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A piecewise trajectory optimization model for connected automated vehicles: Exact optimization algorithm and queue propagation analysis

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  • Li, Xiaopeng
  • Ghiasi, Amir
  • Xu, Zhigang
  • Qu, Xiaobo

Abstract

This paper formulates a simplified traffic smoothing model for guiding movements of connected automated vehicles on a general one-lane highway segment. Adapted from the shooting heuristic proposed by Zhou et al. (2017) and Ma et al. (2017), this model confines each vehicle’s trajectory as a piecewise quadratic function with no more than five pieces and lets all trajectories in the same platoon share identical acceleration and deceleration rates. Similar to the shooting heuristic, the proposed simplified model is able to control the overall smoothness of a platoon of connected automated vehicles and approximately optimize traffic performance in terms of fuel efficiency and driving comfort. While the shooting heuristic relies on numerical meta-heuristic algorithms that cannot ensure solution optimality, we discover a set of elegant theoretical properties for the general objective function and the associated constraints in the proposed simplified model, and consequentially propose an efficient analytical algorithm for solving this problem to the exact optimum. Interestingly, this exact algorithm has intuitive physical interpretations, i.e., stretching the transitional parts of the trajectories (i.e., parts with acceleration and deceleration adjustments) as far as they reach the upstream end of the investigated segment, and then balancing the acceleration and deceleration magnitudes as close as possible. This analytical exact model can be considered as a core module to a range of general trajectory optimization problems at various infrastructure settings. Numerical examples reveal that this exact algorithm has much more efficient computational performance and the same or better solution quality compared with the previously proposed shooting heuristic. These examples also illustrate how to apply this model to CAV control problems on signalized segments and at non-stop intersections. Further, we study a homogeneous special case of this model and analytically formulate the relationship between queue propagation and trajectory smoothing. One counter-intuitive finding is that trajectory smoothing may not always cause longer queue propagation but instead may mitigate queue propagation with appropriate settings. This theoretical finding has valuable implications to joint optimization of queuing management and traffic smoothing in complex transportation networks.

Suggested Citation

  • Li, Xiaopeng & Ghiasi, Amir & Xu, Zhigang & Qu, Xiaobo, 2018. "A piecewise trajectory optimization model for connected automated vehicles: Exact optimization algorithm and queue propagation analysis," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 429-456.
    • Handle: RePEc:eee:transb:v:118:y:2018:i:c:p:429-456
    DOI: 10.1016/j.trb.2018.11.002
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    References listed on IDEAS

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    1. Zhou, Fang & Li, Xiaopeng & Ma, Jiaqi, 2017. "Parsimonious shooting heuristic for trajectory design of connected automated traffic part I: Theoretical analysis with generalized time geography," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 394-420.
    2. Li, Xiaopeng & Peng, Fan & Ouyang, Yanfeng, 2010. "Measurement and estimation of traffic oscillation properties," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 1-14, January.
    3. Ghiasi, Amir & Hussain, Omar & Qian, Zhen (Sean) & Li, Xiaopeng, 2017. "A mixed traffic capacity analysis and lane management model for connected automated vehicles: A Markov chain method," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 266-292.
    4. Jiang, Rui & Hu, Mao-Bin & Zhang, H.M. & Gao, Zi-You & Jia, Bin & Wu, Qing-Song, 2015. "On some experimental features of car-following behavior and how to model them," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 338-354.
    5. Ma, Jiaqi & Li, Xiaopeng & Zhou, Fang & Hu, Jia & Park, B. Brian, 2017. "Parsimonious shooting heuristic for trajectory design of connected automated traffic part II: Computational issues and optimization," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 421-441.
    6. Li, Xiaopeng & Ouyang, Yanfeng, 2011. "Characterization of traffic oscillation propagation under nonlinear car-following laws," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1346-1361.
    7. Tian, Junfang & Jiang, Rui & Jia, Bin & Gao, Ziyou & Ma, Shoufeng, 2016. "Empirical analysis and simulation of the concave growth pattern of traffic oscillations," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 338-354.
    8. Li, Xiaopeng & Wang, Xin & Ouyang, Yanfeng, 2012. "Prediction and field validation of traffic oscillation propagation under nonlinear car-following laws," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 409-423.
    9. Li, Xiaopeng & Cui, Jianxun & An, Shi & Parsafard, Mohsen, 2014. "Stop-and-go traffic analysis: Theoretical properties, environmental impacts and oscillation mitigation," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 319-339.
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    Citations

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    Cited by:

    1. Shi, Xiaowei & Li, Xiaopeng, 2023. "Trajectory Planning for an Autonomous Vehicle with Conflicting Moving Objects Along a Fixed Path – An Exact Solution Method," Transportation Research Part B: Methodological, Elsevier, vol. 173(C), pages 228-246.
    2. Liu, Jinqiang & Wang, Chunyan & Zhao, Wanzhong, 2024. "An eco-driving strategy for autonomous electric vehicles crossing continuous speed-limit signalized intersections," Energy, Elsevier, vol. 294(C).
    3. Varga, Balázs & Tettamanti, Tamás & Kulcsár, Balázs & Qu, Xiaobo, 2020. "Public transport trajectory planning with probabilistic guarantees," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 81-101.
    4. Zhang, Jian & Tang, Tie-Qiao & Yan, Yadan & Qu, Xiaobo, 2021. "Eco-driving control for connected and automated electric vehicles at signalized intersections with wireless charging," Applied Energy, Elsevier, vol. 282(PA).
    5. Liu, Zhaocai & Chen, Zhibin & He, Yi & Song, Ziqi, 2021. "Network user equilibrium problems with infrastructure-enabled autonomy," Transportation Research Part B: Methodological, Elsevier, vol. 154(C), pages 207-241.
    6. Nicola Roveri & Antonio Carcaterra & Leonardo Molinari & Gianluca Pepe, 2020. "Safe and Secure Control of Swarms of Vehicles by Small-World Theory," Energies, MDPI, vol. 13(5), pages 1-28, February.
    7. Li, Li & Li, Xiaopeng, 2019. "Parsimonious trajectory design of connected automated traffic," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 1-21.
    8. Nishi, Ryosuke & Watanabe, Takashi, 2022. "System-size dependence of a jam-absorption driving strategy to remove traffic jam caused by a sag under the presence of traffic instability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).

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