Journal of Jilin University(Engineering and Technology Edition) ›› 2019, Vol. 49 ›› Issue (3): 749-756.doi: 10.13229/j.cnki.jdxbgxb20180120

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Optimal trajectory planning for middle⁃to⁃high speed maglev based on dynamic programming with mutative spacing

Qing⁃ying LAI1(),Jun LIU1(),Ruo⁃yu ZHAO1,Yong⁃ji LUO2,Ling⁃yun MENG1,Ya⁃zhi XU3   

  1. 1. School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China
    2. School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 610031, China
    3. CRRC Tangshan Co. , Ltd. , Tangshan 064000, China
  • Received:2018-02-02 Online:2019-05-01 Published:2019-07-12
  • Contact: Jun LIU E-mail:15114243@bjtu.edu.cn;jliu@bjtu.edu.cn

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Abstract:

A significant approach to save energy of the middle?to?high speed maglev is to optimize the trajectory planning. This paper establishes a model based on dynamic programming with mutative spacing after analyzing the kinetic equations of the middle?to?high speed maglev and the effect of the assistant?stop area. The model firstly uses the crossover point of double protected curve as the foundation of partition. Then, model further divides the partition into small sub?stages with different spacing and formulates the equation of energy and time respectively. Finally, the model is solved by reversing push method under certain constraints. The established model is compared the conventional dynamic programming method through the numerical examples. The results indicate the advantage of the proposed model in energy saving and computational efficiency.

Key words: railway transportation, middle?to?high speed maglev, optimal trajectory planning, dynamic programming with mutative spacing, assistant?stop area

CLC Number: 

  • U293.1

Fig.1

Sketch map of longitudinal force to Maglev train"

Fig.2

Transfer situation of speed"

Fig.3

Crossover point of double protected curve"

Fig.4

Flow chart of dynamic programming with mutative spacing"

Table 1

Position coordinates of assistant?stop area"

编号起始点/km终止点/km编号起始点/km终止点/km
10.000.821032.9733.38
21.612.041138.6839.10
33.373.771242.6843.11
45.776.201346.5947.01
58.819.231450.2150.63
612.3712.781553.0653.46
716.4116.841655.7256.14
821.0121.441757.9958.41
926.2326.631859.2060.43

Table 2

Limit speed of different sections"

区段/km限速/（km?h–1）
0.0~3.6100
3.6~9.1163
9.1~15.0181
15.0~38.2200
38.2~45.5145
45.5~52.7167
52.7~60.0100

Fig.5

Comparison of optimal trajectory planning in different models (travel time = 50 min)"

Fig.6

Comparison of optimal trajectory planning in different models (travel time = 30 min)"

Table 3

Comparison of parameters in different models (expected travel time = 30 min)"

情况方法间距/m阶段数能耗/(kW·h)时间误差/%计算时长/s
一变间距动态规划-551196.40.67101.3
二等间距动态规划601000186.70.42565.6
三等间距动态规划100600245.20.33125.6

Fig.7

Relationship between energy consumed and"

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