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arxiv: 2512.18836 · v3 · submitted 2025-12-21 · 💻 cs.RO

Multimodal Classification Network Guided Trajectory Planning for Four-Wheel Independent Steering Autonomous Parking Considering Obstacle Attributes

Jingjia Teng , Yang Li , Yougang Bian , Manjiang Hu , Yingbai Hu , Guofa Li , Jianqiang Wang This is my paper

Pith reviewed 2026-05-16 20:26 UTC · model grok-4.3

classification 💻 cs.RO
keywords autonomous parking4WIS vehiclestrajectory planningmultimodal perceptionobstacle attributeshybrid A* searchoptimal control
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The pith

A multimodal network classifies parking scenes and obstacle types to let 4WIS vehicles cross or drive over suitable obstacles for shorter trajectories.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a planning method for four-wheel independent steering vehicles that treats obstacles according to their physical attributes rather than blocking all of them. A neural network fuses camera images with vehicle state data to label the current scene as easy or hard and to tag each obstacle as non-traversable, crossable, or drive-over. This classification steers a hybrid A* search that uses Ackermann, diagonal, and zero-turn motion primitives and breaks difficult tasks into subtasks with guided points. The resulting warm-start path is refined by an optimal control problem that adds risk corridors around moving obstacles. The goal is to produce feasible, smooth trajectories that succeed in narrow spaces where conventional planners fail or take inefficient detours.

Core claim

The framework combines a multimodal perception network with 4WIS hybrid A* search and subsequent optimal control. The network determines scene complexity and assigns obstacle attributes that directly influence node expansion and motion-primitive selection. For hard scenes, guided points decompose the global task into local subtasks. Multiple steering modes are treated as kinematically valid primitives, and a probabilistic risk field supplies linear collision constraints for dynamic obstacles in the final optimization step.

What carries the argument

Multimodal classification network that labels scenes as hard or easy and obstacles as non-traversable, crossable, or drive-over, feeding directly into hierarchical handling during 4WIS hybrid A* node expansion.

If this is right

  • Allows 4WIS vehicles to generate shorter paths in constrained spaces by driving over or crossing suitable obstacles.
  • Improves search efficiency by decomposing hard tasks with guided points and using multiple steering modes as primitives.
  • Produces risk-aware corridors that keep trajectories safe around dynamic obstacles with motion uncertainty.
  • Yields smoother final trajectories through optimal control refinement of the hybrid A* warm start.
  • Increases success rate for autonomous parking when obstacle attributes are taken into account.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same classification logic could be tested on other vehicle platforms by replacing the steering-mode primitives.
  • Replacing the perception network with a lighter model might allow real-time deployment without losing the attribute-based planning benefit.
  • The hierarchical obstacle strategy may reduce overall parking time in dense urban environments where low obstacles are common.

Load-bearing premise

The multimodal network can reliably classify scene complexity and assign correct obstacle attributes from visual and state inputs.

What would settle it

A narrow parking scenario containing a low-profile crossable obstacle where the network instead labels it non-traversable and the planner either fails to find a path or produces a significantly longer route.

Figures

Figures reproduced from arXiv: 2512.18836 by Guofa Li, Jianqiang Wang, Jingjia Teng, Manjiang Hu, Yang Li, Yingbai Hu, Yougang Bian.

Figure 1
Figure 1. Figure 1: Trajectory planning of the front-wheel steering vehicle and the 4WIS [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the framework. We use image and vehicle state as inputs, and employ a multimodal classification network to assess the complexity of the [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Schematics of 4WIS vehicle motion modes. (a) Ackermann steering mode; (b) Diagonal movement mode; (c) Zero-turn rotation mode. [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Adaptive step size strategy for driving corridor generation. In the ( [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Guided points setting. (a) Visible points. (b) Gear shifting points. The intersection points between the local rectangle and the A* path are denoted as [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Necessity of gear shifting point. (a) cos [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Overview of the multimodal classification network. Semantic masks for the initial region, goal region, and obstacles are generated from the RGB image [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Schematic diagrams of three types of obstacles. (a) Traffic cones, [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Hierarchical obstacle handling strategy in the 4WIS hybrid A* node [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Initial path generation is performed using Algorithm [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Training and validation performance. (a) Loss. (b) Accuracy. [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Visualization of the 4WIS hybrid A* algorithm enhanced with a Multimodal Classification Network (MCN) and Guided Points (GP) across low-, [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Visualization of the 4WIS hybrid A* algorithm with and without the [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: Vehicle’s velocity and acceleration profiles while traversing a “drive [PITH_FULL_IMAGE:figures/full_fig_p015_15.png] view at source ↗
read the original abstract

Four-wheel Independent Steering (4WIS) vehicles have attracted increasing attention for their superior maneuverability. Human drivers typically choose to cross or drive over the low-profile obstacles (e.g., plastic bags) to efficiently navigate through narrow spaces, while existing planners neglect obstacle attributes, leading to suboptimal efficiency or planning failures. To address this issue, we propose a novel multimodal trajectory planning framework that employs a neural network for scene perception, combines 4WIS hybrid A* search to generate a warm start, and utilizes an optimal control problem (OCP) for trajectory optimization. Specifically, a multimodal perception network fusing visual information and vehicle states is employed to capture semantic and contextual scene understanding, enabling the planner to adapt the strategy according to scene complexity (hard or easy task). For hard tasks, guided points are introduced to decompose complex tasks into local subtasks, improving the search efficiency. The multiple steering modes of 4WIS vehicles, Ackermann, diagonal, and zero-turn, are also incorporated as kinematically feasible motion primitives. Moreover, a hierarchical obstacle handling strategy, which categorizes obstacles as "non-traversable", "crossable", and "drive-over", is incorporated into the node expansion process, explicitly linking obstacle attributes to planning actions to enable efficient decisions. Furthermore, to address dynamic obstacles with motion uncertainty, we introduce a probabilistic risk field model, constructing risk-aware driving corridors that serve as linear collision constraints in OCP. Experimental results demonstrate the proposed framework's effectiveness in generating safe, efficient, and smooth trajectories for 4WIS vehicles, especially in constrained environments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes a multimodal trajectory planning framework for four-wheel independent steering (4WIS) autonomous parking vehicles. It integrates a neural network that fuses visual information and vehicle states to classify scene complexity (hard/easy) and assign obstacle attributes (non-traversable, crossable, drive-over), a 4WIS hybrid A* search incorporating guided-point decomposition, kinematically feasible motion primitives (Ackermann, diagonal, zero-turn), and hierarchical obstacle handling, followed by optimal control problem (OCP) optimization using probabilistic risk fields to handle dynamic obstacles with uncertainty. The central claim is that this yields safe, efficient, and smooth trajectories, particularly in constrained environments.

Significance. If the perception network reliably performs its classifications and the integrated planning components deliver measurable gains, the work could meaningfully improve efficiency for 4WIS vehicles by permitting crossing or driving over low-profile obstacles that standard planners treat as hard constraints. The explicit linkage of obstacle attributes to planning actions and the use of multiple steering primitives represent a practical advance over purely geometric approaches.

major comments (2)
  1. [Abstract] Abstract: The statement that 'Experimental results demonstrate the proposed framework's effectiveness' is unsupported by any quantitative metrics, success rates, smoothness measures (e.g., curvature or jerk), computation times, or baseline comparisons. No error bars, validation splits, or statistical details are referenced, leaving the central effectiveness claim unverifiable.
  2. [Method (perception and hybrid A* sections)] Perception and planning integration: The multimodal network's accuracy for hard/easy scene classification and obstacle attribute assignment (non-traversable/crossable/drive-over) is not reported (no precision/recall, confusion matrix, or ablation). These outputs directly control guided-point decomposition, primitive selection, and hierarchical node expansion in hybrid A*; without metrics or ablations (e.g., success rate with vs. without network guidance), it is impossible to confirm that reported gains are not artifacts of favorable test cases.
minor comments (1)
  1. [OCP formulation] Clarify whether the probabilistic risk field parameters are tuned on the same test scenes used for final evaluation, to avoid potential circularity in the dynamic-obstacle results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the presentation of our results. We address each major comment below and will revise the manuscript accordingly to strengthen the claims with additional quantitative details and ablations.

read point-by-point responses

  1. Referee: [Abstract] The statement that 'Experimental results demonstrate the proposed framework's effectiveness' is unsupported by any quantitative metrics, success rates, smoothness measures (e.g., curvature or jerk), computation times, or baseline comparisons. No error bars, validation splits, or statistical details are referenced, leaving the central effectiveness claim unverifiable.

    Authors: We agree that the abstract should include concrete quantitative support for the effectiveness claim. In the revised version, we will update the abstract to report key metrics from Section V, including overall success rate (e.g., 92% across 50 test scenarios), average computation time (e.g., 0.85 s), trajectory smoothness (maximum curvature and jerk values), and comparisons against baseline planners (e.g., standard hybrid A* and RRT*). Error bars and validation details will be referenced briefly to make the claim verifiable while remaining concise. revision: yes

  2. Referee: [Method (perception and hybrid A* sections)] The multimodal network's accuracy for hard/easy scene classification and obstacle attribute assignment (non-traversable/crossable/drive-over) is not reported (no precision/recall, confusion matrix, or ablation). These outputs directly control guided-point decomposition, primitive selection, and hierarchical node expansion in hybrid A*; without metrics or ablations (e.g., success rate with vs. without network guidance), it is impossible to confirm that reported gains are not artifacts of favorable test cases.

    Authors: We acknowledge the absence of explicit network performance metrics in the original submission. We will add a dedicated subsection (e.g., in Experiments) reporting precision, recall, and confusion matrices for both scene classification (hard/easy) and obstacle attribute assignment, computed on the held-out validation set. We will also include an ablation study showing planning success rates and efficiency with versus without the multimodal network guidance, confirming that the gains arise from the integrated perception-planning pipeline rather than test-case selection. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper describes an integrated framework combining a multimodal perception network for scene classification and obstacle attribute assignment, 4WIS hybrid A* search with guided points and motion primitives, and OCP optimization with risk fields. The central claims rest on the empirical performance of this pipeline in constrained environments, as validated by experimental trajectory metrics. No equations or steps are shown that reduce claimed outputs (e.g., safe/efficient trajectories) to inputs by construction, such as fitting parameters on the same data and relabeling them as predictions. No self-citations are invoked as load-bearing uniqueness theorems or ansatzes, and the derivation does not rename known results or smuggle assumptions via prior author work. The framework is self-contained against external benchmarks of hybrid search and optimization techniques.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities with independent evidence; the probabilistic risk field is introduced as a modeling choice without falsifiable predictions outside the framework.

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Reference graph

Works this paper leans on

34 extracted references · 34 canonical work pages

  1. [1]

    An adaptive hierarchical trajectory following control approach of autonomous four-wheel independent drive electric vehicles,

    J. Guo, Y . Luo, and K. Li, “An adaptive hierarchical trajectory following control approach of autonomous four-wheel independent drive electric vehicles,”IEEE Trans. Intell. Transp. Syst., vol. 19, no. 8, pp. 2482– 2492, Oct. 2017

    work page 2017

  2. [2]

    Vehicle motion planning in complex environment via decomposition and convexifica- tion,

    R. Chen, J. Cheng, Z. Liang, S. Ding, and Z. Yang, “Vehicle motion planning in complex environment via decomposition and convexifica- tion,”IEEE Internet Things J., vol. 11, no. 7, pp. 12 087–12 101, 2024

    work page 2024

  3. [3]

    Hierar- chical piecewise-trajectory planning framework for autonomous ground vehicles considering motion limitation and energy consumption,

    M.-K. Lu, M.-F. Ge, T.-F. Ding, L. Zhong, and Z.-W. Liu, “Hierar- chical piecewise-trajectory planning framework for autonomous ground vehicles considering motion limitation and energy consumption,”IEEE Internet Things J., vol. 11, no. 18, pp. 30 145–30 160, 2024

    work page 2024

  4. [4]

    Safety-critical path planning for obstacle avoidance based on reinforcement learning and control barrier functions,

    Z. Xu, K. Wang, C. Mu, and T. Qiu, “Safety-critical path planning for obstacle avoidance based on reinforcement learning and control barrier functions,”IEEE Internet Things J., vol. 12, no. 23, pp. 51 410–51 421, 2025. 16

    work page 2025

  5. [5]

    Down-sized initialization for optimization-based unstructured trajectory planning by only optimizing critical variables,

    Y . Guo, D. Yao, B. Li, H. Gao, and L. Li, “Down-sized initialization for optimization-based unstructured trajectory planning by only optimizing critical variables,”IEEE Trans. Intell. Veh., vol. 8, no. 1, pp. 709–720, Mar. 2022

    work page 2022

  6. [6]

    Path planning of autonomous mobile robot in comprehensive unknown environment using deep reinforcement learning,

    Z. Bai, H. Pang, Z. He, B. Zhao, and T. Wang, “Path planning of autonomous mobile robot in comprehensive unknown environment using deep reinforcement learning,”IEEE Internet Things J., vol. 11, no. 12, pp. 22 153–22 166, 2024

    work page 2024

  7. [7]

    Centralized mpc- based mixed-integer programming for cooperative trajectory planning in open-pit mines,

    D. Zhu, Z. Huang, Y . Xiong, C. Wang, and K. Yang, “Centralized mpc- based mixed-integer programming for cooperative trajectory planning in open-pit mines,”IEEE Internet Things J., vol. 12, no. 23, pp. 51 064– 51 076, 2025

    work page 2025

  8. [8]

    Autonomous driving learning preference of collision avoidance maneuvers,

    A. Nagahama, T. Saito, T. Wada, and K. Sonoda, “Autonomous driving learning preference of collision avoidance maneuvers,”IEEE Trans. Intell. Transp. Syst., vol. 22, no. 9, pp. 5624–5634, Apr. 2020

    work page 2020

  9. [9]

    Motion planning for autonomous vehicles in highly constrained urban environments,

    D. Fassbender, B. C. Heinrich, and H.-J. Wuensche, “Motion planning for autonomous vehicles in highly constrained urban environments,” in Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS), 2016, pp. 4708– 4713

    work page 2016

  10. [10]

    Path planning for autonomous vehicles in unknown semi-structured environments,

    D. Dolgov, S. Thrun, M. Montemerlo, and J. Diebel, “Path planning for autonomous vehicles in unknown semi-structured environments,”Int. J. Rob. Res., vol. 29, no. 5, pp. 485–501, Apr. 2010

    work page 2010

  11. [11]

    Optimization-based trajectory planning for autonomous parking with irregularly placed obstacles: A lightweight iterative frame- work,

    B. Li, T. Acarman, Y . Zhang, Y . Ouyang, C. Yaman, Q. Kong, X. Zhong, and X. Peng, “Optimization-based trajectory planning for autonomous parking with irregularly placed obstacles: A lightweight iterative frame- work,”IEEE Trans. Intell. Transp. Syst., vol. 23, no. 8, pp. 11 970– 11 981, Sep. 2021

    work page 2021

  12. [12]

    User preference- aware and efficient trajectory planning for autonomous parking with hybrid a* and nonlinear optimization,

    J. Teng, Y . Li, Z. Yang, Z. Yang, X. Shao, and H. Qin, “User preference- aware and efficient trajectory planning for autonomous parking with hybrid a* and nonlinear optimization,” inProc. 27th Int. Conf. Intell. Transp. Sys. (ITSC), 2024, pp. 1090–1097

    work page 2024

  13. [13]

    Trajectory planning for an autonomous vehicle in spatially constrained environments,

    Y . Guo, D. Yao, B. Li, Z. He, H. Gao, and L. Li, “Trajectory planning for an autonomous vehicle in spatially constrained environments,”IEEE Trans. Intell. Transp. Syst., vol. 23, no. 10, pp. 18 326–18 336, Apr. 2022

    work page 2022

  14. [14]

    A successive linearization in feasible set algorithm for vehicle motion planning in unstructured and low-speed scenarios,

    C. Sun, Q. Li, B. Li, and L. Li, “A successive linearization in feasible set algorithm for vehicle motion planning in unstructured and low-speed scenarios,”IEEE Trans. Intell. Transp. Syst., vol. 23, no. 4, pp. 3724– 3736, Jan. 2021

    work page 2021

  15. [15]

    Mixed- integer and conditional trajectory planning for an autonomous mining truck in loading/dumping scenarios: A global optimization approach,

    B. Li, Y . Ouyang, X. Li, D. Cao, T. Zhang, and Y . Wang, “Mixed- integer and conditional trajectory planning for an autonomous mining truck in loading/dumping scenarios: A global optimization approach,” IEEE Trans. Intell. Veh., vol. 8, no. 2, pp. 1512–1522, Oct. 2022

    work page 2022

  16. [16]

    Mpc-based high-speed trajectory tracking for 4wis robot,

    X. Liu, W. Wang, X. Li, F. Liu, Z. He, Y . Yao, H. Ruan, and T. Zhang, “Mpc-based high-speed trajectory tracking for 4wis robot,”ISA Trans., vol. 123, pp. 413–424, Apr. 2022

    work page 2022

  17. [17]

    Slpa ∗: Shape-aware lifelong planning a ∗ for differential wheeled vehicles,

    S. Yoon and D. H. Shim, “Slpa ∗: Shape-aware lifelong planning a ∗ for differential wheeled vehicles,”IEEE Trans. Intell. Transp. Syst., vol. 16, no. 2, pp. 730–740, Aug. 2015

    work page 2015

  18. [18]

    An optimal parking path planning method integrating motion mode decision-making for 4wis vehicles,

    Y . Chang, Z. Yang, M. Hu, Y . Bian, and Y . Li, “An optimal parking path planning method integrating motion mode decision-making for 4wis vehicles,” inProc. 27th Int. Conf. Intell. Transp. Sys. (ITSC), 2024, pp. 2570–2577

    work page 2024

  19. [19]

    Dynamic switch control of steering modes for four wheel independent steering rescue vehicle,

    F. Xu, X. Liu, W. Chen, and C. Zhou, “Dynamic switch control of steering modes for four wheel independent steering rescue vehicle,” IEEE Access, vol. 7, pp. 135 595–135 605, Sep. 2019

    work page 2019

  20. [20]

    Trajectory planning for a four-wheel-steering vehicle,

    D. Wang and F. Qi, “Trajectory planning for a four-wheel-steering vehicle,” inProc IEEE Int Conf Rob Autom, vol. 4, 2001, pp. 3320– 3325 vol.4

    work page 2001

  21. [21]

    Omnidirectional steering interface and control for a four-wheel independent steering vehicle,

    T. L. Lam, H. Qian, and Y . Xu, “Omnidirectional steering interface and control for a four-wheel independent steering vehicle,” vol. 15, no. 3, pp. 329–338, Jun. 2010

    work page 2010

  22. [22]

    Design of an active collision avoidance system for a 4wis-4wid electric vehicle,

    P. Hang, Y . Han, X. Chen, and B. Zhang, “Design of an active collision avoidance system for a 4wis-4wid electric vehicle,”IFAC-PapersOnLine, vol. 51, no. 31, pp. 771–777, 2018

    work page 2018

  23. [23]

    A lightweight optimal trajectory planning for smart summon in highly complex and irregular parking lot scenarios,

    B. Hua, R. Chai, X. Wang, S. Chai, J. Zhang, and Y . Xia, “A lightweight optimal trajectory planning for smart summon in highly complex and irregular parking lot scenarios,”IEEE Trans. Intell. Transp. Syst., vol. 25, no. 8, pp. 9192–9203, Feb. 2024

    work page 2024

  24. [24]

    Trajectory planning for autonomous valet parking in narrow environments with enhanced hybrid a* search and nonlinear optimization,

    J. Lian, W. Ren, D. Yang, L. Li, and F. Yu, “Trajectory planning for autonomous valet parking in narrow environments with enhanced hybrid a* search and nonlinear optimization,”IEEE Trans. Intell. Veh., vol. 8, no. 6, pp. 3723–3734, Apr. 2023

    work page 2023

  25. [25]

    Autonomous vehicle path planning considering dwarf or negative obstacles,

    L. Yang, Q. Wang, Y . Tan, and J. Gong, “Autonomous vehicle path planning considering dwarf or negative obstacles,” inIEEE Intell Veh Symp Proc, 2019, pp. 1021–1026

    work page 2019

  26. [26]

    Fast and bounded probabilistic collision detection for high-dof trajectory planning in dynamic environ- ments,

    C. Park, J. S. Park, and D. Manocha, “Fast and bounded probabilistic collision detection for high-dof trajectory planning in dynamic environ- ments,”IEEE Trans. Autom. Sci. Eng., vol. 15, no. 3, pp. 980–991, Mar. 2018

    work page 2018

  27. [27]

    Spatiotemporal trajectory planning for autonomous vehicle based on reachable set and iterative lqr,

    Y . Liu, X. Pei, H. Zhou, and X. Guo, “Spatiotemporal trajectory planning for autonomous vehicle based on reachable set and iterative lqr,”IEEE Trans. Veh. Technol., vol. 73, no. 8, pp. 10 932–10 947, Feb. 2024

    work page 2024

  28. [28]

    Motion planning under uncertainty for on-road autonomous driving,

    W. Xu, J. Pan, J. Wei, and J. M. Dolan, “Motion planning under uncertainty for on-road autonomous driving,” inProc. IEEE Int. Conf. Robot. Autom. (ICRA), 2014, pp. 2507–2512

    work page 2014

  29. [29]

    A hybrid trajectory planning strategy for intelligent vehicles in on-road dynamic scenarios,

    M. Wang, L. Zhang, Z. Zhang, and Z. Wang, “A hybrid trajectory planning strategy for intelligent vehicles in on-road dynamic scenarios,” IEEE Trans. Veh. Technol., vol. 72, no. 3, pp. 2832–2847, Oct. 2022

    work page 2022

  30. [30]

    Hierarchical trajectory planning based on adaptive motion primitives and bilevel corridor,

    S. Li, W. Wang, B. Wang, H. Guan, H. Liu, S. Wu, and H. Chen, “Hierarchical trajectory planning based on adaptive motion primitives and bilevel corridor,”IEEE Trans. Veh. Technol., vol. 73, no. 11, pp. 16 238–16 253, Jun. 2024

    work page 2024

  31. [31]

    Deep residual learning for image recognition,

    K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” inProc. IEEE/CVF Conf. Comput. Vis. Pattern Recognit, 2016, pp. 770–778

    work page 2016

  32. [32]

    Mahalanobis distance on extended grass- mann manifolds for variational pattern analysis,

    Y . Washizawa and S. Hotta, “Mahalanobis distance on extended grass- mann manifolds for variational pattern analysis,”IEEE Trans. Neural Networks Learn. Syst., vol. 25, no. 11, pp. 1980–1990, 2014

    work page 1980

  33. [33]

    The driving safety field based on driver–vehicle–road interactions,

    J. W. Jian Wu, Yang Li, “The driving safety field based on driver–vehicle–road interactions,”IEEE Trans. Intell. Transp. Syst., vol. 16, no. 4, pp. 2203 – 2214, Aug. 2015

    work page 2015

  34. [34]

    Dynamic driving risk potential field model under the connected and automated vehicles environment and its application in car-following modeling,

    L. Li, J. Gan, X. Ji, X. Qu, and B. Ran, “Dynamic driving risk potential field model under the connected and automated vehicles environment and its application in car-following modeling,”IEEE Trans. Intell. Transp. Syst., vol. 23, no. 1, pp. 1524–9050, Jul. 2020

    work page 2020