A piecewise trajectory optimization model for connected automated vehicles: Exact optimization algorithm and queue propagation analysis
A piecewise trajectory optimization model for connected automated vehicles: Exact optimization algorithm and queue propagation analysis
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DOI：
10.1016/j.trb.2018.11.002
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发表时间：
2018-12
期刊：
影响因子：
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通讯作者：
X. Li;A. Ghiasi;Zhigang Xu;X. Qu
中科院分区：
文献类型：
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作者：
X. Li;A. Ghiasi;Zhigang Xu;X. Qu
本文制定了一种简化的交通平滑模型，用于引导联网自动车辆在一般单车道高速公路路段上的移动。改编自 Zhou 等人提出的射击启发法。 (2017) 和 Ma 等人。 （2017），该模型将每辆车的轨迹限制为不超过五个的分段二次函数，并让同一排中的所有轨迹共享相同的加速度和减速度。与射击启发式类似，所提出的简化模型能够控制联网自动车辆排的整体平稳性，并在燃油效率和驾驶舒适性方面大致优化交通性能。虽然射击启发式依赖于无法确保解决方案最优性的数值元启发式算法，但我们在所提出的简化模型中发现了一般目标函数和相关约束的一组优雅的理论属性，并因此提出了一种有效的分析算法来精确解决该问题的最佳结果。有趣的是，这种精确的算法具有直观的物理解释，即拉伸轨迹的过渡部分（即具有加速度和减速度调整的部分），直到它们到达研究段的上游端，然后尽可能接近地平衡加速度和减速度幅度。这种分析精确模型可以被视为各种基础设施设置下的一系列一般轨迹优化问题的核心模块。数值例子表明，与之前提出的射击启发式算法相比，该精确算法具有更高效的计算性能和相同或更好的解质量。这些示例还说明了如何将该模型应用于信号灯路段和不间断交叉口的 CAV 控制问题。此外，我们研究了该模型的同质特例，并分析地表述了队列传播和轨迹平滑之间的关系。一项反直觉的发现是，轨迹平滑可能并不总是导致更长的队列传播，而是可以通过适当的设置来减轻队列传播。这一理论发现对于复杂交通网络中排队管理和交通平滑的联合优化具有重要意义。
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.