-side blind spot, and rear blind spot [27].

The current method for measuring blind spots typically involves following steps: Placing a light source at the position of the driver’s eyellipse to simulate the eye-point. The emitted light rays simulate the driver’s line of sight. Personnel then manually demarcate the illuminated edges on the ground plane to map the driver’s field of view (FOV) [28]. This approach includes several limitations: The first point is that front seats need removal for access. The second point is that manual measurement and marking are time-consuming and prone to human error. The third point is critical height oversight. Visibility must be evaluated using field of view measurements at corresponding heights relative to the VRU. Using ground-plane FOV to assess obstacle visibility yields inaccurate conclusions.

To address these limitations, this study proposes a ray-tracing-based numerical simulation method for measuring the 3D space of HGV blind spots. The specific procedures are as follows:

(1)

Three-dimensional vehicle model construction: A prototype left-hand drive vehicle was selected, with fiducial targets deployed on the left, front, and right cabin surfaces as calibration benchmarks. Following laser scanner positioning and calibration—including instrument leveling and positional alignment—millimeter-level ranging resolution was set to optimize structural detail capture and processing efficiency. Three-dimensional point cloud data of internal and external cabin structures was subsequently acquired through laser scanning. Post-processing reconstructed the vehicle’s geometric profile as depicted in Figure 1, incorporating cutouts for side windows and the windshield while retaining the following sightline-critical cabin components: steering wheel, instrument panel, and OEM-installed displays.

(2)

Defining the geometric coordinate system: The vehicle model was imported into TracePro70 software, where a right-handed Cartesian coordinate system was established with its origin at the ground projection of the center point of the vehicle’s foremost front edge. The X-axis aligned with the front edge (positive direction toward the right-hand side), the Y-axis followed the vehicle centerline (positive direction forward along the travel path), and the Z-axis extended vertically upward, while the ground reference plane was defined at z = 0 mm.

(3)

Eyepoint configuration: Based on the Seating Reference Point—a fundamental vehicle design attribute defined during initial development—the center of the driver’s eyellipse was determined and marked to establish the eyepoint coordinates. In accordance with the Society of Automotive Engineers Standard [29], the 99th percentile eyellipse was adopted, with the eyepoint positioned at (700 mm, −1140 mm, 2550 mm) (As shown by the red dot in Figure 2). A 4 million ray source was then set at the eyepoint to simulate the driver’s line of sight, with ray count optimized to balance computational efficiency and ray distribution density (at least one ray of light in each 20 mm × 20 mm grid under unobstructed conditions). Rays were emitted omnidirectionally from the source.

(4)

Vehicle surface material configuration: All vehicle surfaces were assigned optically pure absorptive properties with zero reflectance and zero transmittance, ensuring the complete absorption of incident rays upon surface contact.

(5)

Data recording: Spatial coordinates and direction vectors of rays escaping the cabin were systematically recorded and archived.

(6)

Data processing: The escaped rays underwent computational processing to reconstruct the three-dimensional driver visibility volume.

Following the acquisition of the driver visibility space, horizontal planes at varying heights were intersected with this volumetric space to determine blind zone distributions across elevation levels.

As depicted in Figure 2, HGVs exhibit extensive blind zones primarily attributable to structural obstructions from left-side mirrors (angle of obstruction is about 15.5°), left A-pillars (angle of obstruction is about 6°), instrument panels, right-side mirrors (angle of obstruction is about 4°), right A-pillars (angle of obstruction is about 4°), right window frames, and other body components. The left-side mirror and A-pillar generate the largest blind zone area. Right blind zones demonstrate significant lateral width due to body structure occlusion.

For detection planes at varying heights, the 1600 mm plane exhibits a reduced blind zone boundary extent compared with the 1300 mm plane. Obstacles at 1600 mm height demonstrate enhanced detectability when approaching the vehicle. Based on the blind zone atlas, the visibility of external obstacles for heavy vehicle drivers is determined by the obstacle’s central coordinates (x, y) and height (h), governed by the following:

$$f_{visibility}=f(x,y,h)=\left\{\begin{array}{cc}0& \mathrm{if} \mathrm{the} \mathrm{object} \mathrm{is} \mathrm{invisible}\\ 1& \mathrm{if} \mathrm{the} \mathrm{object} \mathrm{is} \mathrm{visible}\end{array}\right.$$

(1)

3. Two-Dimensional Collision Algorithm Considering 3D Visibility of VRU

3.1. The Classification Function of Driving Scenarios

Based on real-world video data, driving scenarios for HGVs and VRUs were established.

Assuming rectilinear motion for both parties, the relative interaction states were categorized into four scenarios (as depicted in Figure 3) based on the angle θ between vehicle and cyclist velocity vectors:

(1)

Scenario 1: Non-intersecting trajectories, VRU is on HGV’s right with 0°≤ θ ≤180° or VRU on HGV’s left with 180° ≤ θ ≤ 360°.

(2)

Scenario 2: Imminent collision, trajectories intersect and VRU is on HGV’s trajectory with 0° ≤ θ ≤ 90° or 270° ≤ θ ≤ 360°.

(3)

Scenario 3: Imminent collision, trajectories intersect and VRU is on HGV’s trajectory with 90° < θ < 270°.

(4)

Scenario 4: Imminent collision, potential conflict-non-aligned paths, trajectories intersect but VRU not on trajectory contour, VRU is on HGV’s right with 180° < θ < 360°, or VRU is on HGV’s left with 0° < θ < 180°.

Thus, the state scenario between the HGV and VRU is determined by parameters including their relative spatial configuration, described by the following parametric function:

$$f_{\mathrm{scenario}}=f(x_1,y_1,x_2,y_2,v_1,v_2,\theta )$$

(2)

where (x₁, y₁) and (x₂, y₂) are the position of the HGV and VRU, respectively; v₁, v₂ are the velocity of the HGV and VRU, respectively; and θ denotes the angle between v₁ and v₂.

3.2. The Extraction Function of 2D Collision Avoidance Scenario

Driving collision risk models are mainly classified into safe distance models and collision time models. Safe distance models primarily include the Mazda model, Honda model, Berkeley model, and TOYOTA model, while collision time models mainly consist of TTC and PET (Post-Encroachment Time) models. Based on the kinematic parameters (e.g., velocity, acceleration, direction) of the ego vehicle and the target, these safety distance models dynamically calculate the required safety distance between them. The actual distance is then compared against this calculated safety distance. If the actual distance is less than the safety distance, a collision risk is indicated; otherwise, driving safety is maintained.

Compared with distance-based models, the TTC model requires fewer parameters (which are easier to obtain) and is more widely adopted. TTC represents the time remaining before the ego vehicle collides with a target obstacle if both continue moving at their current relative speed. It assesses collision risk from a temporal perspective, using relative motion states as the evaluation criterion. The formula is as follows:

$$TTC={\displaystyle \frac{S}{v_{rel}}}$$

(3)

where TTC is the collision time; S is the distance between ego vehicle and object; and v_rel is the relative velocity between ego vehicle and object.

Current TTC models suffer from three critical limitations: they disregard the geometric dimensions of both the ego vehicle and obstacles, relying on oversimplified conflict points that compromise calculation accuracy; they fail to account for bidirectional motion relationships by assessing only longitudinal collisions while ignoring scenarios where obstacles laterally evade predicted collision zones before impact, causing false warnings and unnecessary AEBS activations; and they overlook driver maneuverability constraints and vision obstructions (e.g., blind zones), triggering premature autonomous braking.

The proposed methodology addresses these gaps through size-incorporated collision zone modeling—replacing single-point conflict prediction with dimension-aware regions to refine time-to-arrival calculations—and scenario-based 2D-TTC segmentation that decomposes TTC into longitudinal and lateral components, evaluating escape feasibility where collision is avoided, thereby establishing an integrated spatiotemporal risk analysis framework combining spatial and temporal metrics for adaptive risk assessment.

The proposed model is determined by the following indicators:

$$TT{C}_1={\displaystyle \frac{L_1}{v_1}}$$

(4)

$$t_{11}={\displaystyle \frac{L_{11}}{v_1}}$$

(5)

$$t_{12}=abs({\displaystyle \frac{L_{22}}{v_1\sin \theta }})+abs({\displaystyle \frac{L_{12}}{v_1\tan \theta }})$$

(6)

$$TT{C}_2={\displaystyle \frac{L_2}{v_2}}$$

(7)

$$t_{21}={\displaystyle \frac{L_{21}}{v_2}}$$

(8)

$$t_{22}=abs({\displaystyle \frac{L_{12}}{v_2\sin \theta }})+abs({\displaystyle \frac{L_{22}}{v_2\tan \theta }})$$

(9)

where v₁, v₂ are the velocity of the HGV and VRU, respectively. The distances from their closest points to the predicted collision zone are L₁ and L₂, while their dimensions along their directions of motion are L₁₁ (HGV) and L₂₁ (VRU). Their dimensions perpendicular to their travel directions are L₁₂ (HGV) and L₂₂ (VRU). The times required to reach the edge of the predicted collision zone are TTC₁ (HGV) and TTC₂ (VRU). The durations needed to travel their own body lengths at current speeds are t₁₁ (HGV) and t₂₁ (VRU). The traversal times across the entire collision zone—from entry to exit—are t₁₂ (HGV) and t₂₂ (VRU). Trigonometric singularities are handled as follows: when θ = 90°or 270°, tanθ is approximated as 9,999,999 to avoid infinite values in formulas; when θ = 0°or 180°, sinθ is approximated as 0.0000001 to prevent division by zero. The extraction function of the collision avoidance braking scenario can be described as follows:

$$f_{\mathrm{brake}}=f(L_1,L_2,L_{11},L_{12},L_{21},L_{22},v_1,v_2,\theta ,t_{11},t_{12},t_{21},t_{22})=\left\{\begin{array}{cc}0& \mathrm{no} \mathrm{brake}\\ 1& \mathrm{brake}\end{array}\right.$$

(10)

Based on driving scenarios and 2D-TTC, f_brake can be determined as in

Table 1. The description of f_brake.

Scenario		Description
Scenario 1		Maintain a lateral safety distance to avoid collision.
Scenario 2		If v1 − v2 |cosθ| ≤ 0 or t22 < TTC1, safe without braking, fbrake = 0. Otherwise, collision risk exists at current speed, fbrake = 1.
Scenario 3		If t22 < TTC1, safe without braking, fbrake = 0. If TTC1 < t22, collision risk exists at current speed, fbrake = 1.
Scenario 4 (Symmetric for left/right VRU; illustrated for right side: 180° < θ < 360°)	Sub-scenario 4.1	If 270° ≤ θ < 360° and 0 < TTC2 < TTC1 − t21 − t22, VRU will reach the edge of the predicted collision zone first, and VRU has enough time to cross the predicted collision zone, fbrake = 0.
	Sub-scenario 4.2	If 270° ≤ θ < 360° and TTC1 − t21 − t22 ≤ TTC2 < TTC1 − t21, VRU will reach the edge of the predicted collision zone first. It is necessary to estimate the fbrake according to the Scenario2 after VRU reaches the edge of the predicted collision zone (TTC2 ≤ t < TTC1 − t21).
	Sub-scenario 4.3	If 270° ≤ θ < 360° and TTC1 − t21 ≤ TTC2 < TTC1, VRU will reach the edge of the predicted collision zone first. Collision risk exists at current speed, fbrake = 1.
	Sub-scenario 4.4	If 270° ≤ θ < 360° and TTC1 ≤ TTC2 ≤ TTC1 + t11, HGV will reach the edge of the predicted collision zone first. Collision risk exists at current speed, fbrake = 1.
	Sub-scenario 4.5	If 270° ≤ θ < 360° and TTC1 + t11 < TTC2 < TTC1 + t11 + t12, HGV will reach the edge of the predicted collision zone first. It is necessary to estimate the fbrake according to the Scenario2 after HGV reaches the edge of the predicted collision zone (TTC2 ≤ t < TTC1 + t11 + t12).
	Sub-scenario 4.6	If 270° ≤ θ < 360° and TTC1 + t11 + t12 < TTC2, HGV will reach the edge of the predicted collision zone first, and HGV has enough time to cross the predicted collision zone, fbrake = 0.
	Sub-scenario 4.7	If 180° ≤ θ < 270° and 0 < TTC2 < TTC1 − t21 − t22, VRU will reach the edge of the predicted collision zone first, and VRU has enough time to cross the predicted collision zone, fbrake = 0.
	Sub-scenario 4.8	If 180° ≤ θ < 270° and TTC1 − t21 − t22 ≤ TTC2 ≤ TTC1 + t21 + t22. Collision risk exists at current speed, fbrake = 1.
	Sub-scenario 4.9	If 180° ≤ θ < 270° and TTC1 + t21 + t22 < TTC2, and HGV has enough time to cross the predicted collision zone, fbrake = 0.

.

3.3. The Braking Function of HGVs Under Different Control Modes

As identified in Section 3.2, scenarios requiring braking to avoid collisions have been defined; however, braking mode determines both collision avoidance success and the resulting collision speed. The impact of obstacle visibility on collision risk fundamentally differentiates vehicle braking modes, thereby influencing collision speed between the HGV and VRU. Three primary braking modes exist: driver brake, no brake, and AEBS brake.

When an obstacle suddenly emerges within the driver’s field of view, it requires t₁₁′ for the driver to conduct cognitive processing and decision-making, followed by t₁₂′ to execute foot motion and apply pedal force. These intervals collectively constitute the driver’s reaction time t₁′.

Subsequently, due to brake system dead travel, the pedal force takes t₂₁′ to initiate deceleration, after which deceleration linearly increases from 0 to the target value over t₂₂′ and the deceleration and velocity during t₂₂′ can be described in Equations (11) and (12). These periods form the brake system response time t₂′.

$$a={\displaystyle \frac{a_{\max }}{{t_{22}}^{\prime }}}t$$

(11)

$$v=v_1-{\displaystyle {\int }_0^t\frac{a_{\max }}{{t_{22}}^{\prime }}x\mathrm{dx}}=v_1-{\displaystyle \frac{a_{\max }}{2{t_{22}}^{\prime }}}{t}^2$$

(12)

Finally, the braking system maintains sustained deceleration. Based on this driver–vehicle braking sequence, the full braking process unfolds as follows:

$$S_1=v_1({t_{11}}^{\prime }+{t_{12}}^{\prime }+{t_{21}}^{\prime })$$

(13)

$$S_2={\displaystyle {\int }_0^{{t_{22}}^{\prime }}\left(v_1-\frac{a_{\max }}{2{t_{22}}^{\prime }}{t}^2\right)}\mathrm{dt}=v_1{t_{22}}^{\prime }-{\displaystyle \frac{a_{\max }}{6}}{({t_{22}}^{\prime })}^2$$

(14)

$$a_{\max }\le \mu g$$

(15)

$${t_3}^{\prime }={\displaystyle \frac{v_1-0.5\ast a_{\max }{t_{22}}^{\prime }}{a_{\max }}}$$

(16)

$$S_3=\left(v_1-0.5 \ast a_{\max }{t_{22}}^{\prime }\right){t_3}^{\prime }-0.5\ast a_{\max }{({t_3}^{\prime })}^2$$

(17)

where S₁ is the distance that the HGV travels at constant speed during t₁₁′, t₁₂′, and t₂₁′; S₂ is the distance that the HGV travels under linearly increasing deceleration during t₂₂′; S₃ is the distance that the HGV travels under uniform deceleration during t₃′; a_max is the maximum deceleration of the HGV; μ is the coefficient of rolling friction; g is the gravitational acceleration.

Based on the above analysis, the driver’s braking distance under emergency conditions represents their maximum braking capability, expressed as

$$S_{\mathrm{mode}1}=S_1+S_2+S_3$$

(18)

If the distance between the HGV and VRU is less than S_mode1, it still cannot guarantee the driver’s sufficient reaction time to respond to the emergency even applying maximum braking force. Consequently, vehicle safety during the braking maneuver fails to be ensured.

When the VRU is within the driver’s blind zone, the driver fails to detect the VRU, and the vehicle consequently maintains its current speed until collision occurs. With Equations (11)–(15), braking distance during t₁₁′, t₁₂′, t₂₁′, t₂₂′, and t₃′ can be calculated by

$$S_{\mathrm{mode}2}=v_1\left({t_{11}}^{\prime }+{t_{12}}^{\prime }+{t_{21}}^{\prime }+{t_{22}}^{\prime }+{\displaystyle \frac{v_1-0.5a_{\max }{t_{22}}^{\prime }}{a_{\max }}}\right)$$

(19)

When the VRU enters the sensor monitoring range and the HGV is equipped with an AEBS, sensors provide real-time detection—bypassing driver reaction time—while brake dead travel is also reduced to minimal duration. The vehicle initiates direct braking, with the traveled distance during t₂₁′, t₂₂′, and t₃′ calculated as

$$S_{\mathrm{mode}3}=v_1{t_{21}}^{\prime }+v_1{t_{22}}^{\prime }-{\displaystyle \frac{1}{6}}{a}_{\max }{({t_{22}}^{\prime })}^2+\left({\displaystyle \frac{{v_1}^2}{2a_{\max }}}-{\displaystyle \frac{v_1{t_{21}}^{\prime }}{2}}+{\displaystyle \frac{a_{\max }{({t_{22}}^{\prime })}^2}{8}}\right)$$

(20)

During driver-controlled operation, mode1 executes when the VRU is visible, while mode₂ activates for an invisible VRU. AEBS braking implements mode₃. The vehicle braking process incorporating the visibility of the VRU unfolds as follows:

$$f_{\mathrm{mode}}=\left\{\begin{array}{c}{S}_{\mathrm{mode}1}\\ S_{\mathrm{mode}2}\\ S_{\mathrm{mode}3}\end{array}\right.\begin{array}{c}{f}_{\mathrm{visibility}}=1 \mathrm{and} f_{\mathrm{brake}}=1\\ f_{\mathrm{visibility}}=0 \mathrm{or} f_{\mathrm{brake}}=0\\ \mathrm{with} \mathrm{AEBS} \mathrm{and} f_{\mathrm{brake}}=1\end{array}$$

(21)

3.4. The Driver-2D AEBS Algorithm Considering 3D Visibility

Based on the preceding derivation, the braking behavior of the HGV encountering the 3D visibility of the VRU and the collision speed can be calculated, and the Driver-2D AEBS algorithm is proposed (as depicted in Figure 4).

$$v_{\mathrm{collision}}=f_{\mathrm{mode}}|(f_{\mathrm{brake}},f_{\mathrm{scenario}},f_{\mathrm{visibility}})$$

(22)

4. Algorithm Validation and Analysis

To verify the algorithm, this study examined a typical accident scenario involving a VRU abruptly crossing an intersection laterally (as depicted in Figure 5), where the HGV was often in its initial acceleration phase at low speed. In this critical configuration, the driver either failed to detect the VRU or initiated an insufficient braking response despite detection, culminating in a collision followed by an override event over the VRU.

The HGV and VRU in this study are assumed as rigid bodies; for computational modeling, the HGV is simplified as an 8 m × 2.5 m rectangle (L₁₁ = 8 m, L₁₂ = 2.5 m) and the VRU as a 1.5 m × 0.5 m rectangle (L₂₁ = 1.5 m, L₂₂ = 0.5 m). With the coordinate origin fixed at the center of the HGV’s front edge, the VRU’s center position is defined by coordinates (x, y), where longitudinal clearance L₁ and lateral clearance L₂ are then calculated. The crossing scenario configuration yields the following geometric relationships:

θ = 90°

(23)

L₁ = y − 0.5L₂₂ = y − 0.25

(24)

L₂ = x − 0.5 (L₁₂ + L₂₁) = x − 2

(25)

In terms of the vehicle’s inherent performance capabilities, the maximum deceleration of AEBS can reach approximately 7.5 m/s². However, drivers seldom reach the vehicle’s maximum deceleration during operation of the AEBS. According to the data from NHTSA [30], 95% of drivers achieve acceleration levels less than 5.39 m/s² during regular driving. The response times of a vehicle’s pneumatic brake system for a driver and AEBS are approximately 0.055 s and 0.01 s. The deceleration rise times for a driver and AEBS are approximately 0.5 s and 0.2 s. Based on the previously developed collision assessment algorithm, this framework evaluates three vehicle control modes (uncontrolled free travel, driver-controlled operation, and 2D AEBS-controlled maneuvering) to determine both braking necessity and collision avoidance feasibility.

4.1. The Influence of the VRU’s Position

To analyze the influence of a VRU’s position, the speed of the HGV was set to 2 m/s and the speed of the VRU (h = 1300 mm) was set to 2 m/s. The VRU emerges laterally from point (x, y), where (x, y, h) determines whether the driver can detect the VRU and initiate braking manually.

Table 2. The f_visibility, f_scenario, f_brake, and v_collision when the VRU crosses from different positions.

x/m	y/m	fvisibility	fscenario	Without Control		Driver Control		Driver-1D AEBS		Driver-2D AEBS
				fbrake	vcollision/(m/s)	fbrake	vcollision/(m/s)	fbrake	vcollision/(m/s)	fmode	vcollision/(m/s)
3.00	0.25	0	4	0	2.00	0	2.00	0	2.00	Smode3	0.00
3.00	0.50	0	4	0	2.00	0	2.00	0	2.00	Smode3	0.00
3.00	0.75	0	4	0	2.00	0	2.00	0	2.00	Smode3	0.00
3.00	1.00	1	4	0	2.00	1	0.80	1	0.80	Smode3	0.00
3.00	1.25	1	4	0	2.00	1	0.80	1	0.80	Smode3	0.00
3.00	1.50	1	4	0	2.00	1	0.25	1	0.25	Smode3	0.00
3.00	1.75	1	4	0	2.00	1	0.00	1	0.00	Smode2	0.00
3.00	2.00	1	4	0	2.00	1	0.00	1	0.00	Smode2	0.00
3.00	2.25	1	4	0	2.00	1	0.00	1	0.00	Smode2	0.00
3.00	2.50	1	4	0	2.00	1	0.00	1	0.00	Smode2	0.00
3.00	2.75	1	4	0	2.00	1	0.00	1	0.00	Smode2	0.00
3.00	3.00	1	4	0	2.00	1	0.00	1	0.00	Smode2	0.00
3.00	3.25	1	4	0	2.00	1	0.00	1	0.00	Smode2	0.00
3.00	3.50	1	4	0	2.00	1	0.00	1	0.00	Smode2	0.00
3.00	3.75	1	4	0	2.00	1	0.00	1	0.00	Smode2	0.00
3.00	4.00	1	4	0	2.00	1	0.00	1	0.00	Smode2	0.00
3.00	4.25	1	4	0	2.00	1	0.00	1	0.00	Smode2	0.00
3.00	4.50	1	4	0	2.00	1	0.00	1	0.00	Smode2	0.00
3.00	4.75	1	4	0	2.00	1	0.00	1	0.00	Smode2	0.00
3.00	5.00	1	4	0	2.00	1	0.00	1	0.00	Smode2	0.00
3.00	5.25	1	4	0	2.00	1	0.00	1	0.00	Smode2	0.00
3.00	5.50	1	4	0	0.00	0	0.00	0	0.00	Smode1	0.00
3.00	5.75	1	4	0	0.00	0	0.00	0	0.00	Smode1	0.00
3.00	6.00	1	4	0	0.00	0	0.00	0	0.00	Smode1	0.00
3.00	6.25	1	4	0	0.00	0	0.00	0	0.00	Smode1	0.00

shows the braking trigger status and collision speed when a VRU positioned centrally at (3, y) suddenly crosses laterally from the right side of an HGV. For certain points, such as (3, 0.25), the VRU falls within the driver’s blind spot, preventing brake activation; consequently, the collision speed equals the vehicle’s travel speed. However, the 2D AEBS promptly applied braking to avoid collision. For some points, such as (3, 5.5), the VRU has sufficient time to cross laterally, requiring neither driver intervention nor AEBS braking.

Similarly, braking trigger conditions and collision speeds can be calculated for three conditions—free driving, driver-controlled driving, 1D AEBS-controlled operation, and 2D AEBS-controlled operation—when the VRU traverses laterally from different (x, y) positions, as illustrated in Figure 6. Figure 6 reveals that due to driver blind spots, VRUs in certain zones remain undetected, creating collision risks. The 2D AEBS accurately identifies four statuses: free driving requiring no braking; driver braking preventing collisions; AEBS braking preventing collisions; and unavoidable collisions despite braking. The AEBS integrated with the 2D TTC model significantly reduces collision risk zones while overcoming the limitations of the conventional 1D TTC model that focuses solely on longitudinal risks (a lateral covering width was set as 0.5 m in the 1D TTC model).

By hybridizing driver control and 2D AEBS control, the system leverages the driver’s braking capability while utilizing AEBS as a safety-critical fallback, thereby preventing unnecessary braking interventions.

4.2. The Influence of the VRU’s Height

To analyze the influence of a VRU’s height, the vehicle is assumed in starting motion with a speed set at 2 m/s, and the VRU travels at 2 m/s with heights of 1300 mm or 1600 mm. The VRU’s central point is positioned at (x, y), emerging laterally from the right side of the HGV.

Figure 7 illustrates braking triggers and collision outcomes calculated based on the collision risk model. Comparative analysis reveals that increased cyclist height reduces driver blind spots, expands observable areas, and enlarges coverage zones for driver braking interventions. For instance, when VRUs positioned at central points like (3.5, 0.25) and (3.5, 0.5) increase height from 1300 mm to 1600 mm, drivers can detect them and initiate braking to avoid collisions.

Visibility assessment based on cyclist height and its impact on vehicle braking triggers fully considers drivers’ braking capability while ensuring vehicle safety compliance, thereby reducing AEBS interventions

4.3. The Influence of the VRU’s Speed

To analyze the influence of a VRU’s speed, the HGV is assumed in starting motion with a speed set as 2 m/s, and the VRU travels at 1 m/s, 2 m/s, 3 m/s, or 4 m/s with a height of 1300 mm. The VRU’s central point is positioned at (x, y), emerging laterally from the right side of the HGV.

As indicated in

Table 3. The f_visibility, f_brake, and v_collision with VRU riding at different speeds.

VRU’s Speed/(m/s)	VRU		fvisibility	Without Control		Driver Control		Driver-2D AEBS
	x/m	y/m		fbrake	vcollision/(m/s)	fbrake	vcollision/(m/s)	fbrake	vcollision/(m/s)
1.00	3.00	0.25	0	0	2.00	0	2.00	1	0.00
	3.00	0.50	0	0	2.00	0	2.00	1	0.00
	3.00	0.75	0	0	2.00	0	2.00	1	0.00
	3.00	1.00	1	0	2.00	1	0.00	1	0.00
	3.00	1.25	1	0	2.00	1	0.00	1	0.00
	3.00	1.50	1	0	2.00	1	0.00	1	0.00
2.00	3.00	0.25	0	0	2.00	0	2.00	1	0.00
	3.00	0.50	0	0	2.00	0	2.00	1	0.00
	3.00	0.75	0	0	2.00	0	2.00	1	0.00
	3.00	1.00	1	0	2.00	1	0.80	1	0.00
	3.00	1.25	1	0	2.00	1	0.80	1	0.00
	3.00	1.50	1	0	2.00	1	0.25	1	0.00
3.00	3.00	0.25	0	0	2.00	0	2.00	1	0.00
	3.00	0.50	0	0	2.00	0	2.00	1	0.00
	3.00	0.75	0	0	2.00	0	2.00	1	0.00
	3.00	1.00	1	0	2.00	1	1.12	1	0.00
	3.00	1.25	1	0	2.00	1	0.80	1	0.00
	3.00	1.50	1	0	2.00	1	0.25	1	0.00
4.00	3.00	0.25	0	0	2.00	0	2.00	1	0.95
	3.00	0.50	0	0	2.00	0	2.00	1	0.95
	3.00	0.75	0	0	2.00	0	2.00	1	0.95
	3.00	1.00	1	0	2.00	1	1.12	1	0.00
	3.00	1.25	1	0	2.00	1	0.80	1	0.00
	3.00	1.50	1	0	2.00	1	0.25	1	0.00

, increased VRU speeds result in unavoidable collisions even when visibly detected by drivers. For the AEBS integrated with 2D TTC, collisions are prevented except in extreme cases where VRUs approach at excessive speeds with insufficient distance. In such critical scenarios, while collisions remain unavoidable, the collision speed is reduced by approximately 50%.

5. Discussion and Conclusions

HGVs require access to cities for goods delivery, inevitably leading to spatial overlap with VRUs and causing collision risks. Current AEBS used in HGVs primarily focuses on longitudinal car-following scenarios to prevent collisions between vehicles, with insufficient consideration of collision avoidance between HGVs and VRUs (the accidents are often side impact or intersection conflicts). In this study, a Driver-2D AEBS for HGVs was investigated to solve the limitations of scenarios with less coverage for vulnerable road users, overriding driver control and limited human–machine collaboration mechanisms in critical scenarios, and the insufficient consideration of the 3D blind spot challenge in HGVs. The main conclusions are as follows:

(1)

With the vision space, it is faster and easier to estimate the visibility of VRUs with any heights: The visibility of a VRU influences driving maneuvers (for instance, the brake) directly. In the proposed method, the 3D vision space of an HGV was first built up. Compared with the past blind spots on the ground plane, the vision space provides an accurate and practical basis for dealing with the blind spot risks. The vision space was transferred into the visibility function included in the Driver-2D AEBS.

(2)

The proposed Driver-2D AEBS is designed to address blind spots and 2D collision risks while avoiding excessive intervention: Based on the accident video data, a motion state scenario classification function for HGVs and VRUs was established. With the function, the driving status can be divided into four types. With the scenario classification function and 2D TTC model, the braking scenario extraction function was derived which can directly identify braking-required scenarios. The AEBS control strategy improved the adaptability to the working conditions and braking decision-making rationality. This exceeds the capability of fixed-width lateral triggering AEBS. In addition, three braking modes were included in the algorithm, incorporating the VRU visibility’s influence on driver response.

(3)

The validation results show that the proposed algorithm can significantly reduce collision risk zones while overcoming the limitations of conventional 1D TTC models that focus solely on longitudinal risks. By hybridizing driver control and 2D AEBS control, the system leverages the driver’s braking capability while utilizing AEBS as a safety-critical fallback, thereby preventing unnecessary braking interventions. For the AEBS integrated with 2D TTC, collisions can be prevented except in extreme cases. In such extreme cases, the collision speed is reduced by approximately 50%.

This study proposes a comprehensive scheme for addressing the issue between HGVs and VRUs, and the scheme can be used to reduce 2D collisions, especially in the case of blind spots. Some problems remain to be solved in future research. For example, scenarios involving temporary visual obstructions and combination with VRU detection and tracking algorithms require further investigation. In addition, typical dynamic parameters were used in the proposed algorithm, while the influence of variations in vehicle specifications [31], such as differences in mass, can be explored in future work.