Cooperative Highway Lane Merge of Connected Vehicles Using Nonlinear Model Predictive Optimal Controller

by Syed A. Hussain 1 , Babak Shahian Jahromi 2 and Sabri Cetin 2,*
from vehicles 2020

Abstract

从 direct multiple shooting method 得来的cooperative Nonlinear Model Predictive Control (NMPC)-based optimization method 被用于两辆相连车的高速公路换道。

只有模拟结果。

Intro

纵向控制主要控制加速度和前车距离，视觉、雷达、V2V但是要处理信号延迟、故障相关的问题。

横向主要针对方向盘转向角，不仅要考虑当前车道，还要考虑变道对象的车道。

最小化整体制动诱导车道（Minimizing Overall Braking Induced，MOBIL）是一种更高级别的横向战略控制，可评估强制和可选车道变更期间变更车道所需的规则，in :

Kesting, A.; Treiber, M.; Helbing, D. General Lane-Changing Model MOBIL for Car-Following Models.
Transp. Res. Rec. J. Transp. Res. Board 2007, 1999, 86–94. [CrossRef]

加速度最好符合梯形曲线，需要留足变道过渡时间& 保持驾驶员的舒适度。

针对多车道高速公路探索了最优公式和贝叶斯网络中的遗传算法，以增加高速公路的吞吐量in

Kim, K.; Cho, D.i.; Medanic, J.V. Lane assignment using a genetic algorithm in the automated highway
systems. In Proceedings of the 2005 IEEE Intelligent Transportation Systems, Vienna, Austria, 16 September
2005; pp. 540–545.

Highway Merge Problem

美国三种类型的高速公路车道合并配置:1）平行加速车道，2）锥形加速车道，3）辅助三叶草车道

Rios-Torres, J.; Malikopoulos, A.A. A Survey on the Coordination of Connected and Automated Vehicles at Intersections and Merging at Highway On-Ramps. IEEE Trans. Intell. Transp. Syst. 2016, 1066–1077.[CrossRef]	介绍了通过V2I 来提高变道安全性和效率的研究。
Rios-Torres, J.; Malikopoulos, A.A. A Survey on the Coordination of Connected and Automated Vehiclesat Intersections and Merging at Highway On-Ramps. IEEE Trans. Intell. Transp. Syst. 2016, 1066–1077.	建议的基于 MPC 的合并优化搜索高速公路主车道上一个车队的空隙
Kachroo, P.; Li, Z. Vehicle merging control design for an automated highway system. In Proceedings ofthe IEEE Conference on Intelligent Transportation System, ITSC’97. Boston, MA, USA, 12 November 1997;pp. 224–229.	在优化程序中使用了合作行为
Cao, W.; Mukai, M.; Kawabe, T.; Nishira, H.; Fujiki, N. Gap Selection and Path Generation during MergingManeuver of Automobile Using Real-Time Optimization. SICE J. Control. Meas. Syst. Integr. 2014, 7, 227–23	同上

双车协同变道

车道动力学模型

只有两个车，leading(h)和 merge (m)，假设：

使用融合传感器确定自车以及其他车辆的位置
在MPC 优化期间使用动力学模型来预测未来车辆系统
做出转向、加速和制动的控制决策，以使控制目标最小化并满足约束条

h: $(x_h,y_h,\psi_h,v_h)$ ,位置，转向角，速度，m: $(a_m,\delta_f,m)$ ,加速度和转向角

[\dot{z}]=\left[\begin{array}{c} \dot{x}_m \\ \dot{y}_m \\ \dot{\psi}_m \\ \dot{v}_m \\ \dot{x_h} \\ \dot{v}_h \end{array}\right]=\left[\begin{array}{c} v_m \cdot \cos (\psi+\beta) \\ v_m \cdot \sin (\psi+\beta) \\ \frac{v_m}{l_r} \cdot \sin (\beta) \\ a_m \\ v_h \\ a_h \end{array}\right]

$\beta=\tan ^{-1}\left(\frac{l_r}{l_f+l_r} \tan \left(\delta_{f, m}\right)\right)$

非线性MPC

Direct Multiple Shooting Method

👉看这个【三种最优控制Single/Multiple shooting, collocation method总结】https://zhuanlan.zhihu.com/p/396056002

Comparison between direct and indirect method

	Indirect method	Direct method
Solution Scheme	First optimize, then discretize (e.g. Pontryagin (PMP))	First discretize, then optimize (transfer the infinite problem into finite- dimensional Nonlinear Programming problem (NLP), and solve NLP)
Pros	1. Boundary value problem with only 2n_x ODE 2. can treat large scale systems	1. can use state-of-the-art methods for NLP solution 2. can treat inequality constraints and multipoint constraints much easier
Cons	1. only necessary conditions for local optimality 2. Need explicit expression for control u*(t), singular arcs difficult to treat 3. ODE(常微分方程，Ordinary differential equation ) is strongly nonlinear and unstable 4. inequalities lead to ODE with state-dependent switches	1. obtain only suboptimal/approximate solution
Applications	optimal control e.g. in satellite orbit planning at CNES(法國國家太空研究中心)	most commonly used nowadays due to their easy applicability and robustness

The shooting method (single/multiple) 就是将 boundary value problem 变化为 a series of initial value problems (BVP --> IVP)