Journal of Jilin University(Engineering and Technology Edition) ›› 2025, Vol. 55 ›› Issue (8): 2802-2816.doi: 10.13229/j.cnki.jdxbgxb.20231236

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Trajectory planning for intelligent vehicles based on adaptive sampling

Jun-wu ZHAO1(),Ting QU1,2,Yun-feng HU1,3()   

  1. 1.National Key Laboratory of Automotive Chassis Integration and Bionics，Jilin University，Changchun 130025，China
    2.Chongqing Research Institute，Jilin University，Chongqing 401120，China
    3.College of Communication Engineering，Jilin University，Changchun 130012，China
  • Received:2023-11-11 Online:2025-08-01 Published:2025-11-14
  • Contact: Yun-feng HU E-mail:zhaojw19@mails.jlu.edu.cn;huyf@jlu.edu.cn

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Abstract:

To address the issue of high computational complexity and excessive time consumption of intelligent vehicle trajectory planning in three-dimensional space （X-Y-T）， this paper proposes a dual-layer， three-stage trajectory planning method based on adaptive sampling. By using the Frenet coordinate system， the three-dimensional trajectory planning problem is decomposed into two two-dimensional optimization problems： path planning and speed planning. Firstly， in terms of path planning， an adaptive sampling method based on artificial potential fields is introduced to reduce the number of path planning space sampling points. Dynamic programming is used to calculate the path curve that connects each sampling point with the lowest comprehensive cost， and a quadratic programming problem is constructed to further optimize this path to obtain the final planned path. Secondly，in terms of speed planning， the adaptive sampling area for speed planning space is determined according to kinematic constraints. The dynamic programming method is used to calculate the speed curve that connects each sampling point with the lowest comprehensive cost， and a quadratic programming problem is constructed based on this curve to obtain the final speed planning result. Finally， a trajectory tracking error model is constructed， and lateral and longitudinal controllers are designed to verify the trackability of the planned trajectory. Simulation results show that the proposed method in this paper can reduce the planning time to about 0.1 seconds per planning cycle， providing a planned trajectory with a frequency of 10 Hz for intelligent vehicles， achieving coordination between planning and control.

Key words: vehicle engineering, intelligent vehicles, trajectory planning, adaptive sampling

CLC Number: 

  • U270.1

Fig.1

Overall framework of layered trajectory planning system"

Fig.2

Description of the lane centerline in Frenet coordinate system and Cartesian coordinate system"

Fig. 3

Planned trajectory and reference trajectory in the Frenet coordinate system"

Fig.4

Quintic polynomial curves connecting the sampling points of each column"

Fig. 5

Vehicle geometric profile diagram"

Fig.6

Feasible region formed by the projection of dynamic obstacles in the ST diagram"

Fig.7

Practical trajectory and planned trajectory in Frenet coordinate system"

Fig. 8

Longitudinal position and velocity controller"

Table 1

PID controller parameter setting table"

PID控制器比例系数KP积分系数KI微分系数KD
PID10.50.30.1
PID21.80.50.1

Table 2

Vehicle parameter table"

参 数数值
整车质量/kg1 820
车辆质心至前轴距离/m1.170
车辆质心至后轴距离/m1.770
轮距/m1.620
前轮侧偏刚度/（N·rad-1）52 150
后轮侧偏刚度/（N·rad-1）41 400
绕x轴转动惯量/（kg·m2）1 023.8
绕y轴转动惯量/（kg·m2）3 567.2
绕z轴转动惯量/（kg·m2）4 095.0

Fig. 9

Multi-static obstacle driving scenario"

Fig.10

Spatiotemporal map of the vehicle and static obstacles trajectories"

Fig.11

Planned path， speed， heading angle， and tracking error curves"

Fig.12

Planned path curvature and yaw rate curves"

Fig.13

Multi-dynamic obstacles driving scenario"

Fig.14

Spatiotemporal map of vehicle and dynamic obstacle trajectories"

Fig.15

Planned path， speed， heading angle， and tracking error curves"

Fig.16

Planned path curvature and yaw rate curves"

Fig.17

Computation time of single-step planning"

Fig. 18

Path planning results"

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